GB2430541A - Apparatus for magneto-optical and/or electro-optical manipulation of an atomic beam - Google Patents

Abstract

An apparatus is disclosed for magneto-optical and/or electro-optical manipulation of an atomic beam. The apparatus comprises an optical beam source to provide an optical beam, the optical beam having a frequency which is off-resonance for atoms of the atomic beam; an optical beam controller to control the optical beam to define a transverse intensity distribution in a region of the beam; an atomic beam source arranged to provide an atomic beam passing through the optical beam region; a system for controlling the magnetic field and/or the electric field in the optical beam region such that atoms of the atomic beam pass through the region substantially adiabatically; and a system to adjust the transverse intensity distribution and/or the field to manipulate the atomic beam pattern.

Description

I

Apraratus and Methods for Manipulation of Atomic Beams This invention relates to improved techniques for magneto-optical and/or electro-optical manipulation of an atomic or similar beam.

In recent years it has become possible to deflect ion and atom beams, to trap ions or atoms, even to cool them to very low temperatures; in the case of neutral atoms to temperatures near absolute zero. Now, the ability to handle ions or atoms has reached the ultimate limit: they can be prepared in pure quantum states. With ultra-cold neutral atomic beams great advances in high-resolution spectroscopy have become possible.

New states of matter, Bose-Einstein condensed clouds of atoms, have been synthesized, and atom beam experiments, such as atomic billiards, magnetic guidance and magneto- optical trapping, have been perfonned which were completely intractable only three decades ago.

In several respects the purity of ultra-cold atomic beams makes atoms therein behave much like photons in their optical counterpart, the laser beam. This well known analogy has given rise to the dream of manipulating atoms with the same degree of finesse as we routinely handle photons in laser beam optics. Indeed, a new subfield of atomic physics has emerged: atomic optics' sometimes also called de Broglie optics'.

In optics we manipulate beams of photons (electro-magnetic fields) using matter shaped into lenses, mirrors, holograms and such like; in atom optics the roles are reversed: the beams consist of atoms and the manipulation is perfonned with the help of electromagnetic fields (static, slowly varying, and/or pulsed electric, magnetic, and tailored laser light fields). The field of atom-optics potentially promises to allow us to treat atomic beams in a similar way.

Furthermore atoms in motion typically have a very small associated de Brogue wavelength, such atomic beams hence suffer much less from resolution limiting *1 diffraction effects than laser beams. Atom optics can push the limits of imaging in a vacuum environment. But the real benefit is expected to lie in an area where traditional light optics technology is already struggling with its fundamental limits, in the field of lithography.

Traditional optical lithography is used for the fabrication of tiny structures such as logical components on computer chips. The fabrication of structures in the nanometre- realm is becoming increasingly difficult since structure sizes are expected to shrink ever more. The wavelength of light used in lithographic exposure to achieve this shrinkage would have to shrink too. But it is difficult to create and steer light at ever smaller wavelengths and, even worse, its energy per photon grows with decreasing wavelength, thus, photons with very short wavelengths would degrade the very structures they are supposed to help to build.

Basically, the photons in lithography are transmitters of information, e. g., expose photo- resist to tailor etching and growth processes. If a way is found to manipulate atomic beams at high flux rates with the precision corresponding to their de Brogue wavelength resolution, the much smaller de Brogue wavelength of atoms could be used to beat the optical resolution crisis with which current optical lithography is battling; and if the atoms are directly deposited processing steps such as exposure, fixation and etching may become superfluous.

Recent progress in the cooling and quantum state preparation of atomic clouds has meant that the atomic flux problem has been solved in principle, it is the de Brogue- optical components for atomic beams that currently pose the greater problem. Recent theoretical and experimental work has shown progress but no clear frontrunner has emerged. Schemes for de Brogue optical elements in atom beam manipulation include magnetic lenses, optical standing wave lattices, transmission and reflection gratings, optical evanescent wave mirrors, optical tubes, magnetic tapes, magnetic circuits, and magneto- optical beam splitters. It became possible to reflect, focus and defocus, and split atomic beams. Unfortunately most of these ideas have certain drawbacks.

Commonly, they lack flexibility and versatility.

Magnetic lenses are often made from permanent magnets or wire arrangements and are therefore not completely flexible imaging elements. Optical standing waves have a fixed geometry and are therefore useful for creating many sharp parallel lines of deposited atoms but it is bard to see how this patterning can be changed to other geometries.

Optical lenses are typically part of a standing wave and therefore do not have parabolic but sinusoidal profiles. Transmission gratings absorb some of the atomic and therefore typically degrade and clog up. They also require considerable skill in their production once manufactured they are basically impossible to modify. The same applies to tiny point apertures and reflection gratings, the latter moreover need grazing incidence angles for the atomic beam but can have high reflectivity. Optical evanescent wave mirrors are suitable for plane mirrors but curved geometries are very hard to produce.

Optical tubes can be used for guiding of atomic beams but their transport is ballistic rather than coherent. Magnetic tapes and wire arrangements are more suited for the trapping and guiding of confined atomic clouds and have not been applied for imaging of free atomic beams.

Background prior art relating to the above techniques can be found in D. Meschede, H. Metcalf, Atomic nanofabrication: atomic deposition and lithography by laser and magnetic forces, J. Phys. D: Appl. Phys. 36, 17(2003); H. J. Metcalf and P.van der Straten, Laser Cooling and Trapping (1999) Springer, New York; W. Kaenders, F. Lison, A. Richter, R. Wynands and D. Meschede, Imaging with an atomic beam, Nature 375,214(1995); T. Pfuu, CH. Kurtsiefer, C. S. Adams, M. Sigel and J. Mlynek, Magneto-optical beam splitter for atoms, Phys. Rev. Lett. 71, 3427 (1993); 0.

Steuernagel, Optical Particle Manipulation Systems, UK Patent Application No 0327649.0, (2003); 0. Steuemagel, Coherent Transport and Concentration of Particles in Optical Traps using Vwying Transverse Beam Profiles, J. Opt. A: Pure Appi. Opt.

7,S392-S398 (2005); physics/0502026; 0. Steuernagel, E. Yao, K. O'Holleran, M. Padgeu, Observation of Gouy-Phase-Induced Transversal Intensity Changes in Focussed Beams, J. Mod. Opt. in print (2005); A. Gangat, P. Pradhan, G. Pati and M. S. Shabriar, Two-dimensional nanolithography using atom interferometry, Phys. Rev. A 53,4381 (1996); E.A. Hinds and I. G. Hughes, Magnetic atom optics: mirrors, guides, traps and chips for atoms, J. Phys. D: AppI. Phys. 32, RI 19-46 (1999); and M. Muetzel, U. Rasbach, D. Mescbede, C. Burstedde, J. Braun, A. Kunoth, K. Peithmann and K. Buse, Atomic nanofabrication with complex light fields, Appi. Phys. B 77, 1 (2003); and US 2002/011325.

According to the present invention there is therefore provided a method of magneto- and/or electro-optical manipulation of an atomic beam, the method comprising: providing a preferably substantially continuous wave optical beam, said optical beam having a frequency which is off-resonance for atoms of said atomic beam; controlling said optical beam to define a transverse intensity distribution in a region of said beam; arranging said atomic beam to pass through said optical beam region; controlling a magnetic and/or electric field in said optical beam region such that atoms of said atomic beam pass through said region substantially adiabatically; and manipulating said atomic beam by adjusting one or both of said transverse intensity distribution and said magnetic and/or electric field, in particular to pattern said beam, for example by manipulating or modif'ing a shape of wavefronts of said beam.

Preferably the beam is continuous wave (CW) but the beam could be temporally modulated to widen the frequency spectrum. Alternatively, or additionally, a plurality of CW beams could be used, for example, to address different atomic sub-levels simultaneously. Thus the optical beam, in embodiments of the method or later described apparatus, may comprise coherent or incoherent combinations of substantially continuous-wave, or pulsed optical beams with one or several frequencies and one or several polarization modes or any combination thereof. In some preferred embodiments of the method the electric and/or magnetic field is substantially static and the atoms of the atomic beam are substantially spin-aligned.

Broadly, the light field is detuned so that it is not "seen" by the atoms (except in one interaction region) and then either or both of a magnetic field and an electric field is used to return to a near-resonant condition. In the case of a magnetic field this is via the Zeeman or Stern-Gerlach effect; in the case of an electric field this is via the dc Stark effect. This technique allows the wavefronts of the atomic beam to be manipulated, for example to pattern the wave fronts or change the curvature of the wavefronts to focus the beam or to provide some other modification of the structure of the wavefronts within the beam. In embodiments there is coupling to the optical beam essentially only in a region defined by the controlling electric and/or magnetic field.

In embodiments of the method the atoms have a ground state energy dependent on a combination of the optical intensity and a magnetic field dependent detuning between the frequency of the optical beam and the frequency of an energy difference between the ground state energy and an excited state energy of the atoms. Then the manipulation of the atomic beam may comprise controlling the detuning, for example to pull the atoms of the atomic beam in a direction of either increasing or decreasing optical (laser light)

field.

The magnetic and/or electric) field may either be increased in the optical beam region interacting with the atomic beam or the magnetic field may be locally reduced in this region, for example by applying a substantially uniform magnetic and/or electric field elsewhere over the atomic beam.

The transverse profile of the laser beam can be generated using a spatial light modulator, for example as described in our previous UK Patent Application No. 0327649.0, filed 27th November 2003, and entitled "Optical Particle Manipulation Systems". Alternatively other means can be employed, for example a lens in combination with a stop, or a hologram.

The atomic beam manipulation may comprise focussing and/or defocussing. In embodiments of the method a plurality of interaction regions may be provided for the atomic beam, using one or more optical beams, to pmvide a corresponding plurality of manipulations. The manipulations may therefore be combined in a similar way to the manner in which optical elements can be combined for manipulating an optical beam.

For example such an approach may be employed to provide an "atomic beam telescope" or increased focussing power and/or resolution and/or intensity of the optical beam.

Embodiments of the method may be employed for nanolithography, for example for sculpting a two-or three-dimensional pattern in a material, or for nanofabrication, for example by precisely controlled deposition of material from the atomic beam and/or for the control of a deposition process using the atomic beam.

In another aspect the invention provides apparatus comprising means for manipulating an atomic beam in accordance with a method as described above.

Thus the invention also provides an apparatus for magneto-optical and/or electro-optical manipulation of an atomic beam, the apparatus comprising: an optical source to provide a preferably substantially continuous wave optical beam, said optical beam having a frequency which is off-resonance for atoms of said atomic beam; an optical beam controller to control said optical beam to define a transverse intensity distribution in a region of said beam; an atomic beam source configured to provide an atomic beam to pass through said optical beam region; a system to control a magnetic and/or electric field in said optical beam region such that atoms of said atomic beam pass through said region substantially adiabatically; and a system to adjust one or both of said transverse intensity distribution and said magnetic and/or electric field to manipulate said atomic beam, in particular to pattern said beam, for example by manipulating or modifying a shape of wavefronts of said beam.

These and other aspects of the invention will now be further described, by way of example only, with reference to the accompanying figures in which: Figure 1 shows a plot of the intensity distribution of an interference pattern formed by counter-propagating light beams, showing variations of intensity in the transverse (y) and longitudinal (z) directions; Figures 2a and 2b show plots of example intensity distributions of a pair of counter- propagating light beams, in the vicinity of a common focal point of the beams; Figure 3 shows an electric field distribution in a transverse section of a light beam for concentrating particles into a nairow filament at one edge of the beam; Figure 4 shows coefficients c,,, in a multimode expansion of the field of Figure 3; Figure 5 shows variations of a subset of multimode expansion coefficients for the field of Figure 3 over time which correspond to convergence of the (partial) ring structures of Figure 3; Figure 6 shows a plot of a light intensity distribution corresponding to the field distribution of Figure 3, in a transverse beam slice; Figure 7 shows a laser beam funnel in combination with an array of light crystal traps; Figure 8 shows an electric field distribution in a transverse section of a light beam for concentrating low-field seeking particles towards an edge of the beam; Figure 9 shows longitudinal intensity variations of two orthogonally polarised light

beams, for trapping low-field seeking particles;

Figures lOa and lOb show, respectively, an example of apparatus configured to collect and convey particles, and a variant of the apparatus of Figure 1 Oa configured to provide

an additional stationary particle-trapping field;

Figure 11 shows a flow diagram of a computer programme for controlling the apparatuses of Figure 10; and Figure 12 shows a block diagram programmed computer configured for controlling the apparatuses of Figure 10; Figure 13 shows a schematic diagrams of example embodiments of a system for implementing a method according to the present invention; and Figure 14 shows one example of a practical implementation of the system.

Further Backaround

We have previously described, in GB 0327649.0 filed 27 November 2003 (and equivalents thereof) a method of concentrating particles using light, the method comprising providing an optical beam having a transverse intensity distribution comprising one or more waves; and varying said transverse intensity distribution over time such that a succession of said waves sweep towards a portion of said beam, such that particles within said beam are swept with said waves and concentrated towards said beam portion.

Varying the intensity distribution to sweep particles towards a portion of the beam, for example a small sub region or regions or edge portion of the beam, facilitates the collection of particles over the entire beam volume. Preferably the transverse intensity distribution comprises a set of substantially concentric waves, and varying the intensity distribution causes these waves to converge towards small sub region(s) of the beam.

Preferably the transverse intensity distribution is comprised of a plurality of high-order modes, for example two or more modes of order two or above. This facilitates the implementation of relatively arbitrary intensity profiles (constrained only by the Rayleigh resolution limit), which, in effect, enable the transversal beam shape to be closely controlled over time. Such intensity distributions may be implemented using real-time beam forming techniques, for example by means of computergenerated holograms. It will be appreciated, however, that the patterns for such holograms need not be computed in real-time but may be computed in advance off-line. The method may be used to collect and concentrate particles of micrometer and nanometer size down to molecules and atoms, and including biological particles such as DNA and bacteria. Such particles may be provided to the beam entrained in a fluid, or may wander into the beam due to random thermal motion.

The above described method may be employed for concentrating both high (light) field and low (light) field seeking particles. For low-field seeking particles a light foam' or bubble' beam may be employed, for example created using two interlaced beams.

More particularly the transverse intensity distribution may comprise one or more regions of reduced intensity substantially surrounded or encased by one or more regions of higher intensity with the aim of increasing the likelihood that low-field seeking particles are trapped within the reduced intensity regions. Where the optical beam forms a longitudinal standing wave interference pattern, as described further below, there is a risk that low-field seeking particles may escape through low intensity regions, in particular the nodes of the pattern. Thus a further interference pattern may be created, for example by interlacing two beams of orthogonal polarisation, in order to provide a blocking or inhibiting field at these nodes to increase the effectiveness with which low field seekers are trapped and concentrated.

The method can provide a pair of counter-propagating optical beams configured to form a longitudinal (standing-wave) interference pattern. Such a pattern may be used to transport particles along one or both beams, broadly along the beams' axis, in a controlled fashion, by changing the phase of one of the beams of the pair with respect to the other. In this way the field profile may be shaped to transport particles both transversely and longitudinally and to concentrate particles. Thus preferably the beams have a focus and the transverse intensity distribution of a beam is asymmetric with respect to a beam axis, at least for a time interval. The transverse intensity distribution may be varied from an initial distribution to a second, asymmetric distribution for transporting particles or an asymmetric distribution previously employed for concentrating particles, say along the beam edge, may also be employed for transporting particles longitudinally. In either case the beams' field and intensity profile is essentially symmetric with respect to reflection (inversion) through the focal midpoint but its transversal intensity distribution can be strongly altered due to the dispersive effects of the Gouy-phase in the vicinity of the focus. A consequence of this is that a transversally asymmetric pattern typically shows rapid transversal intensity redistribution (local weakening) in the focal area to the effect that an end region for longitudinally transported particles is provided. Putting this another way, the longitudinal interface pattern is longitudinally asymmetric about the focus such that a portion of the pattern has an end region (or regions). Particles transported along the longitudinal interference pattern to this end region may encounter a field distribution, which substantially releases the particles. They may then be captured and further manipulated by any conventional means.

The end region of the pattern may be near or substantially adjacent the focus, for example less than a few hundred wavelengths from the focus. In a simple case the beam is brighter on one side than on the opposite side (of the beam axis) and the longitudinal interference pattern comprises at least one string of regions of constructive and destructive interference substantially ending at the end region. This may be referred to as a string of pearls'. Then varying the phase of one of the counterpropagating beams with respect to the other sweeps particles along this string of pearls' (or more correctly sweeps the regions of constructive and destructive interference through the end region) and thus transports particles to the beam focus and there releases them; for example handing the particles over to another trapping mechanism for further manipulation.

Broadly speaking this concept is based upon the recognition that nonsymmetric field profiles can show rapid redistribution of light intensity over short distances. This recognition has further led to the appreciation that such an intensity redistribution may be employed to implement, in effect, a particle conveyer belt with an end in the focal region which, in combination with the above described transverse intensity distribution modifications to sweep particles towards small sub region(s) [edge] of beam, may be employed to collect particles over a beam volume and deliver them to (one) localised region(s).

We also described a method of conveying particles using light, the method comprising providing a first pair of counter propagating optical beams, the beams having a focus, to create a longitudinal interference pattern, a said beam having an asymmetric transverse intensity distribution which is inverted when passing longitudinally through said focus, whereby said longitudinal interference pattern comprises a string of regions of constructive and destructive interference substantially ending at an end region; and varying a phase of one of said counter propagating beams relative to the other to translate said regions of constructive and destructive interference in a longitudinal direction to convey particles within said beam towards said end region.

The method may further comprise varying the transverse intensity distribution to convey particles towards a portion such as one or more small sub regions or an edge portion of a said beam in order to concentrate and collect particles over a beani volume.

One or more regions of reduced intensity, for example dark regions or regions of destructive interference, may be provided within a beam, substantially surrounded by a region of increased intensity for example a region of constructive interference or a region of increased intensity provided by a further beam or beams. This facilitates the transport of low-field seeking particles. A second pair of counter-propagating optical beams may be provided, the first and second pairs of counter-propagating optical beams interlacing and having substantially orthogonal polarisation. Jn this, nodes in the longitudinal interference pattern of the first pair of beams and antinodes in an interference pattern formed by the second pair of beams may substantially coincide to help close off escape routes for low-field seeking particles. For both high- and lowfield seeking particles an additional optical field may be provided to capture particles conveyed towards the end region, for example a field defining one or more optical tweezers and/or standing wave traps.

We also described apparatus for concentrating particles using light, the apparatus comprising means for providing an optical beam having a transverse intensity distribution comprising one or more waves; and means for varying said intensity distribution over time such that a succession of said waves sweep towards a portion of said beam, wherein particles within said beam are swept with said waves and concentrated towards said beam portion.

We also described apparatus for conveying particles using light, the apparatus comprising means for providing a first pair of counter propagating optical beams, the beams having a focus, to create a longitudinal interference pattern, a said beam having an asymmetric transverse intensity distribution which is inverted when passing longitudinally through said focus, whereby said longitudinal interference pattern comprises a string of regions of constructive and destructive interference substantially ending at an end region; and means for varying a phase of one or said counter propagating beams relative to the other to translate said regions of constructive and destructive interference in a longitudinal direction to convey particles within said beam towards said end region.

We also described computer program code to, when running, generate pattern data for a spatial light modulator, said pattern data being configured to provide an optical beam with a transverse intensity distribution comprising one or more waves, said pattern data fiuther comprising data to vary said intensity distribution over time such that a succession of said waves sweep towards a portion of said beam, wherein particles within said beam are swept with said waves and concentrated towards said beam portion We also described computer program code to, when running, generate pattern data for a spatial light modulator, said pattern data being configured to provide a pair of counter propagating optical beams creating a longitudinal interference pattern and having a focus, with an asymmetric transverse intensity distribution which is inverted when passing longitudinally through said focus, whereby said longitudinal interference pattern comprises a string of regions of constructive and destructive interference substantially ending at an end region; said code further comprising code for controlling a phase of one or said counter propagating beams relative to the other to translate said regions of constructive and destructive interference in a longitudinal direction to convey particles within said beam towards said end region.

The above described computer programme code may be provided on a carner such as a disk, CD- or DVD-ROM, programmed memory such as read-only memory (Firmware) or on a data carrier such as an optical or electrical signal carrier. The code may comprise any conventional programme code, or micro code, or other programme code such as code for a hardware description language or code for setting up or controlling an ASIC or FPGA. As the skilled person will appreciate such code may be distributed between a plurality of coupled components in communication with one another.

We also described a computer system for storing the above described programme code and configured to control a spatial light modulator or modulators to provide an optical beam or beams as described.

In the following explanation we will first introduce terminology for the description of paraxial beams and then address one- and two-dimensional modifications of the transversal mode profile of paraxial beams over time. This will show how manipulating the mode structure of a laser beam enables the structure to be tailored in such a way that controlled transport of trapped particles across the beam is possible and, more particularly, such that the particles are concentrated into a smaller volume. Further concepts are then introduced which show how particles may be transported in three dimensions towards a point or region in space. The changes in the beam (mode) structure are sufficiently slow and gradual that, in the case of quantum particles, the coherence of the trapped particles may be preserved (see, for example, C Orzel, A K Tucbman, M L Fenselau, M Yasuda, and M A Kasevich, Squeezed States in a Bose- Einstein Condensate, Science 291, 2386 (2001)). We further show how one can concentrate and transport low-field seeking particles. Some examples of apparatus, which may be employed to generate these light fields, are also described.

Thus firstly we consider aspects of structured Gaussian beams and Herrnite-Gaussian TEM-modes (Fransverse Electromagnetic Modes) thereof. In practical applications laser beams, which are not too tightly focussed, are very important Although the ideas presented here are in principle applicable in more general cases, e.g. for very tightly focussed beams or very general fields created by intensity masks or holograms, we will only consider quasi-monochromatic beams in the paraxial approximation. The mode functions of such beams are given by simple closed analytical expressions. The most commonly considered are cylindrically symmetrical modes such as Laguerre-Gaussian modes or those with grid symmetry, such asHermite-Gaussian modes. These are mathematically equivalent since both form complete orthonormal systems. For our description, we choose the Hermite-Gaussian modes because they have grid-symmetry, are the familiar wave-functions of the quantum-mechanical harmonic oscillator, and allow for a simple representation of the effects we want to consider.

The paraxial approximation to Maxwell's equations arises when one neglects the second derivative of the mode functions w with respect to the beam propagation direction z and can simplify Maxwell's equation. Then, possible solutions are the familiar transverse electro-magnetic or TEMmN modes. Here, we describe x -polarized beams propagating in the z -direction with a vector potential A = (AX,A,,, 4) whose only non- zero component is 4 with 4(r,t;k) = ,,(r) eiM), where the scalar mode function y' contains products of Gaussian-Hermite- polyno- mials, i.e. the familiar harmonic oscillator wave functions q,,() = (m 0,12,..) and various phase factors, specifically ,,,(r) =- o_(w) x e" e'.

The dispersion-relation of light in a homogenous medium w = ck was used; x,y arc the transversal and z the longitudinal beam coordinate, t is time and = = /Ab/,r is the relation that links the minimal beam diameter is with the Rayleigh range b. (The Rayleigh range is the distance from the beam waist at which the beam diameter increases by a fictor ofI2 doubling the cross-sectional area.) The beam diameter at distance z from the beam waist (z = 0) obeys w(z) = 4w (1 + z2/b2) and for large z shows the expected amplitude decay of a free wave 1/J z. The corresponding wave front curvature is described by R(z) = (z2 + b2)/z, and the longitudinal phase shift (Gouy-phase) follows 0(z) = arctan(z/b), i.e. varies most strongly at the beam's focus. The beam's opening angle in the fhr-field is arctan(AJfrw0)).

The vector potential 4 of Equation (1) describing a beam traveling in the positive z - direction (k = ki) yields an electric field which is polarized in the x - direction with a small contribution in the z -direction due to the tilt of wave fronts off the beam axis.

According to Maxwell's-equations: E(rt;k) = iv(r) ! {acv(r)]J - where 1,,1 are the unit-vectors and E is in fact the real part of the right hand side of the above Equation. Note, that we will, from now on, omit the small z -component of the electric field and hence only deal with the scalar approximation Ai} Just like the paraxial approximation, the scalar approximation gets better the less focused the beam (the larger the beam waist w0) is.

Since the wave equation is linear and the harmonic oscillator wave functions form a complete orthonormal set, we are free to combine the above solutions to generate many interesting field and intensity configurations. This can, for example, be done holographically, as described later, using dynamic computer-generated absorption and/or refraction gradients mapped into the light beam with transmitting and/or reflective liquid crystal arrays to yield A (r, t; k) = c,,, (t) (v,,(r) e'''.

The coefficients c,,, (t) can be complex (that is, relating to magnitude and/or phase) and do not need to obey normalization restrictions. A large variety of field configurations can be implemented, which can be varied slowly in time (hence c(t)). Since we have trapping in mind let us also assume that we discuss standing wave fields formed from a superposition of (otherwise (assumed) identical) counter-propagating beams. This could, fbr example, be implemented by balanced splitting of one initial beam the two halves of which are then carefully redirected to counter-propagate, (as further described later with reference to Figure lOa). Assuming proper alignment and a high degree of coherence and monochromaticity of the beam our expression for 4 becomes = c,,,,(t) v,,,(r) 2cos(kz+cI(:))e", ii. s.D where we explicitly include an overall longitudinal phase shift factor (D(t) between incoming and retro-reflected beam which again can be varied freely and conirollably (hence Cb(:)), for example slowly, in order to initiate translation of the cos-standing- wave pattern up and down along the beam axis. Note that the resulting intensity distribution (intensity averaged over several optical cycles) only contains terms with a controllable (slow) time-dependence l(r,t;k) occos2(kz+cD(t)) c_,(t)p',(r) We are free to implement the transversal (complex) field or intensity profile we wish to see in a particular slice of the standing wave pattern cos(kz + c1(t)), i.e. at a specified location z. This can be seen from the fact that we are free to choose from a complete orthonormal set of functions v,,,,(r) using the coefficients c(t) we desire. Once the field is specified in this way at one beam plane these initial conditions determine the shape along the entire beam. Understanding the overall beam behaviour is therefore what we will next turn our attention to.

We next consider effectively one-dimensional fransverse profiles.

The expression for 4 (r, t; k) contains the Gouy-phase factor e_iM) (in Icnn), which is important for our discussion, since it describes an effective dispersion of the various transversal beam components c, with the longitudinal beam parameter. To illustrate its effect, consider an odd beam profile, one that consists of a combination of odd mode functions only. Let us pick out one such mode q',,() = -q(.--) with a mode index m =2k + 1. The associated Gouy-phase, when studying the transition from negative to positive far field region (-z a z), shows an increase by a factor = e = -1, in other words, odd mode profiles get flipped. This is of course well known from ray-optics, imaging through a focus flips the image. Even wave functions get shifted by even multiples of -r and do not therefore flip over, although, because of their symmetry, this hardly matters and we can conclude that the field distribution of the beam gets mapped through the focal midpoint (0,0,0) upon the beam passing through the focus. (Strictly speaking this is only true if the overall phase 1Q) =0 so in general it is only correct up to an unimportant phase shift of less than 71.) For illustration consider the effectively one-dimensional superposition in the x- direction (q (-Ix/w(z)) + eq (ifix/iv(z))) ço0(sJiyIw(z)) . Plotting its intensity profile I(x0,z) in the (x,z) plane we can study the influence of the Gouy-phase on the transversal beam structure. Setting the relative phase e =1 we find that there is little change of the intensity distribution in the focus (see Figure 1). Figure 1 shows a plot of the intensity distribution I(x,0z) of a field with TEM-mode structure ((04 (.fix/w(z)) + (Jx/w(z))) . q (fiy/w(z)) near the beam focus z 0. This plot relates to a pair of counter-propagating waves, which generate a longitudinal standing- wave pattern of the form described in the Equation for 4 above.

Alternatively, we can choose a non-symmetric transverse beam profile, such as a profile which is bright on one side of the beam and dark on the other. Such a profile is flipped over' or laterally inverted in the focal region such that the bright and dark areas swap sides. This produces some complex behaviour close to the focus (z 0) as the intensity rapidly decreases on one side of the beam and increases on the other over a distance of a few Rayleigh-lengths b, since this behaviour is governed by the change of the Gony- phase 0 = arctan(z/b). The longitudinal interference pattern forms a string of interleaved regions of constructive and destructive interfrence, which may be likened to a string of pearls. Because the intensity, on one side of the beam (or, for a more complex anti-symmetric beam profile, in one part of one side of the beam) decreases to a low value or substantially zero this string effectively has an end point or region near the focus, as shown by arrow 200 in Figure 2a (although the intensity changes gradually rather than abruptly, this gradual change occurs over a very short longitudinal distance).

One such example of a non-symmetric beam profile may be generated by setting c=i.

As the relative phase of the counter propagating beams is adjusted the "pearls" move.

Figure 2a shows a plot of intensity distribution I(x0,z) of a field with TEM-mode structure (ç ( 'xIw(z)) + isp5(s/xIw(z))) 9 ( y/w(z)) near the beam focus z =0. As the relative phase of the counter propagating beams is adjusted the "pearls" move.

Figure 2b shows the average distribution near z=0 over a cycle (2,r). showing, in effect, an envelope of the pearls and in particular the two end regions formed (one on either side of the beam) to which particles may be delivered.

In this context the fact that the resulting intensity pearl string provides us with an exit (near the endpoint of the arrow in Figure 2a) deserves particular mention and is further discussed below.

We now explain how to concentrate particles into this pearl string region using appropriately tailored two-dimensional transversal profiles with interesting collection properties.

Thus, we next consider effectively two-dimensional transverse profiles One cannot, of course, resolve features below the diffraction limit (of roughly haifa wavelength). The desired field pattern has to be sufficiently smooth to be compatible with the wavelength of the used light. Thus very high orders in the expansions of A in the above Equations cannot be used as they are incompatible with the paraxiality assumption (and therefore do not allow one to go beyond the Rayleigh- limit).

Other than that, as mentioned, when introducing the above Equations we effectively have freedom in choosing the coefficients c_,(t). The main point is that they do not arise from any kind of physical dynamics but can be chosen at will in order to prescribe a desired transversal mode stnicture for the beam depending on time as we wish to choose. This opens up many options in tailoring the transversal trapping potential, for example, for coherent transport, controlled excitations, cross-tunneling and concentration of particles.

Figure 3 shows a plot of an example of a transversal field configuration at constant z, i.e. a slice across the laser beam. Shown is a field that forms ring structures converging at position (xy) = (2,2). The field of Figure 3 can be varied with time to provide concentric waves emerging at the periphery of the trapping beam which then travel across the beam converging at one point (in this example, at (x, y) = (2,2)) on the opposite edge of beam, thus concentrating all captured particles into a small beam region, in this example a narrow filament, if the underlying beam comprises counter- propagating waves this filament becomes a pearl string. As the example beam configuration of Figure 3 is asymmetric the pearl string has the general form shown in Figure 2a, and thus this transverse field configuration may also be used to transport particles captured in the pearl string to an end or region of the string, as described further below. The conveyor belt ends are most pronounced if the pearl string ends are well separated transversely. The skilled person will recognize that different transverse field configurations can be used to concentrate particles into different regions or portions of the beam, not necessarily at the edge of the beam. For example one can configure the transversal profile in such a way that the field pushes an object around via concentric waves that converge on more than one (edge or other) region, in a simple graphical representation, for two attractor regions x': >>> x<<<<<<<-i->>>>>>>x<<< This may be employed in order to, say, align sufficiently long fibers, and/or stretch long molecules.

Figure 4 shows expansion coefficients c, up to 12-th order n,m =0,...,12 for the field shown in Figure 3. The coefficients are real numbers because the electric field is chosen to be real, the observable exchange- symmetry of the coefficient (ii * m) is due to the

specific field's symmetry: E(x,y) = E(y,x).

Figure 4 shows the expansion coefficients c,,(T) at one particular moment in time T uptotwelfthorderin m and n.

Figure 5 depicts the time-development of a subset of the expansion coefficients c1,, (T) and displays the periodic motion underlying the concentration process described above.

Figure 6 shows a plot of the intensity distribution associated with the transversal field distribution of Figure 3, where the transversal field modes have been determined up to 12th order (using the expansion coefficients shown in Figures 4 and 5). In this case expansion up to twelfth order adequately models the field distribution of Figure 3.

It can be seen how tailored two-dimensional potential landscapes that can be changed over time can be created. In particular tunneling or classical escape scenarios may be implemented in this way.

We now consider three-dimensional concentration In a point or region.

To discuss the transport and concentration of particles in a small volume we will assume that a trapping field is present, sufficiently strong to transport and concentrate particles, in conjunction with a (non-essential) and comparatively weak background field. This background field may comprise a single laser tweezer focus or a light crystal, into which we aim to bring particles using the transport and concentration beam discussed in the preceding sections. Even in the case of(a) light crystal as (a) stationary trapping background field, with their rather uniform trapping power it is possible for the transport beam to dominate the particles' behavior throughout the transport across the light crystal and yet release the particles into a small area thus constituting, in effect, a conveyor belt with a well defined end. This is due to the fact that the intensity redistribution in the focal area can lead to a very swift termination of the transport beams' average intensity thus releasing its cargo in a well defined location and yet being able to hold onto it outside this release region; this behaviour is illustrated in Figures 2a, 2bandFigure7.

We have previously described a transverse transport beam structure, which allows the capture of particles substantially throughout the beam volume and which, within every transversal slice, concentrates particles in small subregion(s) of the beam (here at the beam edge: Figure 3 illustrates such a field). Depending upon details of the application and technical implementation the transverse beam pattern may then be (smoothly) switched over to a structure providing a single pearl string, as shown in Figure 2a. This can have the advantage (over the scenario depicted in Figure 3) that particles are trapped in a single pearl string, which is well isolated from other regions of the transport beam with comparable trapping power. This may be necessary in order to ensure that particles are cleanly held by the transport beam in one well defined location up to their delivery point without a significant chance of hopping into a nearby trapping cell (of either transport or background field). In either case can we use the overall phase shift D(t) to subsequently move particles trapped in a pearl string structure into the focal region close to z=0. The beam's transversal intensity is redistributed in the focal region according to the change of the Gouy- phase 0 = arctan(zlb) which varies rapidly around z=0. Consequently, towards the end of the pearl string the beam's cargo (near the endpoint of arrow 200 in Figure 2; see also Figure 2a) is swiftly unlocked in the area where the transport beam's strength falls below that of the trapping field in the background. The distance of a pearl string end from the focal point is of the same order as the Rayleigh length b and is generally less than 2 or 3 b (as the Gouy phase varies most rapidly when z Figure 7 illustrates this scenario (but for clarity only one plane of the light crystal that acts as a stationary background trapping field is plotted). Thus Figure 7 shows one example of a particle concentration and transport system using the previously described field configurations. In Figure 7, a laser beam funnel 700, feeds an array of laser traps 710. An effectively two-dimensional array can actually be implemented using evanescent waves (see, for example, Yu B Ovchinnikov, I Manek and R Grimm, Surface Trap for Cs atoms based on Evanescent-Wave Cooling, Phys Rev Lett 79,2225 (1997)).

As illustrated the trap 710a located at r=(-3,0,0) is being addressed and particles are collected in small subregion(s) of the (funnel) beam and delivered into this trap along the line shown by dashed arrow 720.

As previously mentioned, the controllable and gradual changes in the trapping field (as compared, for example, with changes only to longitudinal beam structure using frequency sweeps or the effective lattice constants by beam angle changes or changes of the trapping strength by overall intensity variation) facilitate coherence-preserving transport in a wide variety of circumstances. Many examples of coherencepreserving transport of quantum particles, their tunneling and classical escape dynamics have already been observed for optically trapped particles. With the additional great variety of trapping potentials now available using the methods described here, it is possible to implement new tailored potentials and thus study such systems further. Tunneling and classical escape processes depend extremely sensitively (exponentially) on the potential barrier size (the Gamov-effect). In this context it is worth highlighting that we can change the intensity of transport or trapping background field and thus change the relative potential strengths between the two and the barrier between them allowing us to make use of this exponential sensitivity. We can hence fine-tune the transfer process from collection beam to stationary trap field. This facilitates the release of trapped particles, as shown in Figure 7, at the intended point by the design. It also allows us to transfer particles coherently e.g. by matching the trapping frequencies in both traps (transport and background) and possibly exploiting other degrees of freedom of the trap (such as the polarization of the trapping light fields) in order to implement a merger of the trapping potentials at the release point. This in turn opens up the possibility of reversible shuttling trapped particles between different parts of the stationary trap, a technique potentially useful for (quantum-) processing of particles.

We next describe configurations for low-field seeking particle concentration and transport.

The preceding description relates to high-field seeking particles, but for many tasks it is useful to be able to trap low-field seekers (see, for example, T Kuga, Y Toni, N Shiokawa, T Hirano, Y Shimizu, and H Sasada, Novel Optical Trap ofAtoms with a Doughnut Beam, Phys Rev Left 78, 4713(1997)). A particular, interesting configuration is that of quasi twodimensional evanescent wave traps such as gravity assisted optical surface traps (see, for example, Yu B Ovchinnikov, I Manek and R Grimm, Surface Trap for Cs atoms based on Evanescent-Wave Cooling, Phys Rev Left 79,2225(1997)).

Broadly speaking, such a trap may comprise a support for trapped atoms, against gravity, provided by an evanescent wave from total internal reflection generating an evanescent wave above a prism surface. It may turn out such a trap is best fed using optical tubes with or without the support of optical fibres (see, for example, M J Renn et al, Phys Rev Lett 75, 3253 (1995); B T Wolschrijn, R A Comelussen, R J C Spreeuw, and H B van Linden van den Heuvell, Guiding of cold atoms by a red-detuned laser beam of moderate power, New J Phys, 4,69(2002)) and gravity to guide atoms towards it, but nonetheless in the general case the above discussion can also be extended to serve the case of low-field seeking particles, using a modified field configuration to provide an optical bubble' or foam' beam.

As one step, the transverse intensity profile, discussed previously with reference to Figure 3, is surrounded by a "light rim" sealing off the beam edge. The beam is also configured such that it contains suitable dark areas which can house low-field seeking particles. Figure 8 shows an example of a field configuration for low field seeking particles: the field surrounds areas of low intensity 800 with high intensity regions 802 thus trapping particles in light bubbles (and in this example concentrating them towards the area around (x,y) = (2,2)).

In a counter-propagating beam scenario this beam would remain leaky though, since particles could escape through the nodes of the longitudinal standing wave pattern. In order to plug this escape route one can create a second standing wave beam acting as a stop-gap that is uniformly bright in the transversal plane and aligned with the rest of the transport beam, but longitudinally shifted by a quarter wavelength (to provide an increased intensity at the nodes of the particle- transporting beam). In order to avoid possible destructive interference between these two parts of the transport beam they should preferably be orthogonally polarized leading to a simple adding up of their respective intensities (see Fig 9). This way one can create a beam with dark inclusions surrounded by bright areas that is, a light-foam' or bubble' beam.

Figure 9 shows a graph of light intensities, along the beam axis z, of a configuration comprising a transversally modulated field 900 in conjunction with a phase shifted orthogonally polarized field of equal strength 902 that puts an effective intensity plug at the nodes of the former. Recalling that according to the trigonometric theorem sin2+ cos2 =1, the two waves can easily be designed to provide a constant longitudinal intensity profile thus securely encasing trapped low-field seeking particles.

We will next describe apparatus which may be employed to implement the above described beam structures. Broadly speaking a preferred approach is to make use of computer-generated holograms, which are well known in the art as a means of generating a desired transverse field configuration. A technique for using computer- generated holograms written on a liquid crystal display to generate dynamic light fields of arbitrary shape is described in M Reicherter, T Haist, U E Wagemann, H J Tiziani, Optical particle trapping with computer-generated holograms written on a liquidcrystal display, Opt Lett 24,608(1999), which is hereby incorporated by reference.

Reference may also be made to US patent applications 2003/0132373 and to W003/001 178. Typically a diffractive element is positioned in a region where the laser beam is wide and its wave fronts substantially parallel. The diffractive element imprints its amplitude (and/or phase) information on the wide parallel beam, the width of which is then suitably shrunk and, generally focused. As is well understood by those skilled in the art the intensity pattern at the focus is the Fourier transform of the pattern of the dithactivc element.

The diffractive optical element may comprise a liquid crystal array or other addressable spatial light modulator, which may readily be driven by a conventional computer system to produce any desired pattern of pixels. Examples of spatial light modulators that have been used include an Epson LCD Panel of a VGA Projector with 640x480 pixels and a pixel pitch of 42 tim. This is a twisted nematic type LCD with a fill factor of 44%, which may be used as a phase hologram if the panel's polarising layer is removed; optionally the display may be mounted on a rotary stage also under computer control (rotating the panel by 85 with respect to the input polarisation facilitates maximising the intensity of the first diaction order), see paper by M Reichertcr, T Haist, U E Wagemann, H J Tiziani, Optical particle trapping with computer-generated holograms written on a liquid- crystal display, Opt Lctt 24, 608 (1999). In another example (see the papers of Grier et al, ibid, hereby incorporated by reference) a Hamainatsu Corporation model X7550 PAL-SLM parallel-aligned nematic liquid crystal spatial light modulator has been employed, which can impose selected phase shifts at each 40 un wide pixel of a 480x480 array, a calibrated phase transfer function providing 150 phase shifts between zero and 2n at a wavelength of 532nm. Light of any visible or non-visible wavelength may be employed; light sources which have been used include Argon lasers providing around 1 watt optical output power at approximately 488nm, and a frequency doubled Nd:YVO4 laser operating at approximately 532nm. Typically a polarised, collimated TEM beam is employed. In order to tightly focus the beam after diffraction, a lens with a high numerical aperture is preferred, such as a microscope objective lens.

As the skilled person will appreciate a spatial light modulator such as a liquid crystal may be used to modify one or both of the amplitude and phase of an input light beam.

Phase modulation is essentially lossless but simple, amplitude modulating LCD displays can run at higher rates thus generating patterns that change faster. To generate a hologram on a spatial light modulator is simply a matter of determining the amplitude and/or phase pattern required and sending this from a computer to the SLM. In the case of an amplitudephase modulating SLM the pattern is simply the Fourier transform, for example calculated using a fast Fourier transform procedure, of the desired field pattern at the focus. For phase-only holograms an iterative algorithm may be employed to calculate the required pattern, for example using the procedure described in RW Gerchberg and WO Saxton, Optik, Vol 35,237(1972) (hereby incorporated by reference) and subsequent modifications to this (see, for example, Curtis, Koss and Grier ibid). The resolution available is continuously increasing as LCD technology progresses. The refresh rate of a display depends upon the available computing power but may be between 1 hertz and 100 hertz; for increased refresh rates a set of patterns may be pre-calculated, stored in memory and then displayed as a repeating sequence.

The transverse field profiles described above have been presented in terms of a multimode expansion, in particular incorporating higher mode components (for example with mode indices greater than two, three, five or more). This is a convenient way of expressing the underlying physics. The aforementioned mode expansions also demonstrate that substantially arbitrary transverse field profiles may be generated. In the focal plane this is just the SLM pattern's Fourier-transform, and it is therefore not always necessary to determine the set of coefficients ce,,,. However, if one wants to understand the behaviour of the optical field outside the focal plane, the Gouy-phase factor, which is mode-dependent, has to be included. This can be done by determining the field's mode expansion of Equations 5 or 6. Since the coefficients c,, are given by simple twodimensional overlap integrals of the form c,,, = Jç (x, y) . E(x, y,0) dx dy this is straightforward.

Figures 1 and 2 moreover show that even simple combinations of mode functions can

yield useful field configurations.

Referring now to figure lOa, this shows a diagram of one example of an apparatus suitable for implementing any or all of the above described beam structures. Referring to figure lOa, the apparatus 1000 comprises a laser 1002 provided with a first lens 1004 to expand and collimate the laser output beam, this expanded beam being provided to a diffractive optical element (DOE) 1006 to modulate the beam, which is then shrunk by second and third lenses 1008, 1010. The diffractive optical element is controlled by a computer 1012. The reduced diameter beam is split by a semi-transparent balanced mirror 1014, one arm of the split beam being provided to a first mirror 1016 and first beam forming lens 1018, the second ann of the split beam being provided to a second pair of mirrors 1020 a, b and thence to a second beam forming lens 1022. This provides two counter propagating laser beams with a defined phase relationship between them.

The second arm of the split beam includes a phase shifter 1024, such as anelectro-optic modulator, also coupled to and under the control of computer 1012. This allows the relative phase of the two counter propagating beams to be varied, allowing computer control of the aforementioned longitudinal phase shift factor. The counter propagating beams 1026 define a region in which particles may be concentrated in small sub region(s) of the beam (for example, its edge) and then moved along a string of pearls' conveyer belt towards an end point of the string in the focal region 1028. It will be understood that the degree of collimation and the relative alignment of the counter propagating beams may be varied. Preferably the apparatus includes an aperture 1030 between the second and third lenses 1008, 1010 to provide a low-pass filter to filter out off-axis diffraction resulting from the regular pixelation of the LCD screen used for diffractive optical element 1006 (See, for example, M Reicherter, T Haist, U E Wagemann, H J Tiziani, Optical particle trapping with computer-generated holograms written on a liquid- ciystal display, Opt Lett 24,608(1999)).

In alternative version of this apparatus mirror 1020b and lens 1022 may be replaced by a curved mirror directed towards focal region 1028 (thereby providing counter propagating beams) and mirrors 1014 and 1020a maybe omitted, phase shifter 1024 then being positioned in front of curved mirror 1020b. In this configuration changing the phase shift is equivalent to moving the curved mirror, so moving the pearl string along the beam.

Figure lOb shows an extension of the apparatus of figure lOa, in which a stationary trapping field is provided in addition to the particle transporting field generated by counter propagating beams 1026. Thus the apparatus of figure lOb includes a stationary field lens 1050 and curved mirror 1052 to generate a substantially stationary standing wave stricture by retro-reflection. In order to ensure mutual stability of the respective intensities of the transport and stationary trapping fields preferably both are derived from the same laser source. This may be accomplished using an additional semi- transparent mirror 1054 to branch off a portion of the output beam of laser 1002, this then being provided via lens 1056 and mirror 1058 to stationary field optics 1050, 1052.

Since the beam focus 1028 is substantially the Fourier transfonn of the amplitude pattern of the diffractive optical element 1006 (apart, that is, from scaling and redirection) it is straightforward to calculate the required pattern on element 1006 using computer 1012, preferably to control DOE 1006 in real-time. Jn this way the collection and transport of particles within and along counter propagating beams 1026 can be controlled in any desired manner.

Figure 11 shows a flow diagram of a procedure for controlling the spatial light modulator 1006 and phase shift element 1024 to concentrate and transport particles in this way. As illustrated the procedure has two main parts, one in which the spatial light modulator (SLM) pattern data is calculated (steps si 100-sI 106), the other in which the calculated pattern data is provided repetitively to the SLM, and in which the phase shifter is controlled, to generate a series of waves which converge towards, one or more, small sub region(s) of the beam to concentrate particles in these small sub region(s), and which then carry the concentrated particles towards the beam focus. Thus at step sI 100 a user inputs transverse beam intensity distribution pattern definition data to the procedure, for example to define a transverse beam intensity pattern which is bright on one side and dark on the other, for example comprising a set of (partial) concentric rings. However, referring back to Figure 2a, a user may wish to define an intensity pattern a short distance away from the beam focus (at around z = -3 in Figure 2a) rather than exactly at the beam focus (although this is not necessarily the case). This allows a user to define an intensity pattern which will result in a string of pearls' pattern with a substantially defined end point or region. The procedure includes a step si 102, of determining the beam intensity distribution at the beam focus in case a user prefers to specify the field profile at a non-focal plane. Broadly speaking this determination is performed using the Gouy-phase as previously described. More specifically, the acquired Gony-phase for the various modes when moving out of the focal plane is accounted for and the corresponding (inverse) phase factors are multiplied into a mode expansion (such as that of Equations 5 or 6). This constructs the focal field distribution from the out-of-focus distribution.

Once the desired field distribution at the beam focus is known the corresponding spatial light modulator pattern can be determined, for example by means of a fast Fourier transform or other algorithm, as previously described (step sI 104). The procedure then repeats (Si 106) as many times as desired to define a sequence of transverse beam intensity distribution patterns, for example each comprising a small modification to a previous pattern to create a succession of waves converging on a small sub region(s) or edge of the beam. The calculated SLM patterns for each of these intensity distributions may be stored and then, at step silOS, repetitively read and output to the SLM to create a series of intensity waves to concentrate particles in small sub region(s) of the beam.

Simultaneously or after a delay, the procedure may also output a phase control signal to sweep the phase of one beam relative to the other to convey particles to the release point in the vicinity of the beam focus (step sill 0). It will be appreciated that the beam structure may be controlled to concentrate particles towards (small) sub region(s) of the beam, or to sweep particles along a beam, or to perform both actions either simultaneously or sequentially.

Figure 12 shows a general purpose computer system 1200 suitable for implementing the procedure of Figure II. The computer system 1200 comprises a data and address bus 1212 to which are connected a conventional display 1216, keyboard 1214 and network interface 1218, as well as an interface card 1220 for phase shifter 1024, and an interface card 1210, for example comprising a conventional LCD driver, for spatial light modulator 1006. Also coupled to bus 1212 are programme memory 1202, optional non- volatile data memory 1204, working memory 1206, and a processor 1208. The programme memory includes transverse beam pattern definition code, transverse beam pattern evolution code, spatial light modulator pattern detennination code, transverse and/or longitudinal sweep control code, and operating system code, and processor 1208 loads and implements this code to provide corresponding fhnctions. Non-volatile memory 1204 may store pre-calculated SLM pattern data. The code in programme memory 1202 may be provided on any conventional data carrier, as illustrated by disk 1222.

Modifications to the above described techniques are possible. For example the polarisation state of the trapping light fields may be changed over time, mismatched retro-refiected beams may be employed to provide additional transverse beam structure such as additional transverse particle-sweeping waves. A second computer-controlled diffractive optical element may be provided so that each of the two counter propagating beams has a dedicated DOE to facilitate the formation of more complex moving beam structures.

Broadly speaking we have described techniques for implementing substantially arbitrary transversal fields with substantially arbitrary time dependents, useful for trapping, coherent manipulation, concentration, and release of particles. We have further described how to construct a form of conveyer belt for particles with an end (in a focal region), using non-symmetric intensity profiles. This facilitates the release of trapped particles at a desired location and inhibits the release of particles elsewhere. These substantially arbitrary fields for concentrating and releasing particles may be implemented using computercontrolled, real-time holography. Further techniques for concentrating and transporting low-field seeking particles have been described, modifications of the methods for low-field seeking particles using additional stop-gap'

fields.

The skilled person will appreciate that many applications of these techniques are possible and the particles which may be manipulated range over several orders of magnitude from atoms and molecules up through bacteria to glass or other beads of many micrometers in size. For example the above described methods may be employed to manipulate atomic clouds, helping to increase their phase space density as they can be simultaneously cooled and spatially concentrated. This facilitates the formation of Bose-Einstein condensates, for example in conjunction with magneto-optical (S Chu, The manipulation of neutral particles; Rev Mod Phys 70,685(1998); C N Cohen- Tannoudji, Manipulating atoms with photons, ibkL 70, 707 (1998); W D Phillips Laser cooling and trapping of neutral atoms, ibid. 70, 721 (1998) ) or all-optical cooling schemes (M D Barrett, J A Saner, and M S Chapman, All-Optical Formation of an Atomic Bose-Einstein Condensate, Phys Rev Left 87,010404(2001)). The ability to replenish lossy ultra-cold atomic clouds may facilitate the construction of a substantially continuous Bose- Einstein-condensatjon-medjated atom laser. Ions, fermions and other mutually repulsive particles may be collected and spatially concentrated, for example to facilitate achieving unit filling factors for particles trapped in, say, an optical lattice which may find applications in grid- based quantum computing (R R.aussendorf and H -J Briegel, A One-Way Quantum Computer, Phys Rev Lett 86, 5188 (2001)).

Complex field structures facilitate the concentration, relative movement and arrangement of particles. They may permit articles to be moved, concentrated, rotated, aligned and released in a controlled fashion. Particularly for oriented particles such as polar molecules, fibres or flexible filaments (such as DNA and other macromolecules, or mineral fibres such as asbestos) should it become possible to align them by employing fields that establish movements along one or several preferred directions.

Fields with multiple concentration points, separating ridges, moving and stationary dark or bright spots may also be devised not only to align but also to stretch suitable filaments. This may be done, for example, by aligning a molecule so that two parts or ends of the molecule are in different attractive regions, then controlling the field(s) to move these regions apart.

This has applications in chemistry, biology, material-science and nanotechnology, particularly when it comes to relative configuration positioning of particles to promote reaction, interaction or assembly of particles. The concentration and release features of the mechanisms described here have applications in all areas where particle sorting, concentration and removal is important. Applications range from contactfree manipulation inside living organisms to improved vacuum technology; to systems where particular particle species are held in place for study of their features or removal from the system.

Detailed descrintion of oreferred embodiments of the invention Broadly speaking we will describe the use of magneto-optical elements for the de Broglie-optics of atomic beams. Embodiments of the system can provide lossless, fmely controllable, versatile operation based on already available components and techniques.

Its inherent flexibility moreover is able to help to overcome design problems because the components can be readjusted quickly during operation allowing us to use feedback learning routines to optimize performance.

The inventor has recognised that laser beams with almost arbitrary tailored transverse profiles can be generated using real-time beam forming techniques which employ computer-addressed spatial light modulators. In combination with localised magnetic fields, effective cross sections of such laser beam profiles can be cut out' to generate localised arbitrary' interaction potentials. When an atomic beam propagating in a vacuum environment is put through one of these regions it gets modified due to the optical dipole force. This results in an atom- optical alteration of the atomic beam which can be used for manipulation and patterning of the beam, in particular it allows for the controlled focussing and defocussing. Several such interaction regions lined up along the atomic beam give us the possibility to build an atomic beam telescope' with a great wealth of possible features. Such a scheme could be applied to all areas where atomic beam manipulation such as imaging or atomic deposition in vacuum is desired, most

prominently in the field of nanolithography.

The inventor has observed that optical and magneto-optical traps for the creation and storage of ultra-cold atoms can be realised with light beams which are tailored in the transverse beam plane. The inventor has previously described (above) how such a substantially arbitrary transverse profile can be generated; also in UK Patent Application No. 0327649.0, filed 27th November 2003, and entitled "Optical Particle Manipulation Systems".

Here, we prepare initially quite wide, preferably quasi monochromatic (low velocity spread) atomic beams which pass through areas with large localized magnetic fields that are simultaneously illuminated by monochromatic laser beams whose transverse beam profiles are tailored. The width of the atomic beam should roughly match the width of the part of the laser beam used for its manipulation. At their waist such laser beams are between a few wavelengths across, up to many micrometers or even millimetres.

Atomic beams with comparable width (or much narrower) may be created without difficulty as described, for example, in Pfau et al (ibid).

Referring to Figure 13, an atomic beam travels towards the exposure screen S. It is travelling (exactly or nearly) parallel to a laser beam L which is detuned from the atoms' transition frequency. in the area B surrounding a magnetized feature a locally sufficiently strong magnetic field brings the atoms closer to resonance with the laser light. In this area, the atoms see' a cross-section of the light beam and get deflected by the near-resonant optical dipole force. The laser beam can be superposed with the atomic beam A using a mirror M with a small hole through which to thread the atom beam. Figure 14 shows one example of a practical implementation of the system, in which counter-propagathig optical and atomic beams are employed, with a target for the atomic beam. In other implementations the two beams intersect at a non-zero angle, which is greatly exaggerated in the plot of Figure 13 illustration purposes. In still further implementations (for example along the lines shown in Figure 14 with the target or a system output displaced vertically below the optical beam) gravity is exploited to let the atoms travel on a curved trajectory which is parallel with the laser beam in the interaction region B of Figure 13.

The laser light is detuned far off resonance and so is not seen' by the atoms except for the interaction region where there is a locally enhanced (static or slow varying) magnetic (and/or electric) field. Effectively the magnetic (and/or electric) field smoothly switches the interaction between atoms and light on and off while the atoms travel through the interaction region. This guarantees smooth, adiabatic performance of the interaction of atoms with light which assures that the atoms' internal state does not change. The atoms remain in the same atomic sublevel and the detrimental random recoil-effects of spontaneous emission are avoidable.

Although the magnetic (and/or electric) fields can be tailored quite considerably the main freedom for the design of magneto-optical de Broglie-optics components generally results from our ability to quickly, smoothly and arbitrarily change the cross sections of the employed laser beams using spatial light modulators. (However, we cannot implement every desired transverse intensity pattern since the employed laser light only provides resolution down to the Rayleigh-limit). With the help of light modulators we are thus able to create quite arbitrary potential landscapes for the manipulation of atomic beams. Such potentials are conservative, stable, and substantially noise-free.

Because the magnetic (and/or electric) and optical fields being used are macroscopic they do not suffer from quantum-noise. Unlike material masks, they cannot be clogged or damaged through exposure to the atomic beams.

The detuning 6 of the laser field's frequency co c/c from the difference between the frequency of the atoms' excited state We and their lower (or ground) state COg is defined as the frequency mismatch 5o)(o. _wg) (1) Strictly speaking should the Doppler-shift COD = - kv be included as well, but this is straightforward to do if one uses an atomic beam with a narrow velocity spread. For simplicity we will discard reference to the Doppler-shift.

In the limit of large detuning 161 F, where F is the spontaneous decay rate of the excited level the optical potentials are conservative and the spontaneous emission rate negligible.

In the presence of a static magnetic field B the different magnetic dipole moments of excited and ground state lead to a further additional energy term in the detuning, the Stern-Gerlach potential. Preferably we operate at a temperature (for the atomic beam) which is sufficiently cold that its velocity spread does not lead to strong chromatic aberration (so that they all spend a similar time in the interaction region).

"An atom in a magnetic field of magnitude B has the magnetic dipole interaction energy Uz = - Pc B, where p the projection of its magnetic moment onto the field direction. Provided the atom. moves slowly enough through the magnetic field and provided zeros of the field are avoide4 the magnetic moment follows the field adi- abatically and the angle between moment field is constant. This is tile case for cold atoms in most experiments. In this adiabatic regime the potential energy of the atom depends on the field magnitude B, but not its direction" (from Hinds et al, ibid).

If the magnetic field is less than -3 DOG, or the atomic transition is from a stretched state (mF = F) to another stretched state, the hyperfine sublevels undergo a linear Zeeman- shift, namely Uz mpgpuBB, where mF is the magnetic quantum number, gj is the Landd g-factor and PB the Bohr magnetron. This linear Zeeman-shift is not essential but simplifies our subsequent description. In our case of an effective two-level atom we therefore find tW = - (itie - . B. An applied magnetic field modifies the detuning by the position-dependent magnetic detuning which is proportional to the magnitude of the magnetic field and depends on the spin orientation of the atoms (for position vector r) S (r) B (r) (2) Combining this with the expression for the optical detuning &, we thus arrive at the total detuning 5(r)5 +Sm(r). (3) It is customary and helpful to describe the influence of the optical dipole force via the AC-Stark shift not in terms of a local intensity dependent detuning but in terms of an optical potential. We will want to express the local light intensity 1(r) = c /(2r)E(r)2 in terms of the saturation intensity I = ta*2r 1(1 2ff) = ,zhcr I(32). The corresponding saturation parameter is (Natarajan et al., ibid; and J. P. Gordon and A. Ashkin, Motion of atoms in radiation traps, Phys.Rev. A 21, 1606 (1980))

I

____

and can be used to calculate the spontaneous scattering rate as F5 ps where p the excited state population. The potential associated with the conservative optical dipole potential arises in the case of large detuning 6 and small intensity I, i.e. s becomes small and so does the spontaneous scattering rate. In this case the expression for the optical dipole potential U( is equal to the shift in ground-state energy Uw=AEg=W62+Q2_8). (5) In the case of very small values of so this can be simplified further to yield -.2.2, (6) 88(r) I, which depends on the position r via the features of the magnetic field through the magnetic field-dependent detuning 8(r) of Eq. (2) and the optical intensity 1(r). The magnetic field dependence allows us to switch the interaction off (161 large) and on (I'l less large). Resonance (5(r) = 0) should typically be avoided when spontaneous scattering of photons is an issue since it destroys spatial quantum coherences. The negative gradient of this potential gives the associated (conservative) dipole force - VU, called gradient, reactive, or redistribution force (Metcalf et al., ibid).

For precise calculations the magnetic energy variation U, = -u* B of the ground and excited states (electrical energy variation U, = -d. E) and the influence of gravity = -nigh (and other possible potentials) would have to be included. But their influence is straight-forward to incorporate and does not change any of the fundamentals of the ideas described here. On a similar note, the influence of the potentials discussed above can be described by simple line integrals' along the particles trajectory, (see Pfau et al., ibid) but, in analogy to the transition from ray-optics to wave-optics a full atom-wave-optical description is necessary in some cases (e.g. near caustics or when the Ranian-Nath-condition is violated).

There are two important cases to distinguish, the optical detuning 6 can be negative (red detuning') in which case the potential U becomes negative and pulls atoms into high-field areas. In this case, depending on the sign of the magnetic moment difference ji the magnitude of the total detuning 8 can be reduced by an increased magnetic field (for positive A.t) or increased (for negative jt). Therefore it maybe necessary to have a magnetic feature with an only local non zero field in the first case, thus reducing the magnitude of the detuning and switching on the interaction between optical fields and atoms. In the other case the contrary is needed, a ubiquitous background field which is locally weakened by a local magnetic feature, again reducing the magnitude detuning and thus switching on the interaction in this area only.

The same applies to the case of negative optical dc-tuning (blue detuning': low-field seeking atoms) with reversed roles for the polarity ofi.

The magnetic field will typically vary over larger distances than the laser field.

Depending on the geometry of the magnetic fields and other details of the setup the interaction between atoms and light may well extend over several millimetres or more.

This means that we can use weak light fields to manipulate the atoms or strong fields to manipulate weakly responding atoms.

In contrast, the variation of the dipole potential U with the light intensity allows us to change the interaction on small spatial scales with considerable freedom.

In order to design an arbitrary' light intensity mask we can make use of the fact that there exist simple complete, orthonormal sets of basis functions, such as the Hermite-Gaussian of Laguerre-Gaussian modes for focussed laser beams. Their overlap with a desired field pattern is straightforward to determine and allows us to work out its composition unambiguously. From a strict mathematical point of view this does not solve the inverse problem for the determination of the mode composition from the desired intensity distribution. Primarily because the intensity is always positive whereas its formal root, the electric field, can be positive or negative. But effectively such a field configuration is straightforward to work out (0. Steuernagel, Coherent Transport and Concentration of Particles in Optical Traps using Varying Transverse Beam Profiles, J. Opt A: Pure Appi. Opt. 7, S392-S398 (2005), physics/0502026), albeit, limited by the Rayleigh-limit (however we cannot implement every desired transverse intensity pattern since the employed laser light only provides resolution down to the Rayleigh-limit). This is an important advantage over the approach where the desired intensity pattern is synthesized from many plane waves (see, e.g. Muetzel et al., ibid).

A specific case of considerable interest is the generation of a large convex atom lens, in other words an atom-optical phase element with (purely) parabolic phase profile (H.

Wallis, Phys.Rep. 255,203 (1995)). Progress regarding the generation of atom lenses has been hampered by the fact that the all-optical setups used so far suffer from large spherical aberration-problems leading to a severe restriction of the useful diameter of hollow beam optical lenses (H. Wallis, Phys.Rep. 255,203 (1995), G. M. Gallatin and P. L. Gould, J. Opt. Soc. Am. B 8,502(1991)). . A suitably chosen pure Laguerre- Gaussian laser mode (LG) and a matched single wire loop (or thin coil) to create a magnetic field with cylindrical symmetry is however sufficient to suppress the fourth order spherical aberration term completely (scenario as in Figure 13- because of the cylindrical symmetry only even orders occur and need suppressing). Adding one more mode (LG) and changing the radius of the wire loop accordingly allows for the simultaneous substantially complete suppression of fourth and sixth order spherical aberration. A specific example for the latter case is a combination of two LaguerreGaussian beam modes with a beam waist of = 71 pm with relative weight K = -0.422 in the superposition 4i - ic2LG + K LG. In combination with a wire loop with radius R = 6.24 mm carrying a current of roughly 5600 A (if it is a single loop).

This magneto-optical combination gives rise to a parabolic profile with suppressed fourth and sixth order. For an VRbatomic beam driven by a laser beam with 35 mW power and a detuning of 5,, = 1000 f on the 2S to 2P -transition 2 ( =a,-) 312 (F-i,-2) this leads to a lens behaviour which focusses an atomic beam travelling at a speed of 263 m/s down to a nanometre sized spot at 35 mm after the laser beam waist. The atomic beam could have a waist of up to 14 pm, about 200 times wider than permitted by all-optical setups considered so far in the literature (0. M. Gallatin and P. L. Gould, J. Opt. Soc. Am. B 8,502(1991) , V. I. Balykin, V. V. Klimov, and V. S. Letokhov, Optics and Photonics News 16,44 (2005)).

We can switch the interaction between laser light and atom beam on and off with the help of magnetic dc-tuning. The laser light mask can be arbitrarily' configured. This allows for the following features and applications in embodiments of the system/method.

1. Layout of every element is intrinsically very flexible 2. E.g.'perfect' lenses, focussing, defocussing and corrective, can be built 3. They can be combined to form atom-optical systems for imaging, writing, patterning, deposition 4. Corrective optical elements can be built 5. Can be combined with material apertures (neutral, magnetized, electrically charged) 6. E.g. material apertures for velocity selection are possible (low velocity spread of atomic beam is typically desired) 7. Conservative potentials can be designed 8. Non-conservative (simultaneously cooling) potentials are possible 9. Flexibility of setup allows free choice of time-variation of potentials, if variable potentials are desired 10. All-over static or variable setup for parallel or serial reading (imaging) and writing (deposition) is possible 11. Effective solution of inverse problem is given 12. Simultaneously intensity and phase modulation of the atomic beam is possible through some modifications, e.g. interferometric setup 13. Combination with near-field laser fields is possible (e.g. evanescent waves) 14. Different frequencies, pulses, polarization of (single or multiple) laser beams can add additional degrees of freedom of manipulation 15. Static or dynamic (local or background) added magnetic fields can add additional degrees of freedom of manipulation 16. Preparing atoms in various superpositions of internal quantum states can addadditional degrees of freedom of manipulation 17. Scheme is suitable for weakly responding atoms (with small dipole moments) because large spatial extension of light and magnetic fields can be implemented giving long interaction times between atoms and potentials 18. Scheme can in principle be used for several atomic species simultaneously if they are spectroscopically distinct and can thus be addressed with different color laser beams 19. Scheme can in principle be used for any other particles (molecules, artificial atoms, dust, bacteria, cells and the like) which behave similarly to atoms when subjected to magnetic and optical fields and in this specification "atomic" is intended to encompass such microscopic or "nano" particles ("atoms").

20. Scheme can in principle be used in non-vacuum environment if quantum coherence is not an issue No doubt many other effective alternatives will occur to the skilled person. It will be understood that the invention is not limited to the described embodiments and encompasses modifications apparent to those skilled in the art lying within the spirit and scope of the claims appended hereto.

Claims (28)

1. CLAIMS: I. A method of magneto-optical and/or electro-optical manipulation

   of an atomic beam, the method comprising: providing an optical beam, said optical beam having a frequency which is off- resonance for atoms of said atomic beam; controlling said optical beam to define a transverse intensity distribution in a region of said beam; arranging said atomic beam to pass through said optical beam region; controlling one or both of a magnetic field and an electric field in said optical beam region such that atoms of said atomic beam pass through said region substantially adiabatically, and manipulating said atomic beam by adjusting one or both of said transverse intensity distribution and said field to pattern said beam.
2. 2. A method as claimed in claim 1 wherein said manipulation comprises manipulation of wavefronts of said atomic beam, and wherein said patterning of said beam comprises modifying a shape of said wavefronts.
3. 3. A method as claimed in claim 1 or 2 wherein said atoms of said atomic beam essentially couple to said optical beam only in a region defined by said controlling field.
4. 4. A method as claimed in claim 1,2 or 3 wherein said manipulation comprises altering a curvature of said wavefronts.
5. 5. A method as claimed in claim 1,2,3 or 4 wherein said manipulation imposes a substantially parabolic phase profile on said atom beam.
6. 6. A method as claimed in any preceding claim wherein said field comprises a

   substantially static field.
7. 7. A method as claimed in any preceding claim wherein said atoms of said atomic beam are substantially spin-aligned.
8. 8. A method as claimed in any preceding claim wherein said atoms of said atomic beam have a ground state energy in said optical beam region dependent upon a combination of said optical intensity and a magnetic and/or electric field dependent detuning between said frequency of said optical beam and a frequency of an energy difference between said ground state energy and an excited state energy of said atoms, and wherein said manipulation comprises controlling said detuning to control a degree of manipulation of said atomic beam.
9. 9. A method as claimed in any one of claims 1 to 8 wherein said atoms of said atomic beam have a ground state energy in said optical beam region dependent upon a combination of said optical intensity and a magnetic and/or electric field dependent detuning between said frequency of said optical beam and a frequency of an energy difference between said ground state energy and an excited state energy of said atoms, and wherein said manipulation comprises controlling said detuning to be negative to pull said atoms in a direction of increasing optical beam intensity.
10. 10. A method as claimed in any one of claims I to 8 wherein said atoms of said atomic beam have a ground state energy in said optical beam region dependent upon a combination of said optical intensity and a magnetic and/or electric field dependent detuning between said frequency of said optical beam and a frequency of an energy difference between said ground state energy and an excited state energy of said atoms, and wherein said manipulation comprises controlling said detuning to be positive to pull said atoms in a direction of decreasing optical beam intensity.
11. 11. A method as claimed in any preceding claim wherein said field controlling comprises applying an increased field to said optical beam region.
12. 12. A method as claimed in any preceding claim wherein said field controlling comprises applying a field to said optical beam which is locally weakened in said optical beam region.
13. 13. A method as claimed in any preceding claim wherein said optical beam comprises a substantially continuous wave optical beam.
14. 14. A method as claimed in any preceding claim wherein said manipulation comprises focussing or defocusing said atomic beam.
15. 15. A method as claimed in any preceding claim comprising controlling one or more of said optical beams and one or more of said fields to provide a plurality of said optical beam regions through which said atomic beam passes such that each said region provides a manipulation of said atomic beam analogous to manipulation of a light beam with an optical element, said magneto-optical andlor electro-optical manipulation of said atomic beam comprising a combination of said manipulations provided by said optical beam regions.
16. 16. A method of nanolithography employing a method of atomic beam manipulation as claimed in any one of claims ito 15.
17. 17. A method of atomic deposition employing a method of atomic beam manipulation as claimed in any one of claims 1 to 15.
18. 18. Apparatus for magneto-optical and/or electro-optical manipulation of an atomic beam, the apparatus comprising: an optical source to provide an optical beam, said optical beam having a frequency which is off-resonance for atoms of said atomic beam; an optical beam controller to control said optical beam to define a transverse intensity distribution in a region of said beam; an atomic beam source configured to provide an atomic beam to pass through said optical beam region; a system to control one or both of a magnetic field and an electric field in said optical beam region such that atoms of said atomic beam pass through said region substantially adiabatically; and a system to adjust one or both of said transverse intensity distribution and said field to manipulate said atomic beam to pattern said beam.
19. 19. Apparatus as claimed in claim 18 wherein said manipulation comprises manipulation of wavefronts of said atomic beam, and wherein said patterning of said beam comprises modi1cing a shape of said wavefronts.
20. 20. Apparatus as claimed in claim 18 or 19 wherein said optical beam comprises a substantially continuous wave optical beam.
21. 21. Apparatus as claimed in claim 18, 19 or 20 wherein said atoms of said atomic beam essentially couple to said optical beam only in a region defined by said controlling

    field.
22. 22. Apparatus as claimed in any one of claims 18 to 21 wherein said apparatus comprises a phase mask.
23. 23. Apparatus as claimed in any one of claims 18 to 22 wherein said manipulation comprises altering a curvature of said wavefronts.
24. 24. Apparatus as claimed in any one of claims 18 to 23 wherein said apparatus comprises a convex or concave atom-lens.
25. 25. Apparatus as claimed in claim 24 wherein said atom lens has a parabolic phase profile.
26. 26. Apparatus as claimed in any one of claims 18 to 23 wherein said apparatus comprises a corrective atom optical element.
27. 27. A method or apparatus as claimed in any preceding claim wherein said magneto- optical and/or electro-optical manipulation consists of magneto-optical manipulation, and wherein said electric and/or magnetic field consists of a magnetic field.
28. 28. A method or apparatus as claimed in any preceding claim wherein said atoms comprise one or more of atoms of chemical elements, molecules, artificial atoms, or the like.