Deterministic generation and partial retrieval of a spin-wave excitation in an atomic ensemble

In this paper, we report a generation of a spin-wave excitation (SWE) with a near-unity () probability in a given time (~730). Such deterministic generation relies on a feedback scheme with a millisecond quantum memory. The millisecond memory is achieved by maximizing the wavelength of the spin wave and storing the SWE as the magnetic-field-insensitive transition. We then demonstrate partial retrievals of the spin wave by applying a first read pulse whose area is smaller than the value of . The remained SWE is fully retrieved by a second pulse. Anti-correlation function between the detections in the first and second readouts has been measured, which shows that the partial-retrieval operation on the SWE is in the quantum regime. The presented experiment represents an important step towards the realization of the improved DLCZ quantum repeater protocol proposed in Phys. Rev. A 77, 062301 (2008).


Introduction
The distribution of entanglement states over long distances is crucial for quantum communication and large-scale quantum networks [1,2]. However, due to unavoidable transmission losses in quantum channels and the no-cloning theorem for quantum states, such distribution task is still a challenge. One possible solution is the use of quantum repeaters (QRs) [3]. The basic ideal of the QR protocol is dividing the long distance L into N shorter elementary links. Entanglement generation attempt is independently performed in each link. Quantum memories are required for storing the created entanglement in a link until entanglement has been established in the adjacent links. By entanglement swapping between the adjacent links, entanglement will be ultimately extended to the full distance [3].
The Duan-Lukin-Cirac-Zoller (DLCZ) protocol [4] ， which is using atomic-ensemble-based quantum memory, is attractive because it is relatively simple [2].The DLCZ scheme relies on spontaneous Raman scattering [2,4], which can probabilistically create a pair of correlated excitations, namely, one spin-wave excitation (SWE) and a single photon. The spin-wave excitation can be stored in an atomic ensemble and the photon can be sent to a center station between two remote atomic ensembles. Based on the detection of a photon which could come from either of the two remote atomic ensembles, the entanglement between the remote memories can be established. Along with the DLCZ scheme, many experiments have demonstrated the generation of the pair of correlated excitations via spontaneous Raman scattering (SRS) [5][6][7][8][9][10][11][12][13][14]. The lifetime and retrieve efficiency of the quantum memories have been significantly improved. For example, the retrieval efficiency and lifetime of storing a single spin wave in laser-cooled Rb 87 atoms could up to 76% and 3ms [10]. However, the DLCZ protocol has some practical drawbacks. On the one hand, the entanglement generation via single-photon detections requires long-distance phase stability, which is a technique challenge [2]. On the other hand, in order to suppress multi-excitations, the probabilities of preparing the spin-wave-photon quantum correlation or entanglement have to keep very low [2,15], which lead to a very low quantum repeater rate [15]. To overcome these drawbacks, several improved DLCZ QR protocols have been proposed [15][16][17][18][19]. The proposed protocol in [15], N. Sangouard et al shows that the local creation of high-fidelity entangled pairs of spin-wave excitations (SWEs) in combination with the use of two-photon detections for remote entanglement generation, holds promise to implement much robust and efficient quantum repeaters. In this improved protocol, the local entanglement creation relies on partial read-out operations on four DLCZ-like quantum memories. The procedure of this creation may be explained in the following. Via the detection of a single Stokes photon emitting from one atomic ensemble, one may herald the storage of one spin-wave excitation in the atomic ensemble. After the four ensembles are charged, the spin-wave excitations are simultaneously partially readout, creating a probability amplitude to emit an anti-Stokes photon. Based on a coincident detection of two anti-Stokes photons at a polarizer beam splitter, the atomic ensembles will be projected into an entangled state [15]. The key requirement in such local entanglement creation is that the SWE memory in each ensemble can be deterministically created within a given time and then be partially readout at a predetermined time. The deterministic creation of one SWE has been demonstrated in several previous experiments [12][13][14]. Limiting to the storage lifetime of 20 30μs  , the creation probabilities of the SWE are in a range of~10-30% in these experiments, which still remain an improvement. In a recent experiment, Li, J. et al. demonstrated deterministic generation of single SWEs via Rydberg blockade in atoms [20]. However, due to experimental imperfections, such as spatial intensity inhomogeneity of the manipulation laser beams and fluctuation of atom numbers, the preparation probability for single excitation is about 55%. The partially read out of single Rydber SWEs [21] and ground-state SWEs [22] have been experimentally demonstrated, respectively. However, the autocorrelation function between two partially readouts of a single SWE has not been experimentally demonstrated yet.
Here, we achieve a millisecond quantum memory by maximizing the spin-wave wavelength and selecting a magnetic-field-insensitive transition to store the spin wave (SW) [7]. Based on the long-lived quantum storage and detection-based feedback scheme, we generate one spin-wave excitation (SWE) with a near-unity probability within a given time of 730 μs . By applying a read pulse whose area is less than π , we demonstrate partial read out of the SWE. The remained SWE is fully retrieved by a second read pulse. The anti-correlation function between the first and second readouts is measured when the retrieval efficiencies for two retrievals are the same. The measurement result shows that the readout operations on the SWE are in single-quanta regime. The experimental setup is shown in Fig. 1(a). The atomic ensemble is a cloud of cold 87 Rb atoms, whose relevant atomic levels are shown in Fig. 1 [23] and then direct to a single-photon detector labeled by S D . Before the detector S D , we use a polarization beam splitter (PBS) to block the V-polarized Stokes photons into the detector S D . Thus, only the H-polarized photons may arrive in the detector S D . In this case, the detection of a photon at the detector S D heralds the storage of one magnetic-field-insensitive SWE. For suppressing the dephasing effect resulting from atomic motions, we make the Stokes field and writing light beams collinearly go through the cold-atom cloud along the z-direction [see Fig. 1(a)]. The uses of magnetic-field-insensitive SW and the collinear propagations promise us to achieve a long-lived SWE storage. The SWE can be efficiently converted into an anti-Stokes photon by applying a reading laser pulse with its frequency being tuned to the transition

Experimental setup and analysis
The reading laser pulses, labeled by R, propagate along the z-axis, which has the wave-vector of R W k k   . According to the phase matching condition, the wave-vector of the retrieved anti-Stokes photon is +

Experimental results
For showing the lifetime of the storage of the SWE as well as the quantum correlation between the Stokes photon and the SWE in our memory system, we measure the retrieve efficiency and the cross-correlation function between Stokes and anti-Stokes fields as the function of the storage time t. The time sequence for the measurement is shown in Fig. 1(c), where, the experimental run, which includes n trails is performed after the atoms are loaded to a magneto-optical trap (MOT). Each trail contains a cleaning pulse, a write pulse and a read pulse. The cleaning pulse is used to prepare (or pump) the atoms to (or back to) the state , 1 F a m  . The cleaning laser includes three pumping laser beams, which are labeled by C1, C2 and C3 in the Fig. 1(a). The σ  -polarized C1 laser beam and σ  -polarized C2 laser beam, whose frequencies are tuned on the transitions, respectively, are combined on a polarization-beam-splitter (PBS) and then go through the atoms at an angle of about 3 relative to the z-axis. The σ  -polarized C3 laser beam, whose frequency is tuned to the 1 a e  transition, goes the atoms at an angle of about 3   relative to the z-axis.
The three laser beams C1, C2 and C3 overlap at the center of the atoms. In the measurement, the stored SWE is fully retrieved and converted into an anti-Stokes photon by a read pulse with a duration of 50 δt ns  and a power of 0 300 P μW  after a storage time t. The read pulse area for such a case is π . The cross-correlation function is defined as (2) , the equation (2) may be rewritten as (2) , and zero-delay retrieval efficiency 0 17.5% γ  . From the Fig. 2(b), we can see that (2) , AS S g is well above 2 at 2 t ms  , meaning that the SWE and the Stokes photon are non-classically correlated [2] at this time.
The detection of a Stokes photon at S D will herald the creation of one magnetic-field -insensitive SWE, which is denoted by † 0 0 s , where † 0 s ( 0 ) refers to the creation operator of the SWE (vacuum state). For performing the scheme in [15], N. Sangouard et al, the SWE is required to be partially readout, which may be done by using the read pulse whose area is smaller than π . We may demonstrate the partial readout by using the read pulse whose duration is kept unchanged ( 50 δt ns  ) and power is set to be less the fully-read-out value 0 300 P μW  . Assuming that such a read pulse, denoted by 1 R (first read pulse), is applied onto the atoms after the storage time t1, it will convert the SWE † 0 0 s into an anti-Stokes photon in the time bin 1 AS , with a partial retrieval efficiency   To demonstrate that our partial readout operate in the single-quanta regime, we measure the second order correlation functions between the detections at the time 1 t and 2 t , which is defined as AS . The above second order correlation function is the anti-correlation parameter of anti-Stokes photons, whose value 0 α  corresponds to an ideal single photon and 1 α  corresponds to classical light. The time sequence for the measurement of α is shown in Fig. 1(d), the write sequences, each of which contains a cleaning pulse and a write pulse, are applied to the atoms to generate the SWE. As soon as the detector S D detect a photon, the storage one SWE is heralded and the followed write sequences are terminal. After a storage time of t , i.e., at the time 1 t t  , the read pulse 1 R with an area of 2 π is applied to partially retrieve the SWE. At the time of 2 t t t   V with 1 t μs  V , the read pulse 2 R is applied to fully retrieve the remained SW. The measurement results of α as a function of the storage time t for 1 t μs  V and 3% χ  are shown in Fig. 4. From the Fig. 4, we can see that the measured α values are well below the classical bound of , which implies that the quantum nature of the SWE may be conserved for~1.3ms. The probability of generating one SWE per write-pulse is equal to that of detecting a Stokes photon, which is 0.006 S S p χη   in the above measurement. For the proposed scheme [15], the SW excitation is required to be able to be deterministically generated in a given time. To do this task, one may apply the measurement-based feedback protocol [13,14]. The time sequence for the feedback protocol is shown in Fig. 1(e), where, a series of write sequences, each of which has a period of 1.6 w δt μs  , applied to the atoms. Each write sequence contains a cleaning pulse and a write pulse. Once a Stokes photon is detected by S D at a write sequence, for example, at j-th write sequence, a field programmable gate array (FPGA), which is used for registering the detection event, will send out a feedback signal and then the further write sequence is stopped. At the predetermined time T [see Fig. 1  , we apply the first read pulse with an area of 2 π and then apply the second read pulse with an area of π at 2 t [see Fig. 1(e)]. We then measure the anti-correlation parameter α between the two readouts as a function of the time separation ( 2 1 t t t   V ) and show the measurement results in Fig. 6. All the measured values are well below the classical bound of 1 α  , which implies that the quantum nature of the SW generated by the feed-back protocol may be preserved for more than 1 millisecond. We then measure the anti-correlation parameter α between two readouts of a single SWE as a function of the write-sequence number N for 3% χ  , the result is shown in Fig. 7. In the measurements, the two readouts are achieved by applying two read pulse, where, the first one has an area of 2 π and is applied at time 1 w t T N t    and the second one has an area of π and is applied at time 2 1 t T μs   [see Fig. 1(e)]. The separation time between the two readouts is 2 1 1 t t t μs    V . In Fig. 7, 450 N  corresponds to the case that the SWE is generated with the probability of 0.996 0.003  at predetermined time of 730 T s   .
At this point, the measured autocorrelation α value is 0.35 0.09  . Such a measured α value is significantly below the classical bound, showing single-excitation character of the spin wave.

Conclusion
Based on the millisecond quantum memory and the feedback scheme, we generate one SWE with a near-unity ( 0.996 0.003  ) probability during a given time of 730 T μs  . By applying a read pulse with power less than fully-retrieval value, we partially read out the SWE. Then the remained SW is fully read out by another read pulse after a storage time. The anti-correlation function between two readouts have been measured, which shows that the partial-retrieval operation on the SW is in the quantum regime. In the presented experiment, the required time for deterministically generating one SWE is several hundreds of microsecond, which is too long and will lead to a low quantum repeater rate. However, this is not a fundamental question. By decreasing the durations of write and cleaning pulses as well as the feedback delay time, the write-sequence period will be significantly shorten and then the required time will be greatly improved. In the presented experimental set up, some leakages of the laser beams which result from the imperfect switching off of the beams will lead to the light scattering in the atoms and then result in decoherence of the SWE. By improving the switching off, we may expect a further increase in the lifetime. The presented results represent a first step towards the realization of the improved DLCZ quantum repeater protocol [15].