WO2011073656A1

WO2011073656A1 - Quantum memory

Info

Publication number: WO2011073656A1
Application number: PCT/GB2010/052096
Authority: WO
Inventors: Klaus Franz Reim; Joshua Nunn; Ian Alexander Walmsley; Virginia Olga Lorenz; Benjamin Jacob Sussman
Original assignee: Isis Innovation Limited
Priority date: 2009-12-15
Filing date: 2010-12-15
Publication date: 2011-06-23
Also published as: GB0921917D0

Abstract

A quantum memory comprising: a storage medium, the storage medium having a ground state energy level, an excited state energy level and a storage state energy level; a first radiation source arranged to generate a pulsed control field for reading and writing to the storage medium by stimulating off-resonant transitions between the storage state and the excited state; a second radiation source arranged to generate a pulsed signal field containing a signal to be written to the storage medium, said second radiation source being arranged to stimulate off-resonant transitions between the ground state and the excited state; and a third radiation source arranged to generate a pump field for stimulating transitions out of the storage state of the storage medium. The highly off resonant approach of this scheme is distinguished from the previously demonstrated cold-atom approach in that the detuning can be significantly greater than (e.g. approximately four times) the inhomogeneous linewidth, rendering it both immune to inhomogeneous broadening, and thereby suited to room-temperature or higher operation, and amenable to large optical bandwidths.

Description

Quantum memory

The invention relates to quantum memories, in particular quantum memories based on off-resonant Raman interactions. The invention also relates to the use of such memories in quantum repeaters.

Quantum memories, capable of controllably freezing and releasing a photon, are a crucial component for quantum computers and quantum communications. In general terms, quantum computing data is stored or transferred in the form of quantum bits (or qubits). Photons are ideal carriers of quantum information, being fast moving and weakly affected by environmental decoherence. Photons can therefore be used to transfer qubits over large distances. Storing qubits on the other hand is best done in relatively stationary structures such as atoms, atomic ensembles or quantum dots for example. A quantum memory therefore has to be able to transfer the quantum information coherently from a photonic ("flying") qubit into a storage ("stationary") qubit and to transfer the quantum information coherently back into a photonic qubit again on demand. Recently, sources, detectors, gates and protocols have been developed that enable the construction of large-scale photonic quantum computers with unique

capabilities, as well as inter-continental quantum networks that are immune to espionage. However, the elements comprising these devices function

probabilistically, meaning that an array of photonic components will produce the desired results only rarely. This difficulty is removed if it is possible to store photons, since this allows complex protocols to be orchestrated by holding the output of successful computations until all operations have been correctly executed. For this reason, quantum memories are a burgeoning research frontier, with a great deal of interest focussed on the reversible mapping of photons into collective atomic excitations. Various existing memory protocols make use of techniques including

electromagnetically induced transparency (EIT), controlled reversible

inhomogeneous broadening (CRIB) and atomic frequency combs (AFC). EIT based memories utilize the extreme dispersion of an induced transparency window to modify the group velocity, and controllably stop, store and retrieve light pulses.

CRIB is a photon echo technique that uses an artificial inhomogeneous broadening of the atomic resonance. The reversing of this broadening during the readout process causes the atomic spins to rephase and collectively re-emit the original signal. In the AFC protocol one artificially creates an atomic frequency comb which absorbs an incident signal. The periodic structure of the absorption spectrum results in a subsequent re-phasing and re-emission of the stored signal. As well, off-resonant light storage has previously been implemented via four-wave mixing, stimulated Brillouin scattering and via the gradient echo memory (GEM) protocol. For these resonant and off-resonant protocols typical storage times have ranged from microseconds to milliseconds and efficiencies of from 1% to 15% have been achieved. The reported bandwidths range from kHz to MHz and the memories have been very sensitive to the experimental environment.

Key desirable characteristics for quantum memories are typically a long storage time and a high memory efficiency, as well as the ability to store multiple modes (i.e. multiple distinct photons), and to have a high bandwidth (i.e. fast operation). This last property is generally difficult to achieve with atomic memories, since photons must be stored in long-lived atomic states with narrow linewidths. But it is desirable to store temporally short photons (which have broad spectra) since then quantum information can be processed at a higher 'clock rate', extending the number of computational cycles that can be completed before decoherence sets in.

Robust, higher bandwidth (faster) quantum memories operating with very short laser pulses are a prerequisite for reliable and broadband quantum technology devices that allow for high-speed quantum processing and high data transfer rates in completely secure quantum networks. A quantum memory based on off-resonant Raman interactions was proposed and theoretically analysed in "Mapping broadband single-photon wave packets into an atomic memory" by J. Nunn et. al., Physical Review A (Atomic, Molecular and Optical Physics) 75 (1), 011401-011404. This theory is briefly summarised in the Appendix.

In the storage process of such a memory, a strong broadband control pulse maps a weak broadband signal pulse into a collective atomic coherence called a spin wave. During read-out, a strong subsequent read pulse reverses the read-in process and extracts the stored excitation into a well-defined spatio-temporal optical mode. The Raman memory's robustness, controllability and vast increase in speed open the path to reliable high-speed quantum networks and quantum processing.

According to a first aspect of the invention there is provided a quantum memory comprising: a storage medium, the storage medium having a ground state energy level, an excited state energy level and a storage state energy level; a first radiation source arranged to generate a pulsed control field for reading and writing to the storage medium by stimulating off-resonant transitions between the storage state and the excited state; a second radiation source arranged to generate a pulsed signal field containing a signal to be written to the storage medium, said second radiation source being arranged to stimulate off-resonant transitions between the ground state and the excited state; and a third radiation source arranged to generate a pump field for stimulating transitions out of the storage state of the storage medium. This novel memory interaction takes place via a far off-resonant two-photon transition in which the memory bandwidth is dynamically generated by the strong control field. This interaction allows a much higher bandwidth which in turn allows for an increase in data rates by a factor of almost 1000 compared to existing quantum memories.

In this Raman memory, the bandwidth is generated dynamically by ancillary write/read pulses, which dress the narrow atomic resonances to produce a broad virtual state to which the signal field couples. The off-resonant nature of this scheme confers some advantageous features. These include: (i) the ability to store broadband pulses (the large detuning guarantees that the atomic polarization adiabatically follows the pulse envelopes, even when they are temporally short); (ii) insensitivity to inhomogeneous broadening (the Raman transition is detuned far beyond the Doppler linewidths, and (iii) the property that any unstored light is transmitted without attenuation. This last feature is useful since the partial storage of a single photon entangles the memory with the optical mode of the transmitted signal. Such light-matter entanglement operations are primitives for the construction of quantum repeaters (discussed further below).

The highly off resonant approach of this scheme is distinguished from the previously demonstrated cold-atom approach in that the detuning can be significantly greater than (e.g. approximately four times) the inhomogeneous linewidth, rendering it both immune to inhomogeneous broadening, and thereby suited to room-temperature or higher operation, and amenable to large optical bandwidths. Both of these characteristics are highly advantageous.

This memory provides the experimental realization of an efficient and broadband Raman memory with coherent storage and retrieval of sub-nanosecond low intensity light pulses with spectral bandwidths exceeding 1 GHz.

The type of radiation sources used will depend upon the storage medium and the energy levels involved. The sources may generate electromagnetic radiation of various wavelengths, including visible light, infrared or ultraviolet light or they may generate microwave radiation. Preferably the first radiation source is a laser and/or the second radiation source is a laser and/or the third radiation source is a laser. It will be appreciated that different types of lasers can be used depending on the circumstances. In many instances the flexibility of tunable lasers will be beneficial.

Different radiation sources may be used for each of the control and signal fields. However in a preferred embodiment the control field and the signal field are derived from the same radiation source. As the transition energies required of the control and signal fields will often be very close, a single source can be used to generate side bands of different wavelengths. The main source and/or one or more side bands may then be used as different sources which can subsequently be recombined by any normal beam combining techniques.

In one particularly preferred embodiment, the control field and the signal field are derived from a titanium-sapphire laser. Titanium sapphire lasers are tunable over a range of useful spectral frequencies (about 650 to 1100 nm) and can generate extremely short pulses and are therefore suitable for generating broadband photons.

The pump field may be a diode laser, although any other radiation source suitable for maintaining a net transfer away from the storage state energy level may be used. In order to store information within the memory, i.e. to stimulate transitions into the storage state energy level, it is necessary that the control field and the signal field arrive at the storage medium at the same time. Although in some instances it may be possible to direct the two pulses from different directions and ensure that they meet at the right place at the right time, it is preferred that the control field and the signal field are arranged to propagate coaxially in the same direction through the storage medium. This ensures that the two pulses are spatially overlapped throughout their propagation and thus ensures a high interaction area within the storage medium. Where the signal field and the control field are spatially overlapped and propagating coaxially in the same direction, the problem of separating the two fields becomes important. As the signal field is in general much weaker than the control field, it becomes very important to isolate the signal field from the control field with a high degree of rejection of the control field so that the signal field can be detected above the noise. As the two fields are of different wavelengths, gratings or etalons could be used to separate the two fields. However, if the wavelengths of the two fields are very similar (i.e. if the energies of the ground and storage states are very similar) then gratings and etalons may either provide insufficient separation or may be too inefficient. It is therefore preferred that the first and second radiation sources are arranged to generate the signal field and the control field with orthogonal polarizations. The memory may then further comprise a polarizing beam splitter arranged to separate the control field and the signal field after they have passed through the storage medium. The polarizing beam splitter can be aligned so that it allows the signal field to pass, but deflects the control field to a high degree. This therefore provides a convenient way of separating the two beams if the ground and storage states are close together in energy. The use of polarization is not however necessarily always a good solution as the polarization of the light affects the selection rules for allowable transitions within the storage medium. Polarization cannot be used to separate the fields if the selection rules would result in a decrease in the strength of the already weak signal field. The pump beam must also be directed at the storage medium in order to interact therewith at the same time as the control and signal fields. The pump beam may be directed at the storage medium at an angle to the control and signal fields, or it may be directed perpendicular to the control and signal fields. However, for maximised interaction area, it is preferred that the pump field be arranged to propagate coaxially in the same direction as or coaxially in the opposite direction to the signal and control fields through the storage medium. This arrangement maximizes the overlap between the three fields and therefore provides the greatest interaction area, although it introduces the problem of coaxially overlapping the various beams. Although the pump field may be arranged to travel with the control and signal fields in a co-propagating manner (i.e. in the same direction), it is preferred to arrange the pump field in a counter-propagating manner (i.e. in the direction directly opposite to that of the control and signal fields). The counter-propagating arrangement results in less noise at the detection end as the pump field does not need to be filtered out in the same way as it does if co-propagating.

It is particularly preferred that the polarizing beam splitter be arranged to combine the pump field with the control and signal fields in a counter-propagating manner so as to direct the pump field through the storage medium coaxially with the control and signal fields, but in the opposite direction. This dual use of the polarizer (i.e. to filter out the control signal and to coaxially combine the pump field with the other fields is advantageous as it reduces the number of components required in the system. For example, in order to combine the pump field in a co-propagating manner, an additional element is required in order to redirect the pump field into the same direction as the other two fields, but the polarizing beam splitter (or alternative separation device) is still required. The provision of this extra element necessarily reduces the intensity of one of the other fields (inevitably the control field as the signal must be preserved).

The memory may be arranged in a number of different shapes and sizes depending on the type and volume of storage medium being used and the types of radiation source. However in general it is desirable to reduce the size of any components which will form part of a computer architecture. As the size decreases, the geometry becomes more complicated and it becomes more difficult to align all of the components. Therefore in a preferred form, the storage medium is placed inside a waveguide and the control field, the signal field and the pump field are directed along the waveguide in order to interact with the storage medium.

In the preferred embodiments, the storage medium has a lambda-level structure comprising the ground state energy level, the excited state energy level and the storage state energy level, and transitions between the ground state energy level and the storage state energy level are forbidden such that the storage state energy level has a long lifetime relative to the other energy levels in the atom. In order to maximize the benefits of the memory, the selection rules have to be carefully analyzed and a level structure chosen which has a long-lived storage state which is accessible via an off-resonant Raman transition. The frequency of the signal field may correspond to the transition from the ground state energy level to the excited state energy level, but detuned from resonance by a detuning amount and the frequency of the control field may correspond to the transition from the storage state energy level to the excited state energy level, but detuned from resonance by substantially the same detuning amount. Detuning far from the resonant excited state transitions reduces the system noise by ensuring that the control and signal fields do not interact strongly with the resonant transitions. Also, detuning from resonance means that the bandwidth of the off-resonant virtual state is dependent upon the bandwidth of the control field rather than being dependent on the power of the control field which is the case on-resonance. Thus the bandwidth can be easily increased simply by increasing the bandwidth of the control field and without requiring additional power. The control and signal fields should preferably have a common detuning. Any difference between the detuning amounts of the control field and the signal field will reduce the efficiency of the memory.

In preferred embodiments the detuning amount corresponds to approximately twice the separation of the ground state and storage state energy levels. Even if the ground state and storage state energy levels are close together in energy, this will generally provide sufficient detuning from the resonant transitions as described above.

Preferably the detuning amount corresponds to the free spectral range of an etalon which is used to separate the control field from the signal field. The pump field, tuned to resonance will inevitably scatter some light on resonance which also needs to be filtered. With the control field tuned exactly one free spectral range off resonance, the etalon can be set for maximum extinction of both the pump field (on resonance) and the control field (one free spectral range off resonance), while providing maximum transmission for the signal field half way between the two.

The detuning amount is preferably at least 5 GHz away from the resonant transitions. More preferably, the detuning amount is at least 10 GHz and more preferably still it is between 10 and 20 GHz. In one preferred embodiment, the detuning is 18.4 GHz from resonance. In principle, there is no upper bound to the detuning amount, but as the interaction probability drops with the inverse square of the detuning, larger detunings require larger/denser ensembles. In general, the detuning amount must be much greater than the bandwidth of the signal pulses which are to be stored. Therefore the detuning amount will be selected as the smallest detuning amount which meets this criterion. Many different storage media exist. The storage medium may in some embodiments simply be a single atom. However due to the low interaction probabilities caused by the off-resonance reaction, it is preferred that the storage medium comprises an atomic ensemble. Likewise, the storage medium could be a collection of atoms in a crystal or it could be a liquid. However, in a preferred form, the storage medium comprises a hot vapour. Typically this would take the form of a quantity of atoms of the storage medium suspended in a buffer gas such as neon or another noble gas. Among the various different possible storage media, cesium has been found to be a

133

good candidate. In particular, the stable isotope Cs is a preferred storage medium and therefore in preferred embodiments the storage medium may comprise at least one cesium atom. When cesium is used as the storage medium, the preferred lambda level structure is

133 2 based on the Cs D₂ line, wherein the ground state energy level is the 6 Si_/2, F = 3 level, the excited state energy level is the 6 P_3/2 level and the storage state energy level is the 6 Si/₂, F = 4 level. The temperature of the cesium gas can be important. The density of the vapour varies exponentially with the temperature. Generally, a higher density produces a better memory efficiency, but it can be problematic to optically pump very dense vapours, so the state preparation by optical pumping limits the density that can be used. On the other hand, if the temperature is too low, the memory efficiency becomes too low. Preferably the cesium gas temperature is in the range 55 to 70 degrees Celsius. More preferably, the gas temperature is in the range 60 to 65 degrees Celsius and most preferably the gas temperature is approximately 62.5 degrees Celsius.

The hot cesium gas may be contained within a closed cell. The dimensions of the cell can also affect the efficacy of the memory. The memory efficiency is proportional to the length of the cell (i.e. to the number of atoms illuminated by the incident radiation fields), so longer cells are generally beneficial to the coupling. Longer cells are more expensive and it can be difficult to focus beams over very long distances. In waveguides, longer ensembles may be used.

The cell is preferably of a length less than 10 cm. The cell is also preferably greater than 5 cm in length and is most preferably about 7 cm in length. This provides a good interaction area and a high efficiency for the memory. The energy of the control field pulses will depend on the circumstances, including the size and type of the storage medium. However due to the off-resonant nature of the Raman interactions of this memory, the read and write pulses need to be much stronger than the signal field pulse in order to ensure that the writing or reading transition has a high probability of success. Therefore preferably the control field comprises pulses having an energy of greater than 5 nJ. More preferably the pulses have an energy of greater than 20 nJ. More preferably still, the pulses have an energy greater than 50 nJ.

In the preferred embodiments, the bandwidth of the control and signal fields is less than 3 GHz. This upper bound on the bandwidth is derived from the splitting of the storage state and the ground state. The two fields (signal and control) must not overlap spectrally, so their bandwidths must be much less than the splitting. In the case of a splitting of 9.2 GHz between ground and storage states, 3 GHz is a reasonable upper limit for bandwidth. If storage media with larger level splittings are used, larger bandwidths can be used. But the larger the bandwidth, the larger the detuning has to be, which in turns demands a higher density. The pump field may also be a pulsed field, but in the preferred embodiments it is a continuous wave field so as to provide continuous pumping of the storage state. In the preferred embodiments the pump field has a power of 500 microwatts to 10 milliwatts. It has been found that cesium vapour cannot be optically pumped effectively with powers of less than 500 microwatts. With powers greater than 10 milliwatts, there can be significant scattering and the spin wave coherence begins to degrade.

As discussed above, this memory has a particular advantage in that when the memory is not operational, e.g. when the control field is switched off, the storage medium is transparent to the signal field. In the other types of quantum memory discussed above, the memories are opaque to the signal when they are not in use. This means that any signal not stored is lost. By contrast, with the system of the present invention, any signal not stored passes straight through the memory.

Therefore a memory with less than 100% efficiency will result in entanglement between the memory and the ongoing signal. This enables the memory to be used in a quantum repeater for increasing the distance over which quantum information can be transmitted without decoherence analogously to a classical fibre optic repeater. When a photonic qubit is sent over a large distance it will gradually lose coherence and the information will be lost. Quantum repeaters use a quantum memory to capture and store the qubit before the photon loses coherence. The memory can then be read, thereby generating a fresh photonic qubit which can travel some distance further before losing coherence. In this way quantum information can be transferred coherently over large distances.

Therefore according to a second aspect, the invention provides a quantum repeater comprising a memory as described above. Although entanglement will occur with anything less than 100% storage efficiency, optimal entanglement will occur when 50% of the signal is stored and 50% is transmitted, thus generating an equal superposition of states. Therefore in a preferred embodiment the quantum repeater is arranged to have a memory with a storage efficiency of 50%.

The invention also extends to methods of operation of the device. Accordingly, the invention provides a method of storing a signal in a quantum memory, the quantum memory comprising a storage medium, the storage medium having a ground state energy level, an excited state energy level and a storage state energy level; the method comprising the steps of: a first radiation source generating a pulsed control field for writing to the storage medium by stimulating off-resonant transitions between the storage state and the excited state; a second radiation source generating a pulsed signal field containing the signal to be written to the storage medium, said second radiation source stimulating off-resonant transitions between the ground state and the excited state; and a third radiation source generating a pump field for stimulating transitions out of the storage state of the storage medium.

The invention further provides a method of reading a signal from a quantum memory, the quantum memory comprising a storage medium, the storage medium having a ground state energy level, an excited state energy level and a storage state energy level; the method comprising the steps of: a first radiation source generating a pulsed control field for reading from the storage medium by stimulating off- resonant transitions between the storage state and the excited state;

It will be appreciated that all of the preferred features described above in relation to the apparatus also apply equally to the methods of operation.

Certain preferred embodiments of the invention will now be described, by way of example only, and with reference to the accompanying drawings in which:

Fig. 1 illustrates schematically the principle on which the invention works;

Fig. 2 illustrates storage and retrieval efficiencies at various pulse energies;

Fig. 3 illustrates the transmission of the memory when no signal is present versus when a signal is present; Fig. 4 illustrates the correspondence of actual memory measurements compared with theoretical predictions.

Fig. 5(a) shows the lambda level structure of the cesium atoms used in an embodiment of the invention;

Fig. 5(b) shows the set-up of an embodiment of the invention;

Fig. 6 shows the interference pattern when the stored and received signals are interfered, demonstrating coherence;

Fig. 7 shows an embodiment of the invention with a co-propagating pump beam; Fig. 8 shows an embodiment of the invention with a counter-propagating pump beam; and

Fig. 9 shows an embodiment of the invention with the storage medium embedded in a waveguide.

The following detailed description of preferred embodiments of the invention demonstrates the storage of signal pulses in a Raman-based quantum memory with a bandwidth 7000 times larger than the natural width of the cesium D2 line that mediates the interaction. Signal pulses with bandwidths greater than 1 GHz are coherently stored and retrieved. This is an increase of almost a factor of 1000 compared to existing quantum memories. Storage efficiencies up to 30% and retrieval efficiencies as high as 50% have been observed. The memory works with a total efficiency of 15% and its coherence is demonstrated by directly interfering the stored and retrieved pulses.

Fig. 1 shows a Raman memory and its principle of operation. As illustrated in Fig. 1(a), a signal is directed into the memory along with a bright write pulse and is stored in the memory. If the storage is partial, any unstored signal is transmitted through the memory. A subsequent read pulse extracts the stored excitation, which emerges along with the transmitted read pulse. In the apparatus shown in Fig. 1 , a strong write pulse 2 and a weak signal pulse 3, both broadband, are spatially and temporally overlapped and sent together into a cesium vapor cell 1 where the Raman interaction with the storage medium takes place (see Figs.1(b) and 5(a)). The signal pulse 3 is mapped via a two-photon transition with the write pulse 2 into a collective atomic excitation called a spin wave. At a later time a strong read pulse 4 is sent into the vapor cell 1 and converts the spin wave into an optical output signal that is measured on a fast detector.

As shown in Fig. 1, the portions of the write pulse 2, the signal pulse 3 and the read pulse 4 that are not absorbed in the storage medium 1 are indicated at 2', 3' and 4' respectively. The signal which has been retrieved from cell 1 by read pulse 4 is shown at 5.

Fig. 2(a) shows experimental data for the storage and retrieval processes. The storage of a signal pulse takes place at time t = 0 and the retrieval of the stored information is carried out 12.5 ns later. The storage and retrieval efficiencies depend on the write and read pulse energy. As can be seen, with no write pulse present (i.e. 0 nJ), there is 100% transmission - nothing is stored and nothing can be retrieved. This contrasts with resonant storage protocols, in which the memory becomes absorbing when 'inactive'. With the highest write/read pulse energies (4.8 nJ) the transmission drops to 70%, indicating that 30%> of the incident signal is stored. At t = 12.5 ns, 50% of the stored information is retrieved giving a total memory efficiency of 15%.

Fig. 2(b) shows a close-up of the retrieved signal field showing the measured full width at half maximum (FWHM) temporal duration of 1 ns, limited by the detector response time. This shows that the bandwidth of the retrieved signal exceeds 1 GHz.

Figure 3 presents an instance of the storage and retrieval processes with the short pulse durations clearly visible. The solid line shows the transmission of the incident signal field without the presence of a write/read field, i.e. no storage and no retrieval. Increasing the write and read pulse energy decreases the transmitted fraction of the incident signal and increases the retrieved signal. The dashed line shows the transmission of incident signal field in the presence of write/read fields (not visible). It can be seen that 30% of the incident signal field is stored (leaving 70% transmission) and that 50% of that stored signal is retrieved, resulting in 15% total transmission (i.e. 15% overall efficiency).

The measurement of the pulse duration shown in the inset of Fig. 3 is limited by the response time of the detector, which is 1 ns, corresponding to a bandwidth of 1 GHz. The Raman memory scheme theoretically operates at the full bandwidth of the control field, which is 1.5 GHz.

The time-bandwidth product N of a memory quantifies the number of distinct time bins available for computational operations in a hypothetical quantum processor using the memory. With the storage time in this embodiment of 12.5 ns we have N ~ 15 . Decoherence is negligible over the storage time, which is much shorter than the timescale characterizing atomic diffusion. It is anticipated that the storage time of the memory is limited to several hundred microseconds (typical coherence times in hot atomic vapors), so that time- bandwidth products as high as N ~ 10⁵ are realistic.

Fig. 4 shows the dependence of the memory efficiency on write/read pulse energy. Figs. 4(a) and 4(b) show a comparison of the measured efficiencies for storage and retrieval with the predictions of a theoretical model. Fig. 4(a) shows storage efficiency and Fig. 4(b) shows total efficiency. Dots and error bars indicate experimental data and solid lines represent predicted theory. Precise measurement of the pulse shapes requires greater temporal resolution than was available with the detector used, so to apply the theory we assume Gaussian temporal profiles for all pulses; the timing and duration of the signal pulse are then adjusted to account for the dispersive effects of the etalons used to spectrally filter the signal. The observations stand in good agreement with the theory.

The theoretical model does not include Doppler broadening, spontaneous emission, diffraction or decoherence, so the close correspondence indicates that the observed memory efficiency is not limited by these processes, but by the experimentally accessible Raman coupling C_max ¾ 1 (see Appendix). This could be enhanced by heating the cesium cell and thereby increasing the vapor density; efficient optical pumping though, then becomes problematic. Alternatively, higher efficiencies could be achieved if more energetic control pulses were available.

The retrieval efficiency ?7_ret = η_ΧοΧ I ?7_store is significantly larger than the storage efficiency ?7_store , since the total efficiency η_ΧοΧ exceeds ?7_store ² . This is a sign that the shape of the signal pulse is sub-optimal, since an ideal memory has equal storage and retrieval efficiencies. Correct mode matching of the signal to the control pulse profile should allow for a significant increase in efficiency.

Fig. 4(c) shows an extrapolation of the theoretical prediction for η_ΧοΧ to larger write/read pulse energies. This indicates that η_ΧοΧ ~ 30% is achievable for pulse energies ~ 15 nJ. Also plotted is the optimal attainable efficiency in the present configuration with retrieval in the forward direction (dashed line), along with the optimal efficiency for backward retrieval (dotted line). To achieve these bounds the signal field requires appropriate shaping - the distortion due to the etalons should be compensated, along with the dynamic Stark shift due to the strong write field. Re- absorption of the signal limits the efficiency to around 60% for forward retrieval, but efficiencies above 90% can be reached employing phase-matched backward retrieval. The shaded area denotes the range of pulse energies accessible with the present embodiment. Forward retrieval is where the read-out control field is sent in the same direction as the storage control field. This has limited efficiency because the retrieved signal field has to propagate across the whole ensemble, and it can be re-absorbed. In backward retrieval, the retrieval control pulse is sent into the ensemble from the backward direction, and the signal field is retrieved back along the direction it originally came from. This reduces the re-absorption, and can in principle allow perfect efficiency. Fig. 5(a) shows the atomic states of cesium involved in the Raman protocol (i.e. the Λ - level scheme for the Raman memory described herein). In operation, the atoms are prepared in the ground state 11) by optical pumping. The signal is tuned into two-photon resonance with the write field; both are detuned from the excited state

into the storage state

13) via Raman scattering stimulated by the write field. Upon retrieval the interaction is reversed. The F=3,4 'clock states' of the ground-level hyperfme manifold serve as the states 11) and 13) , which are connected to the excited state 12) (the 6²P₃/₂ manifold) via the D2 line at 852 nm.

The set-up of the present embodiment is shown in Fig. 5(b). A cesium vapor cell 10 is optically prepared with a diode laser 12. The cesium is heated to 62.5°C, so that the resonant optical depth ( d « 1800 ) associated with this transition is high. In time bin ti an incoming signal pulse 14 is mapped by a strong write pulse 16 into a spin wave excitation in the atomic cesium ensemble. At t₂ a strong read pulse 18 reconverts the excitation into a light pulse 20. After polarization filtering (Pol) 22, the retrieved signal is detected by a high speed avalanche photo detector (APD) 24. Vertical polarization is indicated as ( $ ) and horizontal polarization as ( ->). Δ is the detuning from the atomic resonance.

The read, write and signal pulses are derived from a Ti:Sapph oscillator 26 and have a FWHM of 300 ps (1.5 GHz bandwidth). The oscillator 26 generates pulses at a frequency of 80 MHz, i.e. one pulse every 12.5 ns. The fundamental Ti:Sapph laser frequency is tuned 18.4 GHz to the blue of the 12) - 13) transition (see Figure 5(a)).

A Pockels cell 28 selects two consecutive pulses, separated by 12.5 ns. The laser beam is split into a strong control arm 30 with vertical polarization (% ) and a very weak signal arm 32 with horizontal polarization ( ->). The control arm 30 is delayed by 12.5 ns with respect to the signal arm 32 such that the first pulse 16 in the control arm 30 overlaps in time with the last pulse 14 in the signal arm 32. An electro-optic modulator (EOM) 34 is used in the signal arm to generate sidebands 9.2 GHz shifted from the fundamental laser frequency. After spectral filtering with Fabry Perot etalons 36 only the 9.2 GHz red-shifted sideband corresponding to the 11) - 12) transition is transmitted and used as the signal field. The control 30 and the signal 32 beam, spectrally separated by 9.2 GHz, are recombined and made collinear (at polarizing beam splitter (PBS) 38). They are focused with a beam waist of 350 ym into the 7 cm long vapor cell 10 filled with cesium and 20 torr of neon buffer gas. Polarization- filtering 22 and spectral- filtering 40 are used after the cell 10 to extinguish the strong write 16 and read 18 pulses and transmit the signal field 20 only. A high-speed avalanche photo detector 24 with a bandwidth of 1 GHz detects the very weak signal pulse 20. The atomic ensemble 10 is initially prepared in the ground state 11) by optical pumping using an external cavity diode laser 12 tuned to resonance with the

To investigate the coherence properties of the memory, a copy of the incident signal field is attenuated, delayed and overlapped with the retrieved signal in a Mach- Zehnder configuration. After matching the intensities of the two interfering pulses, fringes are observed in the detected signal, as shown in figure 6, by scanning the phase in the interferometer using a piezoelectric actuator. The calculated fringe visibility is 86 ± 5%. This shows that the memory is coherent - a pre -requisite for operation at the single-photon level. On the other hand, direct application of the theoretical model predicts a distortion of the retrieved field due to dispersion and Stark shifts (these can be eliminated with backward retrieval), yielding a maximum visibility of 83%.

Fig. 6 shows the combined intensity of stored and retrieved signal. The circles indicate experimental data and the solid curve is a least square fit. It can be seen that a linear scan of the path length difference in the interferometer results in sinusoidal oscillations of the total intensity. This indicates constructive and destructive interference. As described above, the high visibility of 86% (normalized for interferometer instability) of the interference demonstrates the coherence of the memory and matches with the theoretical calculations, indicating that the memory interaction is perfectly coherent. Note that because we retrieve the stored signal after just 12.5 ns (the round-trip time of our oscillator), the efficiency and coherence we observe are not limited by decoherence; instead, these are a direct probe of the intrinsic efficiency and coherence of the Raman memory interaction.

Figures 7, 8 and 9 schematically show three different embodiments of a Raman- based memory cell as described above. Figure 7 shows a memory cell 10 with the control field 60 and the signal field 62 co-propagating through the memory cell, Although the fields are schematically shown parallel, but offset, in practice the fields are coaxial and travelling in the same direction. A pump field 64 is also combined with the control field 60 and signal field 62 to co-propagate with them, coaxially and in the same direction. As the three fields 60, 62, 64 originate from different sources, it is necessary to employ beam splitters in order to combine the fields. First a beam splitter 54 combines the control field 60 and the pump field 64. Next the signal field 62 is combined with these two fields at polarizing beam splitter 50. After propagation through the memory cell, the weak signal 62 must be separated from the strong pump 64 and control 60 in order that it may be detected. A polarizing beam splitter 52 is used for this purpose. In this arrangement the control field 60 and the pump field 64 are of one polarization and the signal field 62 is of an orthogonal polarization. The polarization beam splitter 52 therefore separates the signal field with high efficiency. Further separation is performed via etalon 53 which is tuned for maximum transmission at the signal field wavelength and for maximum extinction at the control and pump wavelengths.

Figure 8 shows an embodiment which is the same as that of Figure 7 in all respects except that the polarizing beam splitter 52 is used to combine the pump field 64 with the control field 60 and the signal field 62 in a counter-propagating manner, i.e. the pump field is arranged (in practice, but not in the figure) coaxially with the other fields, but travels in the opposite direction. There are two main advantages to this arrangement. Firstly, the arrangement requires fewer components (there is no need for the beam splitter 54 of Fig. 7. This means that the losses 66 in the pump field 64 and the control field 60 are avoided. Instead, the polarizing beam splitter 52 provides a dual use of diverting the control field 60 away from the signal field 62 and directing the pump field 64 into the memory cell 10. Secondly, as the pump beam is counter-propagating, it does not need to be filtered out from the signal field 62 for read-out.

Figure 9 shows an embodiment which is the same as that shown in Figure 8 except that the memory cell 10 is replaced by a waveguide 100. This arrangement allows for maximising the length of the storage medium which provides a good interaction area and allows other dimensions of the system to be reduced.

In the embodiments described herein, the signal pulses contain several thousand photons. However, the memory interaction is linear and coherent, meaning that the Raman protocol represents a genuine quantum memory that in principle also works in the single photon regime.

If the incident signal field is blocked, no retrieved signal is detected. Given the sensitivity of the detector (-60 photons per pulse), the retrieval noise can be bounded at less than 2%. This is consistent with the claim that the Raman memory operates in the linear regime without introducing spontaneous emission noise and therefore is suitable for the storage of single photons.

With no changes to the current set-up, simply doubling the laser power should give a storage efficiency of 50%. Because unstored light is transmitted, sending a single photon through such a memory produces a maximally entangled state of optical and spin wave modes, with only a vacuum contribution introduced in the event of photon loss. In the context of entanglement swapping, post-selection based on photon detection purifies errors of this type. This should be contrasted with the failure mode of DLCZ-type protocols, in which losses can admix higher photon number contributions that are not corrected by heralding. These embodiments will therefore be advantageous as a component in quantum repeater architectures based on photon detection and linear optics and could form the basis of fast, controllable and robust photonic quantum information processors in the near-future.

Appendix

The storage and retrieval efficiencies are calculated by solving the semi-classical linearized Maxwell-Bloch equations for the system. The signal field, with amplitude A , propagates through an ensemble of Λ - level atoms in the presence of the write field, whose temporal profile is described by the time-dependent Rabi frequency Ω(Γ) . Provided that the detuning Δ is the dominant frequency in the problem, the optical polarization can be adiabatically eliminated, yielding an explicit expression for the spin wave amplitude B at the end of the storage interaction. The spin wave can be expressed as,

*_Μ(^ζ) = Γ /( ⁽ 2CV(l - iy(r))zj4_in (r)dr (SI)

where A_M- is the amplitude of the incident signal field to be stored, J₀ is a Bessel function, and the number C² = d/W / Δ² quantifies the Raman memory coupling, with d the resonant optical depth and γ the homogeneous linewidth of the excited state 12 . Here we introduced the dimensionless integrated Rabi frequency ω(τ) ⁼ ~ j |^(^r')| ² dr ' , and the normalized Stark-shifted Rabi frequency f(r) = Ce^iWm{T)'^AQ(T)/ w . The constant W , proportional to the control pulse energy, is defined so that ω{∞) = 1 , while the longitudinal coordinate z is normalized so that z = 1 represents the exit face of the ensemble.

The storage efficiency ?7_STORE = N_MEM / N_IN is the ratio of the number iV_mem = j^" _o|5_mem(z)|² dz of final spin wave excitations to the number Nm = ί _in (i")|² dr of incident signal photons. If upon retrieval

N_OUT = ί \A _T (TY dr photons are recovered from the memory, the total efficiency η _ο = N_OUT I N_M- can be computed using the formula

for the retrieved signal field. In general A_out is different to A_m- . Physically these differences originate in the dispersion associated with propagation through the ensemble, and the Stark shift due to the time varying control field. The visibility of interference between the incident and retrieved signals is therefore smaller than 1 , even for a perfectly coherent memory. If optimal storage and backward retrieval are possible, these distortions can, however, be eliminated.

Claims

1. A quantum memory comprising:

a storage medium, the storage medium having a ground state energy level, an excited state energy level and a storage state energy level;

a first radiation source arranged to generate a pulsed control field for reading and writing to the storage medium by stimulating off-resonant transitions between the storage state and the excited state;

a second radiation source arranged to generate a pulsed signal field containing a signal to be written to the storage medium, said second radiation source being arranged to stimulate off-resonant transitions between the ground state and the excited state; and

a third radiation source arranged to generate a pump field for stimulating transitions out of the storage state of the storage medium.

2. A memory as claimed in claim 1, wherein the first radiation source is a laser and/or the second radiation source is a laser and/or the third radiation source is a laser.

3. A memory as claimed in claim 1 or 2, wherein the control field and the signal field are derived from the same radiation source.

4. A memory as claimed in 3, wherein the control field and the signal field are derived from a titanium-sapphire laser.

5. A memory as claimed in any preceding claim, wherein the pump field is derived from a diode laser.

6. A memory as claimed in any preceding claim, wherein the control field and the signal field are arranged to propagate coaxially in the same direction through the storage medium.

7. A memory as claimed in claim 6, wherein the first and second radiation sources are arranged to generate the signal field and the control field with orthogonal polarizations.

8. A memory as claimed in claim 7, further comprising a polarizing beam splitter arranged to separate the control field and the signal field after they have passed through the storage medium.

9. A memory as claimed in claim 6, 7 or 8, wherein the pump field is arranged to propagate coaxially in the same direction as or coaxially in the opposite direction to the signal and control fields through the storage medium.

10. A memory as claimed in claims 8 and 9, wherein the polarizing beam splitter is arranged to combine the pump field with the control and signal fields in a counter- propagating manner so as to direct the pump field through the storage medium coaxially with the control and signal fields, but in the opposite direction.

11 A memory as claimed in any preceding claim, wherein the storage medium is placed inside a waveguide and wherein the control field, the signal field and the pump field are directed along the waveguide.

12. A memory as claimed in any preceding claim, wherein the storage medium has a lambda-level structure comprising the ground state energy level, the excited state energy level and the storage state energy level, wherein transitions between the ground state energy level and the storage state energy level are forbidden such that the storage state energy level has a long lifetime.

13. A memory as claimed in claim 12, wherein the frequency of the signal field corresponds to the transition from the ground state energy level to the excited state energy level, but detuned from resonance by a detuning amount and wherein the frequency of the control field corresponds to the transition from the storage state energy level to the excited state energy level, but detuned from resonance by substantially the same detuning amount.

14. A memory as claimed in claim 13, wherein the detuning amount corresponds to approximately twice the separation of the ground state and storage state energy levels.

15. A memory as claimed in claim 14, further comprising an etalon for separating the control field from the signal field after they have passed through the storage medium and wherein the detuning amount is equal to the free spectral range of the etalon.

16. A memory as claimed in claim 13, 14 or 15, wherein the detuning amount is between 10 and 20 GHz.

17. A memory as claimed in any preceding claim, wherein the storage medium comprises an atomic ensemble.

18. A memory as claimed in claim 17, wherein the storage medium comprises a hot vapour.

19. A memory as claimed in any preceding claim, wherein the storage medium comprises at least one cesium atom.

20. A memory as claimed in any of claims 12 to 18 and claim 19, wherein the

133

lambda level structure is based on the Cs D₂ line and wherein the ground state

2 2 energy level is the 6 Si_/2, F = 3 level, the excited state energy level is the 6 P_3/2 level and the storage state energy level is the 6 Si_/2, F = 4 level.

21. A memory as claimed in claim 19 or 20, wherein the storage medium comprises a cesium vapour comprising a plurality of cesium atoms and a buffer gas.

22. A memory as claimed in claim 18 and claim 19, 20 or 21, wherein the cesium gas temperature is in the range 55 to 70 degrees Celsius.

23. A memory as claimed in claim 22, wherein the vapour temperature is in the range 60 to 65 degrees Celsius.

24. A memory as claimed in claim 23, wherein the vapour temperature is approximately 62.5 degrees Celsius.

25. A memory as claimed in any of claims 18 to 24, wherein the hot vapour is confined in a cell of length less than 10 cm.

26. A memory as claimed in claim 25, wherein the hot vapour is confined in a cell of length greater than 5 cm.

27. A memory as claimed in claim 26, wherein the hot vapour is confined in a cell of length approximately 7 cm.

28. A memory as claimed in any preceding claim, wherein the control field comprises one or more pulses, each pulse having an energy between 5 nJ and 50 nJ.

29. A memory as claimed in any preceding claim, wherein the bandwidth of the control and signal fields is less than 3 GHz.

30. A memory as claimed in any preceding claim, wherein the pump field is continuous wave.

31. A memory as claimed in claim 30, wherein the pump field has a power of 500 microwatts to 10 milliwatts.

32. A quantum repeater comprising a memory as claimed in any preceding claim.

33. A quantum repeater as claimed in claim 32, wherein the memory is arranged to have a storage efficiency of 50%.

34. A method of storing a signal in a quantum memory,

the quantum memory comprising a storage medium, the storage medium having a ground state energy level, an excited state energy level and a storage state energy level;

the method comprising the steps of:

a first radiation source generating a pulsed control field for writing to the storage medium by stimulating off-resonant transitions between the storage state and the excited state;

a second radiation source generating a pulsed signal field containing the signal to be written to the storage medium, said second radiation source stimulating off-resonant transitions between the ground state and the excited state; and

a third radiation source generating a pump field for stimulating transitions out of the storage state of the storage medium.

35. A method of reading a signal from a quantum memory,

the method comprising the steps of:

a first radiation source generating a pulsed control field for reading from the storage medium by stimulating off-resonant transitions between the storage state and the excited state;