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The ability to filter unwanted light signals is critical to the operation of quantum memories based on neutral atom ensembles. Here we demonstrate an efficient frequency filter which uses a vapor cell filled with 85Rb and a buffer gas to attenuate both residual laser light and noise photons by nearly two orders of magnitude with little loss to the single photons associated with our cold 87Rb quantum memory. This simple, passive filter provides an additional 18 dB attenuation of our pump laser and erroneous spontaneous emissions for every 1 dB loss of the single photon signal. We show that the addition of a frequency filter increases the non-classical correlations and the retrieval efficiency of our quantum memory by ≈ 35%.
© 2015 Optical Society of America
1. Introduction
Distribution of entangled quantum states over significant distances is important to the development of future quantum technologies such as long-distance cryptography, networks of atomic clocks, distributed quantum computing, etc. [1–5]. Quantum repeaters can overcome the problems of exponential losses in direct transmission of single photons over quantum channels through entanglement swapping of remotely placed quantum memories via single photon detection [6]. Long-lived quantum memories and single photon sources are building blocks for systems capable of efficiently and securely transferring quantum information over extremely long distances. Quantum memories are a very active area of research with many different quantum systems as viable candidates, including ions [7], neutral atom ensembles [8], Rydberg atoms [9–11], single neutral atoms [12], quantum dots [13], and nitrogen vacancy centers [14]. Cold ensembles of neutral atoms are a favorable platform for quantum memories and single photon sources as they can store single excitations in long-lived ground states that lead to extremely long coherence times [15, 16].
The ability to store and retrieve single excitations efficiently and background-free is crucial to building quantum memories based on neutral atom ensembles [17]. The generation (retrieval) of these excitations usually requires a strong laser beam to create a coherent excitation in the atomic ensemble that can be heralded (read out) by the detection of a single photon from the ensemble. The detection of classical pump photons at the single photon detector is a source of error in standard quantum communication protocols that needs to be eliminated. This strong pump can be filtered by a variety of means: spatial, polarization, frequency, etc. Spatial filtering is achieved using the off-axis geometry in a cold atomic ensemble pioneered in [18]. By aligning the single photon arms a few degrees off-axis from the pump arms, noise suppression > 40 dB is possible, usually limited by scattering off the surfaces near the memory. Polarization filtering is accomplished by post-selecting single photons that are orthogonally polarized to the corresponding pump fields using properly aligned waveplates and polarizing optical elements. Birefringence of optical elements and imperfect polarizers usually limit noise suppression to ~40 dB as well [19]. Optical cavities [12], optically pumped atomic vapor cells [15], and fiber Bragg gratings [20] are just a few examples of frequency selective elements that have been used in various quantum memory experiments to reject sources of noise. It is possible to achieve extremely high levels of noise rejection (> 100 dB) though usually at the cost of lower transmission probability (≈ 10%) [19]. Each of these frequency filters require complicated electronics, significant temperature stabilization, external references, or additional lasers.
In this paper, we show how the serendipitous near degeneracy of spectral lines in 85Rb and 87Rb allow one to construct an efficient frequency filter for both the classical pump beams and erroneous atomic decays in a neutral atom quantum memory, without strong filtering of the desired signal that herald the creation of these coherent excitations. To accomplish this we use the two naturally-occurring isotope of rubidium, 87Rb for use as a quantum memory and a vapor cell filled with isotopically-pure 85Rb to filter the pump photons associated with this process (Fig. 1). By properly choosing the correct transition in 87Rb for the creation of spin-waves, the frequency of the Write beam and Noise single photons are nearly resonant with a transition in 85Rb, while the single photons that are correlated to the created spin-waves are much further detuned from any transition in 85Rb. The Noise single photons arise from spontaneous decays back to the original ground state (5S1/2,F = 2). This method for filtering radiation is well known in the atomic clock community [21], and has been used in warm vapor quantum memory experiments previously [22–25]. Such a filter cell is attractive due to its relative simplicity, without the need for an optical reference to lock an external cavity, drifts from cavities or etalons, significant temperature stabilization, or additional lasers for optical pumping.
Fig. 1 The relevant energy levels and transitions of 87Rb and 85Rb used in this paper. The write beam is 20, 40, or 60 MHz blue-detuned from the 5S1/2,F = 2→5P1/2,F = 2 (D1) transition. Atoms excited to the 5P1/2,F = 2 state can decay to either the 5S1/2,F = 1 or the 5S1/2,F = 2 ground state in 87Rb. The write beam and the emission from the 5P1/2,F = 2 → 5S1/2,F = 2 state are detuned from the Doppler-broadened 5S1/2,F = 3 → 5P1/2 transition in 85Rb by ≈ 790 MHz. The emission from the 5P1/2,F = 2 → 5S1/2,F = 1 state is detuned from the Doppler-broadened 5S1/2,F = 2 → 5P1/2 transition in 85Rb by ≈ 3000 MHz. This difference in the detuning of these transitions serves as the basis for using a 85Rb vapor cell as a frequency filter in our quantum memory experiment. The read beam is resonant with the 5S1/2,F = 1 → 5P3/2,F = 2 (D2) transition in 87Rb. Drawing not to scale.
First, we build a simple model to predict the utility of such a filter under conditions that can be verified experimentally. Then, we perform an experiment where the filter is used to block spontaneously emitted photons not associated with the creation of spin-waves, which would contribute to a reduced retrieval efficiency. The result is a quantum memory with higher retrieval efficiency, hence higher single photon rates and greater nonclassical correlations.
2. Theory
To construct a frequency filter that is capable of attenuating the undesired background radiation it will be necessary to calculate the strength and the lineshape of the filter as a function of vapor cell temperature and buffer gas pressure. In the limit that the frequency of the input light is much more narrow-band (roughly the atomic linewidth Γ/2π ≈ 5.8 MHz) than the bandwidth of the frequency filter (≫ 100 MHz) [26],
where a(δ,T,P)is the attenuation per unit length that depends on the detuning from the nearest resonance line δ, temperature of the filter cell T, and buffer gas pressure P, while z is the length of the filter cell. The lineshape of the filter function may depend on both the inhomogeneous broadening due to the Doppler effect of atoms at a temperature T with a characteristic FWHM of δvD(T) and the homogeneous broadening due to collisions with a buffer gas at pressure P with a characteristic FWHM of γ(P). The vapor cell filter is considered in two limits: when Doppler effects dominate and when atomic collisions dominate.In the Doppler-broadened case:
where f (T) is proportional to the vapor cell atom number and increases exponentially with cell temperature [27], δvD(T) is the Doppler-broadened FWHM of the 85Rb lines, and δi is either the Noise or Signal frequency detuning from the nearest 85Rb resonance shown in Fig. 1(a).One would like a simple/passive frequency filter for strong attenuation of unwanted background radiation with weak attenuation of the signal photons associated with the created spin waves. Figure 2(a) shows that an optically thick vapor cell of pure 85Rb with no buffer gas would accomplish this due to the exponential falloff of the filter strength as a function of δ2 and the detuning of the light associated with the desired transition is roughly four times further detuned than the light associated with the undesired transition (790 MHz vs 3000 MHz). However, contamination of the cell with a small amount of near-resonant 87Rb can have a significant effect on the attenuation of the Signal photons. If the ratio of 87Rb/85Rb is on the order of a few times 10−3 (which is roughly the level of purification available commercially) this will result in roughly equal attenuation of the Noise photons by 85Rb and Signal photons by 87Rb, negating the utility of the frequency filter in Fig. 2(b). It is therefore prudent to consider the frequency filter in the presence of a buffer gas to see if the effect of 87Rb can be mitigated.
Fig. 2 Plots of the transmitted light through the vapor cell filter as a function of temperature in the Doppler-broadened limit (Eq. (2)) for a filter cell length of 1 inch. (a) The pure 85Rb filter cell acts nearly perfectly by attenuating the undesired light strongly (blue, dotted) and no attenuation of the signal (magenta, dashed) leading to large difference in attenuation between the two signals (gold, solid). (b) Small concentrations of 87Rb (87Rb/85Rb fraction of 0.2%) result in strong attenuation of the resonant background and signal fields. The emission from the cold 87Rb ensemble is assumed to be hyperfine specific but the absorption by the warm 85Rb vapor cell transitions are assumed to be Doppler-broadened and not hyperfine specific (See Fig. 1).
In the pressure-broadened case [26]:
where β is the coefficient for the linear frequency shift with a value of −6.7 MHz/Torr and α is the linear coefficient for the pressure-broadened linewidth with a value of 21 MHz/Torr at T = 300 K for the D1 transition due to collisions of Rb with an Argon buffer gas. Since we will only vary the temperature of the vapor cell by ~ 10% it will be a good approximation to say that these pressure-dependent coefficients are constant as a function of temperature. Figure 3 is a plot of Eq. (1) with a(T,P) from Eq. (3) which shows how the introduction of 47 Torr of an Ar buffer gas changes the filter response as a function of vapor cell temperature. The Ar pressure of 47 Torr was chosen such that the filter could be modeled in the pressure-broadened limit (αP > δνD) where the filter is most effective. Increasing the buffer gas pressure significantly would dilute the filter strength by broadening the filter response function.Fig. 3 Normalized measured transmission of classical laser light at the Noise (circles) and Signal (squares) frequencies and the difference between the two signals (diamonds) at a variety of vapor cell temperatures with 47 Torr of Ar in a 1 inch long 85Rb vapor cell. The corresponding solid lines are calculations of the transmitted light through the vapor cell filter as a function of temperature with 47 Torr of Ar using the filter response from Eq. (3).
Signal absorption decreases from the Doppler-broadened filter (Fig. 2(b)) to the pressure-broadened filter (Fig. 3) due to the differences between the Gaussian and Lorentzian line-shapes of their absorption profiles respectively. The Signal is absorbed strongly in the Doppler-broadened filter due to the strong central peak of the Gaussian-shaped absorption profile of the near-resonant 87Rb present in the vapor cell filter. Whereas, the Lorentzian lineshape of the pressure-broadened vapor cell contains significantly more absorption in the wings of its profile and less near resonance thus leading to less Signal absorption in the presence of a buffer gas. For Noise photons, the weakening of the 87Rb component in the pressure-broadened filter is counterbalanced by an increase of filter strength of the far-detuned 85Rb component as one transitions from a Gaussian absorption profile to a Lorentzian absorption profile. The result is a frequency filter that absorbs Noise photons more strongly than Signal photons. From Fig. 3 one can extract an 18 dB attenuation from the Noise for every 1 dB attenuation of the Signal over the range of filter cell temperatures measured. Disagreements between data and theory at higher filter cell temperatures may be explained by either violations of assumptions made in our simple model (such as temperature independent γ(P)) or greater 87Rb contamination in the vapor cell than the specification from the manufacturer (87Rb/85Rb ≈ 0.2%)
The optimum operating temperature for the vapor cell filter should correspond to roughly the maximum difference between the Signal and Noise if one assumes roughly equal contributions of Signal and Noise before the frequency filter. This strikes a balance between increasing the Retrieval Efficiency and g(2) correlations (strong attenuation of Noise) while maximizing the coincident count rate (weak attenuation of Signal). With a buffer gas of sufficient pressure and high enough operating temperature it is possible to achieve significant attenuation of the background light with only a small amount of signal loss.
3. Experimental results and methods
3.1. Neutral atom quantum memory
A magneto-optical trap (MOT) of 87Rb atoms produces an optically thick atomic ensemble for our experiment (Fig. 4(a)). Approximately 25 mW/cm2 of cooling light, detuned 15 MHz below the 5S1/2,F = 2 → 5P3/2,F = 3 transition in 87Rb, and 5 mW of repump light, on resonance with the 5S1/2,F = 1 → 5P3/2,F = 2 transition, are delivered collinearly to the vacuum system. Loading from a room-temperature Rb vapor, a cloud of ~ 1.8 × 108 atoms at a temperature of ~100 μK is produced in roughly 5 seconds with a magnetic field gradient of 10 G/cm (subsequent reloading of the MOT is performed in 30 ms as seen in Fig. 4(b)). This is then followed by a compressed MOT stage that consists of simultaneously lowering the intensity of the repump and increasing the gradient of the quadrupole magnetic field to 22 G/cm for 6 ms before turning the field off. The cooling light is turned off 100 μs later, and the repump light 2 μs after that, leaving all of the atoms in the 5S1/2,F = 2 ground state.
Fig. 4 (a) Counter-propagating Write and Read light pulses interact with a cold 87Rb ensemble while emitted single photons are detected off-axis by Si APDs. Arrival times of the photons are measured by a time-interval analyzer (TIA). Emitted Write photons are filtered by a warm 85Rb vapor cell to attenuate Noise photons. (b) A MOT is loaded and compressed to create a cold, dense cloud at a rate of 27 Hz. The MOT magnetic and laser fields are then extinguished for a 1 ms duration and a series of 600 Read-Write pulses interact with the system. (c) Log-Log plot of as a function of pA with filter cell at 336 K and Δw/2π = 20 MHz. Write probability (pA) is varied from 10−2 − 10−4 and the corresponding values of increase from ≈ 8 to > 160.
A sequence of 1000 trials with individual durations of ~ 1 μs is performed as follows: a weak, linearly-polarized, Write pulse, tuned 20, 40, or 60 MHz above the 5S1/2,F = 2 → 5P1/2,F = 2 (See Fig. 1) transition is shone on the atomic ensemble. The Write pulse has a 400 μm waist and 50 ns duration set by acousto-optical modulator and an electro-optic modulator. For low enough excitation probability (10−2 − 10−4) a photon detection within an 80 ns time interval at Si avalanche photodiode (APD) A heralds the transfer of one 87Rb atom in the ensemble from the F = 2 ground state to the F = 1 ground state in a particular spatial mode. The polarization of the generated single photon is post-selected to be orthogonal to the Write pulse with appropriate waveplates and linear polarizers. After a hold time of 200 ns, a strong, linearly-polarized (orthogonal to the Write), resonant Read pulse of duration 300 ns and 400 μm waist interacts with the ensemble, producing a photon that is detected by APD B within a 100 ns window. The generated photon has a polarization orthogonal to the Read pulse. The single photon detection arms are aligned at an angle of 3° relative to the classical pump beams. By aligning the single photon arms a few degrees off-axis from the pump arms, the pump light is suppressed by a measured value of ≈ 40 dB in the single photon detection arms. The APD signals are sent to a time-interval analyzer (TIA) for data collection and analysis.
The strength of the correlations between the photon-pairs generated by the atomic ensemble can be measured by the normalized intensity cross-correlation function:
where pAB is the probability to detect a photon pair, pi is the probability for an event click at detector i, and RE is the retrieval efficiency defined as pAB/pA. A plot of over a range of different write probabilities, pA, is shown in Fig. 4(c). Figure 4(c) shows a series of measurement of over a range of values for pA (10−2 − 10−4) with Δw/2π = 20 MHz and a constant filter cell temperature of 336 K. The value of saturates at low pA due to dark counts in the APDs and contamination of the readout arm by classical Read light. The transmission values for the Noise and Signal photons in Fig. 3 at a filter cell temperature of 336 K are 12% and 88% respectively. The filter cell attenuates the Noise photons significantly which increases the measured F and for a given pA while not significantly attenuating the Signal photons. Attenuation of the Signal photons would lead directly to a decrease in the coincidence probability, pAB, an undesirable outcome for entanglement creation and entanglement swapping operations.3.2. Filtering single photon noise
In this section we study the effect of a 85Rb filter on the operation of a cold 87Rb quantum memory. This was done by varying the temperature of AR-coated vapor cell filled with isotopically-pure 85Rb and 47 Torr of Argon from 298 K to 336 K. Based upon Fig. 3 we would expect the presence of 85Rb vapor cell filter to have only a small effect on the quantum memory parameters (pA, F, ) at an operating temperature of 298 K. At this temperature the filter cell absorbs only 10% of the Noise photons and less than 1% of the Signal photons. However, as the filter cell temperature is increased, an increasing percentage of Noise photons (pump and emitted) are filtered by the cell with corresponding decreases in pA and increases in F and . Figure 5(a) shows the decrease in write probability as a function of filter cell temperature. For Δw/2π = 20 MHz the Write probability decreases from a value of 6.5 × 10−4 to 5 × 10−4 as the filter cell temperature is increased from 298 K to 336 K. For Write detunings of 40 MHz and 60 MHz the Write probability decreases from 7×10−4 to 5×10−4 over the same temperature range. Most of this decrease can be attributed to the vapor cell filter absorption of Noise photons emitted by the cold ensemble taking into account the results of Fig. 3. At a filter cell temperature of 336 K only 6% of Noise photons are transmitted through the vapor cell while > 85% of Signal photons are transmitted. The vapor cell also filters out pump photons from the Write beam that scatter off of the vacuum system glass walls. However the effect on the quantum memory parameters is minimal because the pump contamination in the Write detection arm is only ~ 1 × 10−5. Since the filter cell has little effect on the coincident counts between detectors A and B, there is then a corresponding increase of ≈ 35% in the measured Retrieval Efficiency as seen in Fig. 5(b) for Δw/2π = 40 and 60 MHz and ≈ 15% for Δw/2π = 20 MHz. Retrieval Efficiency increases from 6% to 7% for a Write detuning of 20 MHz, from 5.8% to 7.5% for a Write detuning of 40 MHz, and 5.5% to 7% for a Write detuning of 60 MHz.
Fig. 5 Probability of detecting a write photon and Retrieval Efficiency as a function of the filter cell temperature for Δw/2π =20, 40, and 60 MHz. (a) The write probability decreases by ≈ 40% over the range of filter cell temperatures used in this experiment for each write beam detuning. (b) A significant increase in Retrieval Efficiency as the filter cell temperature is increased is observed. The decrease in Noise photon detection in the Write arm leads to an ≈ 35% increase in the Retrieval Efficiency for Δw/2π = 40 and 60 MHz and 15% for Δw/2π = 20 MHz. Each point in plots (a) and (b) correspond to ~ 10000 write detection events and ~ 500 coincident counts respectively. The running time required to obtain a single data point is ≈ 12 minutes. Error bars are calculated assuming Poissonian statistics.
Any change in the Retrieval Efficiency due to the vapor cell filter necessarily should lead to a change in as the filter cell has no effect on pB. Following the increases in F seen in Fig. 5(b), a similar ≈ 35% increase in the value of for Δw/2π = 40 and 60 MHz is seen in Fig. 6 as the absolute values of increase from 95 to 130 and 100 to 135 respectively. For Δw/2π = 20 MHz a smaller increase in of ≈ 15% (from 95 to 110) corresponds closely to the similar increase of F seen in Fig. 5(b) as well.
Fig. 6 correlations as a function of filter cell temperature for Δw/2π =20, 40 and 60 MHz. The strength of the correlations increase by ≈ 15% for Δw/2π = 20 MHz, ≈ 35% for Δw/2π = 40 MHz, and ≈ 35% for Δ/2π = 40 MHz. The increase in non-classical correlations follows directly from the increase in Retrieval Efficiency seen in Fig. 5. Error bars are calculated assuming Poissonian statistics.
The difference in the performance of the vapor cell filter for the three write detunings can be partially explained by effective optical depth of the atomic ensemble at different Write beam detunings. Based upon Δw/2π = 20 MHz (3.3Γ) and a measured ODres = 12 for the atomic ensemble, one would expect an effective optical depth of the cloud for the created photons to be OD3.3Γ ≈ 0.24 from the equation: ODΔ = ODres(1 + (2Δ/Γ)2)−1 [28]. However that assumes the emitted single photons interact with the entire ensemble. The probability for excitation is proportional to the atomic density which is largest in the center of the ensemble. As a consequence, the average single photon would only see half the atoms in the cloud. The resulting OD (≈ 0.12) leads to ≈ 11% attenuation of Noise single photons emitted by the ensemble. For the dataset with Δw/2π = 40 (60) MHz there is only 3% (1%) attenuation of Noise single photons due to the smaller effective optical depth from the larger detuning. Since there are slightly more Noise photons for the larger Write detuning, the vapor cell has a relatively larger effect on the write probability, retrieval efficiency, and non-classical correlations for Δw/2π = 40 and 60 MHz.
4. Conclusions
In this paper we have shown how a temperature-controlled vapor cell filled with isotopically-pure 85Rb filled with 47 Torr of Ar buffer gas increases the Retrieval Efficiency and the non-classical correlations between the single photons emitted from the cold 87Rb ensemble. The filter cell achieves a substantial reduction in the detection of Noise photons by frequency-selective absorption with little effect on the detection of Signal photons. Our model showed that a buffer gas in the vapor cell was required to eliminate the detrimental effect of the 87Rb contamination in commercially available isotopically-pure 85Rb vapor cells. Our experiments showed that for Write detunings of 40 and 60 MHz the measured Retrieval Efficiency and of our quantum memory increased by ≈ 35% as the filter cell temperature was tuned from 298 K to 336 K due to the significant decrease in the detection of Noise photons. Less dramatic effects were seen for a Write detuning of 20 MHz which were partially explained by the detuning-dependent optical depth of the cold atomic ensemble. These results are important to maximizing the operating parameters that are critical to the realization of a quantum network based on neutral atom quantum memories.
Acknowledgments
We would like thank N. Solmeyer, D. Matsukevich, and A. Gorshkov for discussions on the quantum memory and P. Kunz for discussions on the vapor cell. DS is an Oak Ridge Associated Universities (ORAU) postdoctoral fellow. Research was sponsored by the Army Research Laboratory. The views and conclusions contained in this document are those of the Authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
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