EP4618107A1

EP4618107A1 - Particle beam velocity squeezer and a method for velocity squeezing a particle beam

Info

Publication number: EP4618107A1
Application number: EP24382259.0A
Authority: EP
Inventors: Adrià Salvador Palau; Adrian Parveet James Sidhu
Original assignee: Lace Lithography AS
Current assignee: Lace Lithography AS
Priority date: 2024-03-11
Filing date: 2024-03-11
Publication date: 2025-09-17
Also published as: WO2025193106A1; TW202603749A

Abstract

A particle beam velocity squeezer and a method for velocity squeezing an incoming particle beam (b) with a beam direction z, wherein the particle beam velocity squeezer comprises;
- a first electromagnetic radiation source (11) arranged to provide a first beam of coherent light (11a) in the beam direction,
- a second electromagnetic radiation source (21) arranged to provide a second beam of coherent light (21a) opposite the beam direction z, wherein the first and second beam of coherent lights coincide at least partly with the particle beam (b).

Description

TECHNICAL FIELD

The present invention relates to the field of particle beam velocity shaping, and more specifically to the field of modifying the velocity profile of particle beams, such as atomic or molecular beams to provide velocity distributions with distinct one or more peaks, such as monochrome, bichrome or polychrome beams.

BACKGROUND

Monochromators are well known from the field of optics to derive monochromatic light from incoming polychromatic light. The monochromator separates incoming light into more distinct and narrow wavelengths by dispersion and allowing only the selected wavelength to escape through a slit.
In neutron and X-Ray optics it is known to use Bragg scattering for diffraction of an incoming wave.
However, common for these types of monochromators is that the efficiency is very low due to the small flux throughput of the devices due to the filtration of the wavelengths.
For particles, the de Broglie wavelength is a function of the speed, where the wavelength decreases when the speed increases. Thus, a difference in speed between particles in a beam means that the beam is not monochromatic.
Certain applications require intense monochromatic or polychromatic beams to achieve the desired effects. Such demand may e.g., come from industry and science in applications related to the use of diffraction patterns. Particles from available particle beam sources will have a broad velocity distribution that are less applicable for such purposes without shaping the velocity distribution.
Traditional velocity shapers, such as e.g., Zeeman slowers can obtain some degree of monochromacity at temperatures on the order of a few Kelvin and corresponding large de Broglie wavelengths. In addition, the intensity is affected by particle loss across the beam line.

SHORT SUMMARY

A goal of the present invention is to disclose a method and a system solving the problems related to prior art.
In particular the invention is efficient, in that a large fraction of the incoming particles are captured and participate in the produced particle beam.
The produced particle beam has a high intensity due to reduced particle loss across the beam line.
A large incoming velocity range can be captured.
The produced particle beam may be more monochromatic than for prior art devices.
A bichromatic or polychromatic beam may also be produced.
The mean velocity of the output velocity distribution can be kept constant or increased, if required.
The length of the device may be shorter than the length of comparable devices. This in turn improves applicability.
There are nearly no "residual particles" with unwanted velocities.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 illustrates the working principle of the invention. An incoming particle beam with a velocity distribution vdi as indicated to the left enters the beam velocity squeezer at its entrance at z0, where z is in the particle beam direction. The vertical axis here indicates the velocity for particles along the z-axis. Most of the incoming particles have a velocity between the input higher and lower capture velocities vch0, vcl0, and will be captured by the beam velocity squeezer. At the end of the squeezer, at z1, the particle beam has an output velocity distribution vdo . This final velocity distribution is much narrower than the initial distribution, with all particles having very similar velocities. This results in an intense monochromatic particle beam. The converged velocity vo is between the input higher and lower capture velocities vch0, vcl0.
Fig. 2 Shows a simulation of the particle capture of the particle beam velocity squeezer according to an embodiment of the invention, where all the particles converge to the same velocity vo, except sporadic particles that are outside the velocity capture range, or are missed due to imperfections in the system.
Fig. 3 illustrates in a simplified sketch, a working principle of a particle p in a particle beam b travelling in the beam direction z with a velocity v. A first electromagnetic radiation source 11 emits a first beam of coherent light 11a in the beam direction, and a second electromagnetic radiation source 21 emits a second beam of coherent light 21a in a direction opposite the beam direction. The particle falls within the cross-section of both the first and second beam of coherent lights 11a, 21a. Further, the second electromagnetic radiation source 21 has a lower frequency than the first electromagnetic radiation source 11.
Fig. 4 illustrates in a simplified sketch, further aspects of the working principle of first and second particles p1, p2 with different velocities.
Fig. 5a illustrates in a simplified schematic drawing a system where the particle beam velocity squeezer according to an embodiment of the invention is applied. The system comprises e.g. a particle source 31, a collimator 32, first and second electromagnetic radiation sources 11, 21, first and second beam expanders 12, 22, a coil section 33 and first and second mirrors with holes 13, 23.
Fig. 5b illustrates in a simplified schematic drawing an embodiment of a laser input mechanism 50 that may be applied instead of the mirrors used to feed the laser beams into the particle beam. A laser deflector 51 is used to deflect the output particle beam b1, and hence the second beam of coherent light 21a can enter on-axis with the output particle beam without blocking it. A similar laser input mechanism can be used to deflect the input particle beam b1 on the input side of the particle beam velocity squeezer to allow the first beam of coherent light to enter on-axis with the incoming particle beam without blocking it. In embodiments with more than one capture region, any of the input mechanisms in Fig. 5a or 5b may be multiplied, or as an alternative, the sources could be spatially merged in an optical coupler prior to entering the laser input mechanism. Note that the laser 51 and beam of coherent light 21a have different frequencies and that the atoms are effectively transparent to beam 21a. To ensure this is the case, the deflector should be used in a region of zero (or very near-zero, < 1mT) magnetic field.
Fig. 6 illustrates in a graph the result in output velocity distribution vdo versus the incoming velocity distribution vdi as a result of applying the particle beam velocity squeezer.
Fig. 7 shows longitudinal particle velocities vs. longitudinal particle distance at each simulation. Note that the particles being accelerated from 660 m/s to 1000 m/s are captured with much greater efficiency than the slowing laser from 1340 m/s to 1000 m/s. The vertical line is the end of the magnetic field.
Fig. 8 illustrates particle velocity squeezing in an alternative embodiment, comprising two capture ranges vcr1 and vcr2. Each of the capture regions will cover a part of the velocity distribution vdi of the incoming particle beam. As can be seen, the upper capture curve for each of the capture regions slows the particles, while the respective lower capture curves speed up the particles. Further, it can be seen that by extending the magnetic field B, beyond z1, four distinct peaks would be present at the output.
Fig. 9 illustrates in a graph a particle beam velocity squeezer output velocity distribution, where the beam velocity squeezer has first and second distinct velocity capture ranges vcrl, vcr2 as shown in Fig. 8.
Fig. 10 shows longitudinal particle velocities vs. longitudinal particle distance at each simulation for the where the beam velocity squeezer has first and second distinct velocity capture ranges vcrl, vcr2 as shown in Fig. 8. The vertical line is the end of the magnetic field.

EMBODIMENTS OF THE INVENTION

In the following description, various examples and embodiments of the invention are set forth in order to provide the skilled person with a more thorough understanding of the invention. The specific details described in the context of the various embodiments and with reference to the attached drawings are not intended to be construed as limitations. Rather, the scope of the invention is defined in the appended claims.
The embodiments described below are numbered. In addition, dependent embodiments defined in relation to the numbered embodiments are described. Unless otherwise specified, any embodiment that can be combined with one or more numbered embodiments may also be combined directly with any of the dependent embodiments of the numbered embodiment(s) referred to.
Chamber length and length of magnetic field L are used interchangeably in this document and should be seen as the active part of the beam velocity shaper in the beam direction z, i.e. the region where the magnetic field B is present and where photons may resonate with particles in the particle beam. Although the actual, or optimized field does not match the target field exactly, the chamber length and the target field have been given a length L. However, the active magnetic field is slightly longer than the length L, which means that even outside the target area, photons can still resonate with particles, but the effect is greatly reduced due to the inhomogeneity of the magnetic field.
ED1-1. A particle beam velocity squeezer for an incoming particle beam b with a beam direction z, wherein the beam velocity squeezer comprises;

a first electromagnetic radiation source 11 arranged to provide a first beam of coherent light 11a in the beam direction,
a second electromagnetic radiation source 21 arranged to provide a second beam of coherent light 21a opposite the beam direction z, wherein the first and second beam of coherent lights coincide at least partly with the particle beam b.

ED1-2. The particle beam velocity squeezer of ED1-1, wherein the first beam of coherent light 11a is configured to increase the speed of the slower particles in the particle beam b, and the second beam of coherent light 21a is configured to slow down the speed of the faster particles in the particle beam b.
ED1-3. The particle beam velocity squeezer of ED1-1 or ED1-2, wherein the first electromagnetic radiation source 11 has a first wavelength λ1 that is smaller than a second wavelength λ2 of the second electromagnetic radiation source 21.
ED2-1. The particle beam velocity squeezer of any of ED1-1 to ED1-3, comprising; - a magnetic field generator arranged to provide a magnetic field B in the beam direction.
ED2-2. The particle beam velocity squeezer of ED2-1, wherein the magnetic field B is configured to Zeeman-shift the resonant frequency of the slower particles as they increase their speed to match the increasing Doppler shift and detuning of the coherent light beam, and to Zeeman-shift the resonant frequency of the faster particles as they decrease their speed to match the decreasing Doppler shift and detuning of the coherent light beam, with the Zeeman shift that all particles experience being the same at some point zp in the chamber
ED2-3. The particle beam velocity squeezer of ED2-1 or ED2-2, wherein the magnetic field B decreases in the beam direction z and the polarization of the first electromagnetic radiation source is RHC polar, while the second electromagnetic radiation source 21 is LHC polar.
ED2-4. The particle beam velocity squeezer of ED2-1 or ED2-2, wherein the magnetic field B increases in the beam direction z and the polarization of the first electromagnetic radiation source first LHC polar, while the second electromagnetic radiation source 21 is RHC polar.
ED2-5. The particle beam velocity squeezer of any of ED1-1 to ED2-4, wherein the magnetic field B is positively or negatively oriented along the beam axis z.
ED3-1. The particle beam velocity squeezer of any of ED1-1 to ED2-5, wherein the incoming particle beam b has an input velocity distribution vdi and a converged velocity distribution vdo, wherein the converged velocity distribution comprises one or more peaks that are more monochromatic than the input velocity distribution.
ED3-2. The particle beam velocity squeezer of ED3-1, wherein the monochromator has an incoming velocity capture range vcr0 defined by a difference between high and low input capture velocities vch0, vcl0 at a start position of the magnetic field B.
ED3-3. The particle beam velocity squeezer of ED3-2, wherein a majority of the particles of the velocity distribution falls within the incoming velocity capture range vcr0.
ED3-4. The particle beam velocity squeezer of Any of ED3-1 to ED3-3, wherein a majority of the particles in the converged velocity distribution vdo has a converged velocity vo.
ED3-5. The particle beam velocity squeezer of ED3-4, wherein the converged velocity vo is defined for an end position z1 of the magnetic field.
ED3-6. The particle beam velocity squeezer of any of ED3-1 to ED3-5, wherein the converged velocity vo is between the incoming high and low capture velocities vch0, vcl0.
ED3-7. The particle beam velocity squeezer of any of ED3-1 to ED3-6, wherein the converged velocity distribution vdo and the converged velocity vo are defined where the low and high capture velocities vcl, vch converge.
ED4-1. The particle beam velocity squeezer of any of ED2-1 to ED3-7, wherein a high capture velocity vch decreases between a start position and an end position z1, and a low capture velocity vcl increases between the start position and the end position z1.
ED4-2. The particle beam velocity squeezer of ED4-1, wherein the high capture velocity vch decreases from the incoming high capture velocity vch0 to the converged velocity vo, and the low capture velocity vcl increases from the incoming low capture velocity vcl0 to the converged velocity vo.
ED4-3. The particle beam velocity squeezer of ED4-1 or 4-2, wherein the magnetic field B ends at the convergence of the low and high capture velocities vcl, vch. This will result in an intense monochromatic beam.
ED4-4. The particle beam velocity squeezer of ED4-1 or 4-2, wherein the magnetic field B extends beyond the convergence of the low and high capture velocities vcl, vcl1, vcl2, vch, vch1, vch2. This will result in two intense monochromatic peaks, i.e. a bichromator. In Fig. 1 and Fig. 8, the stapled lines to the right of z1 shows how the converged beam will split into a beam with two or four well defined separate velocities if the magnetic field extends beyond the convergence distance z1.
ED4-5. The particle beam velocity squeezer of ED4-1 or ED4-4, wherein the low and high capture velocities vcl, vch are functions of the magnetic field B and the first and second wavelengths λ1, λ2 of the first and second electromagnetic radiation sources, respectively.
ED4-6. The particle beam velocity squeezer of any of ED1-1 to ED4-6 comprising

additional one or more electromagnetic radiation sources arranged to provide a first beam of coherent light in the beam direction, and
additional one or more electromagnetic radiation sources arranged to provide a second beam of coherent light opposite the beam direction z, wherein the first and second beam of coherent lights coincide at least partly with the particle beam b.

ED4-7. The particle beam velocity squeezer of any of ED4-6, wherein pairs of counterpropagating electromagnetic radiation sources define a set of adjacent capture ranges vcrl, vcr2 for the incoming particle beam b. An example is given in Fig. 8 and 9.
ED5-1. The particle beam velocity squeezer of any of ED1-1 to ED4-7, wherein the magnetic field B has a first length in the beam direction z, ranging from a start position zo to an end position z1.
ED5-2. The particle beam velocity squeezer of ED5-1, having a beam input and a beam output, where the particle beam enters into the beam input with the input velocity distribution vdi and exits the beam output with an output velocity distribution vdo.
ED5-3. The particle beam velocity squeezer of ED5-2, wherein the beam input and output are arranged at the start position and the end position z1, respectively.
ED5-4. The particle beam velocity squeezer of any of ED5-1 to ED5-3, wherein the magnetic field generator comprises electromagnets with one or more coils arranged stacked in the beam direction.
ED5-5. The particle beam velocity squeezer of any of ED5-1 to ED5-4, wherein the magnetic field generator comprises permanent magnets.
ED6-1. The particle beam velocity squeezer of any of ED1-1 to ED5-4, wherein the particle beam b is bent outside the magnetic field B. I.e. outside the first length of the magnetic field.
ED6-2. The particle beam velocity squeezer of ED6-1, comprising any of lasers or electromagnets configured to bend the beam b.
ED6-3. The particle beam velocity squeezer of any of ED1-1 to ED5-4, comprising one or more mirrors 13, 23 to reflect the beams of coherent light 11a, 21a.
ED6-4. The particle beam velocity squeezer of ED6-3, wherein the one or more mirrors each comprise a hole for the particle beam b.
ED6-5. The particle beam velocity squeezer of any of ED1-1 to ED6-4, comprising one or more beam expanders 12, 22.
ED6-6. The particle beam velocity squeezer of any of ED1-1 to ED6-5, wherein the particle beam b comprises helium atoms.
The invention is also a method EM1-1 for squeezing an incoming particle beam (b) with a beam direction z, wherein the method comprises;

providing a first beam of coherent light (11a) in the beam direction,
providing a second beam of coherent light (21a) opposite the beam direction z, wherein the first and second beam of coherent lights coincide at least partly with the particle beam (b).

EM1-2: The method of EM1-1 comprising;

Zeeman-shifting the resonant frequency of the slower particles as they increase their speed to match the increasing Doppler shift, and
Zeeman-shifting the resonant frequency of the faster particles as they decrease their speed to match the decreasing Doppler shift.

The Zeeman shift being the same for all particles (sped up/ slowed down particles) at some point z.
Further, EM1-1 or EM1-2 may in different embodiments comprise any of the features of claims ED1-1 to 6-6.
A more detailed explanation of the technical concepts involved will now be given in an example with reference to the drawings. The coherent light sources may be lasers and the particles may be atoms such as e.g. helium atoms.
In Fig. 3 a particle beam b comprising atomic particles p travel in a beam direction z.
A first laser 11 emits a first laser beam 11a in the beam direction z, and a second laser 21 emits a second laser beam 21a in a direction opposite the beam direction z. Particles in the particle beam will therefore experience the two laser beams coming from opposite sides, provided the lasers are active simultaneously, since the first and second laser beams are anti-parallel, and both laser beams coincide at least partly with the particle beam b.
If we first consider only a single particle p of the particle beam b, the resonance frequency of the particle will be red shifted, i.e. experience a decrease in frequency with regards to the first laser 11, and blue shifted, i.e. experience an increase in frequency with regards to the second laser 21 due to the doppler shift.
If the first laser beam 11a has a relative frequency similar to the red shifted resonance frequency of the particle, a photon in the first laser beam 11a will excite the particle. Due to the photon momentum the particle will be accelerated in the beam direction z.
Likewise, if the second laser beam 21a has a relative frequency similar to the blue shifted resonance frequency of the particle, a photon in the second laser beam 21a will excite the particle. Due to the photon momentum the particle will be accelerated in the beam direction z.
If the particle had been able to absorb photons from each side with equal momentums, the net momentum on the particle in Fig. 3 would have been zero. However, since the laser detunings from the two opposite directions are so different with regards to each other, they will not be in resonance with the particle's energy states at the same time.
In a real particle beam the particles will have a certain velocity distribution. This is illustrated in Fig, 4 for two of the particles, where particle p2 has a higher velocity v2 than the velocity v1 of particle p1. For illustration purposes, the particles and lasers have been dislocated from their normal position where the particle beam and lasers co-incide.
In this scenario the first laser beam 11a will be able to accelerate the first particle p1 in the beam direction, provided the first laser beam 11a has a relative frequency similar to the red shifted resonance frequency of the particle p1.
The second laser will be tuned to the reference frequency of the second particle p2, and it will not be able to transfer momentum to the first particle with a lower velocity.
Similarly, the second laser beam 21a will be able to decelerate the second particle without impact from the first laser beam.
The net effect is that slower moving particles are accelerated and faster moving particles are decelerated, and that the velocity distribution of the particle beam is altered. E.g., in Fig. 4 the two initial velocities v1 and v2 are moved closer to each other.
When the particles are accelerated and decelerated as explained above, the relative frequencies between the particles and the lasers will change due to a change in the velocity-dependent Doppler shift. Thus, the lasers will not be able to excite the particles and transfer momentum since the lasers are no longer tuned to the doppler shifted resonant frequencies of the particles when the velocities change.
In an embodiment, a decreasing magnetic field B in the beam direction z is applied to the system.
Referring to Fig. 4, and the first particle p1, its L2-1 energy and resonance frequency will be small when the particle enters into the magnetic field from the left with a low speed v1. The photons of the first laser beam 11a will resonate with the transition energy of the first particle, resulting in photon absorption, transferring momentum in the right direction, and the particles speed will increase and move right. This speed increase leads to a doppler red shift relative to the first laser 11. As the particle gradually increases its speed along the trajectory, the resonance frequency will continue to decrease to compensate the increasing Doppler shift.
For the second particle p2, the situation is different. This particle will also enter into the magnetic field from the left, but with a higher velocity v2 than the velocity v1 of the first particle p1. The photons of the second laser beam 21a will resonate with the transition energy at L2-2 of the second particle, transferring momentum in the left direction, and the particles speed will decrease and continue to move right with a lower velocity. The second laser sees the particle as less and less blue-detuned. Laser frequencies
The second laser which travels antiparallel to the particle has a lower frequency than the first laser. This is because when the particle sees the laser travelling towards it, the frequency the atom sees will be increased due to Doppler shift. Thus, to counteract the Doppler shift, the second laser is detuned lower. In the same way, the atom will see the first laser with a lower frequency, so the first laser is detuned to a higher frequency to counteract this effect.
The first and second particles p1, p2 in the example above may represent the low and high capture velocities vcl, vch handled by the system. Slower or faster particles will rarely be in resonance with the lasers and will pass right through.
However, the particles with velocities in the range between the low and high capture velocities will start accelerating or decelerating at some position inside the magnetic field when resonance with the respective laser occurs.
The slower moving particles, i.e. the particles that are to be accelerated, will start resonating with the first laser beam 11a, and the faster moving particles will start resonating with the second laser beam 21a. From there they will continue to accelerate or decelerate as long as the resonance is maintained. This means that the slower atoms will converge towards a first converged velocity vfl and the faster atoms converge towards a second converged speed of vfh.
The length of the magnetic field B in the beam direction will determine how long the velocity changes takes place. If the length of the magnetic field is chosen to be where the first and second converged velocities vfl, vfh are identical, the distributed velocity distribution has been converted to an intense monochromatic particle beam.
The working principle for an embodiment of the invention where the magnetic field B is applied, will now be explained more in detail.
The resonant slowed velocity profile at z for a given laser detuning ΔL for the second laser 21 is given by; $υ (z) = \frac{(Δ_{L}^{B} + k_{z}^{B} \sqrt{υ_{c}^{2} - 2 az}) - Δ_{L}}{k_{z}^{'}} = \frac{(Δ_{L}^{B} - Δ_{L}) + k_{z}^{B} υ_{1} (z)}{k_{z}^{'}} .$
Where $Δ_{L}^{B}$ is the detuning the magnetic field is tailored to, and $k_{z}^{B} = k_{z} + \frac{Δ_{L}^{B}}{c}$ . The velocity profile $v_{1} (z) = \sqrt{v_{c}^{2} - 2 az}$ is the resonant profile for the detuning $Δ_{L}^{B}$ . Here v_c , is the capture velocity and $a = η \cdot a_{\max} = (\frac{s_{0}}{1 + s_{0}}) \cdot \frac{{ℏk}_{z} Γ}{2 m}$ is the constant acceleration the particles experience, given that they stay on resonance. s0 is the on-resonance saturation parameter, and is equal to I / I0. Note that the parameters of the magnetic field are not physical, but rather numbers to define the ideal magnetic field profile.
Here the effective wave number is $k_{z}^{'} = k_{z} + \frac{Δ_{L}}{c}$ .
The resonant speeding velocity profile at z for a given laser detuning ΔL for the first laser 21 is given by; $υ (z) = \frac{(Δ_{L}^{B} - Δ_{L}) + k_{z}^{B} υ_{1} (z)}{- k_{z}^{'}} .$
In the example provided below, a particle beam velocity squeezer for a He-4 beam is disclosed. The setup is generally applicable to all atom beams and most molecular beams.
Consider a beam of metastable helium-4 (from now on simply helium) in metastable state 2³S₁ with a mean longitudinal velocity in the beam direction z of 1000 m/s and a full width at half maximum (FWHM) of 400 m/s4, with the longitudinal velocity being Gaussian distributed.
In Fig. 5a, a particle beam velocity squeezer, according to the invention, producing a monochrome beam b1 is illustrated in a system comprising a helium source 31, a collimator 32, first and second lasers 11, 21, and beam expanders 12, 22. To produce the magnetic field B, a tubular coil section 33 surrounds the helium beam and the laser beams. The coil section has a decreasing magnetic field in the beam direction z and comprises coils with decreasing number of windings in that direction. The length of the coil section and the magnetic field areas is L, corresponding to the distance between the start and end position, zo, z1, as explained previously, while L2 is the total length of the chamber. L and L2 are 1.30 and 1.38 m, respectively, and the bore of the coil section is 0.08m. The helium particle beam b and the laser beams are illustrated with different pattern fills.. Although the laser beams have different wavelengths, they are illustrated with the same pattern in the sketch.
The first and second laser beams are reflected into the coil section from respective sides by first and second mirrors 13, 23 arranged -/+ 45 degree with regards to the beam direction, wherein they both have center hole to allow the particle beam to pass through.
In the setup the first laser 11 is RHC polar, while the second laser 21 is LHC polar. Since the first laser is parallel to the magnetic field direction (+z direction), and the second laser is antiparallel, such polarisations ensure that both lasers induce sigma+ transitions, and optically pump the system into M_J = +1, where the M_J = +1 ---> M_J = +2 transition is accessed throughout the chamber.
The particle beam velocity squeezer will start capturing Helium atoms from both 1340 m/s and 660 m/s simultaneously.
In addition to the information provided above, the following parameters are used:

Frequency of the first and second lasers: 1083 nm corresponding to the 23S1→23P2 transition in helium-4.
Initial magnetic field: B(z=0) = 35 mT;
Laser intensity: I = 0.51 mW/cm2;
Laser intensity distribution (intensity vs. space in the transverse plane): Gaussian;
Laser intensity Gaussian FWHM: 5 cm;
Atomic beam diameter: 5 cm5 cm
Chamber length: L=1.3 m (theory suggests = 1.28 mL=1.28 m in ideal case)
Capture velocities: initial high capture velocity vch0 =1340 m/s, initial low capture velocity vcl0 = 660 m/s.
Magnetic field laser detuning: $Δ_{L}^{B} = - 896 MHz$ . This corresponds to an initial magnetic field capture velocity of 1500 m/s to ensure that B(z=0)=35 mT;
Laser detunings (ordered w.r.t. capture velocities): Δ_L=-748 MHz, 1098 MHz.

The result is that around 81% of the atoms in the beam are converged into two well defined peaks as seen in Fig. 6. The first peak is centred at - 995 m/s and has a FWHM of 1.5 m/s, while the second peak is centered at - 1005 m/s and also has a FWHM of - 1.5 m/s.
In this case, the two peaks are the result of a monochromator with a magnetic field that extends slightly longer in the beam direction z than where the velocities converge. This can be understood by looking at Fig1, where the stapled lines to the right of z1 indicates that the capture velocity curves cross each other. Thus, the two lines are the result of the chamber length of 1.3 m being slightly longer than the theoretical length of 1.28m. This illustrates that one or more monochromatic beams may be achieved by adjusting the parameters of the system, such as the magnetic field strength or the extension of the magnetic field in the beam direction z.
It can be shown that the particles being accelerated with the first laser 11 are captured with much greater efficiency than the slowing second laser 21. This is presented graphically in Fig. 7. This is due to the fact that the magnetic field spatial gradient is very low relative to the spatial gradient of the slower particles, as it is suited for a much higher capture velocity (1500 m/s) paired with the fact that these are slower atoms. Thus, the chance they go off resonance with the magnetic field and the laser is very low.
Fig. 8 and Fig. 9 illustrate the use of multiple capture regions to produce an output beam with two or more velocity peaks. The velocity capture ranges are here [660, 1000] and [1000, 1340] m/s, for vcr1 and vcr2, respectively. There are two distinct peaks with more than 82% of the particles shaped into these two peaks with widths less than 3 m/s. Within these two peaks, 61% of the particles lie within a <1.5 m/s width. These results are slightly better than the results of the single capture range squeezer shown in Fig. 6.
Some additional parameters are given below:

Length L: 0.678 m;
% captured: >82%;
Capture velocity and detuning of magnetic field: 1500 m/s, -896 MHz (high capture velocity and magnetic field detuning to increase capture efficiency)
Magnetic field B start value: ~35 mT
Actual laser detunings: for capture range [660 m/s, 1000 m/s] (speeding, slowing) = [1100 MHz, -434 MHz]. For capture range [1000 m/s, 1340 m/s] (speeding, slowing) = [1414 MHz, -748 MHz]. Speeding/ slowing translates to blue detuned/ red detuned lasers respectively.

In the exemplary embodiments, various features and details are shown in combination. The fact that several features are described with respect to a particular example should not be construed as implying that those features by necessity have to be included together in all embodiments of the invention. Conversely, features that are described with reference to different embodiments should not be construed as mutually exclusive. As those with skill in the art will readily understand, embodiments that incorporate any subset of features described herein and that are not expressly interdependent have been contemplated by the inventor and are part of the intended disclosure. However, explicit description of all such embodiments would not contribute to the understanding of the principles of the invention, and consequently some permutations of features have been omitted for the sake of simplicity or brevity.

Claims

A particle beam velocity squeezer for an incoming particle beam (b) with a beam direction z, wherein the monochromator comprises;
- a first electromagnetic radiation source (11) arranged to provide a first beam of coherent light (11a) in the beam direction,

- a second electromagnetic radiation source (21) arranged to provide a second beam of coherent light (21a) opposite the beam direction z, wherein the first and second beam of coherent lights coincide at least partly with the particle beam (b).
The particle beam velocity squeezer of claim 1, wherein the first beam of coherent light 11a is configured to increase the speed of the slower particles in the particle beam b, and the second beam of coherent light 21a is configured to slow down the speed of the faster particles in the particle beam b.
The particle beam velocity squeezer of claim 1 or 2, wherein the first electromagnetic radiation source 11 has a first wavelength λ1 that is smaller than a second wavelength λ2 of the second electromagnetic radiation source 21.
The particle beam velocity squeezer of any of claim 1 to 3, comprising;
- a magnetic field generator arranged to provide a magnetic field B in the beam direction.
The particle beam velocity squeezer of claim 4, wherein the magnetic field B is configured to Zeeman-shift the resonant frequency of the slower particles as they increase their speed to match the increasing Doppler shift, and to Zeeman-shift the resonant frequency of the faster particles as they decrease their speed to match the decreasing Doppler shift.
The particle beam velocity squeezer of claim 4 or 5, wherein the magnetic field B decreases in the beam direction z and the polarization of the first electromagnetic radiation source first RHC polar, while the second electromagnetic radiation source 21 is LHC polar, or the magnetic field B increases in the beam direction z and the polarization of the first electromagnetic radiation source is LHC polar, while the second electromagnetic radiation source 21 is RHC polar.
The particle beam velocity squeezer of any of claim 4 to 7, wherein the incoming particle beam b has an input velocity distribution vdi and a converged velocity distribution vdo, wherein the converged velocity distribution is more monochromatic than the input velocity distribution.
The particle beam velocity squeezer of Claim 7, wherein the monochromator has an incoming velocity capture range vcr0 defined by a difference between high and low input capture velocities vch0, vcl0 at a start position of the magnetic field B.
The particle beam velocity squeezer of Claim 8, wherein a majority of the particles of the incoming velocity distribution vdi falls within the incoming velocity capture range vcr0.
The particle beam velocity squeezer of any claim 7 to 9, wherein a majority of the particles in the converged velocity distribution vdo converge to a converged velocity vo.
The particle beam velocity squeezer of any of the claims 1 to 9, comprising
- additional one or more electromagnetic radiation sources arranged to provide a first beam of coherent light in the beam direction, and

- additional one or more electromagnetic radiation sources arranged to provide a second beam of coherent light opposite the beam direction z, wherein the first and second beam of coherent lights coincide at least partly with the particle beam b.
A method for velocity squeezing an incoming particle beam (b) with a beam direction z, wherein the method comprises;
- provide a first beam of coherent light (11a) in the beam direction,

- provide a second beam of coherent light (21a) opposite the beam direction z, wherein the first and second beam of coherent lights coincide at least partly with the particle beam (b).
The method of claim 12, comprising;
- a provide a magnetic field B in the beam direction.
The method of claim 13, comprising, comprising
- Zeeman-shifting the resonant frequency of the slower particles as they increase their speed to match the increasing Doppler shift, and

- Zeeman-shifting the resonant frequency of the faster particles as they decrease their speed to match the decreasing Doppler shift.
The method of claim 14, comprising;
- any of the features of claims 1 to 11.