Storing single photons emitted by a quantum memory on a highly excited Rydberg state

Abstract

Strong interaction between two single photons is a long standing and important goal in quantum photonics. This would enable a new regime of nonlinear optics and unlock several applications in quantum information science, including photonic quantum gates and deterministic Bell-state measurements. In the context of quantum networks, it would be important to achieve interactions between single photons from independent photon pairs storable in quantum memories. So far, most experiments showing nonlinearities at the single-photon level have used weak classical input light. Here we demonstrate the storage and retrieval of a paired single photon emitted by an ensemble quantum memory in a strongly nonlinear medium based on highly excited Rydberg atoms. We show that nonclassical correlations between the two photons persist after retrieval from the Rydberg ensemble. Our result is an important step towards deterministic photon–photon interactions, and may enable deterministic Bell-state measurements with multimode quantum memories.

Introduction

Efficient photon–photon interactions require a highly nonlinear medium that strongly couples with a light field, a single-photon source compatible with the medium and the ability to coherently map the photon in and out of the nonlinear medium¹. In addition, for quantum repeaters applications for long-distance quantum communication, the single photon should be part of a correlated photon pair generated by a quantum memory (QM), which allows for synchronization along the communication line². Nonlinearity at the single-photon level has been demonstrated with a variety of systems, including single atoms and atomic ensembles^{3,4,5,6,7,8,9,10,11,12,13} as well as nonlinear crystals albeit with small efficiency¹⁴. However, the coupling of true single photons with a highly nonlinear medium has been demonstrated so far only with single atoms^11,12. These systems are inherently nonlinear but suffer from low light–matter coupling in free-space and therefore require experimentally challenging high-finesse cavities.

Using highly excited Rydberg states of atomic ensembles can be a simpler alternative. The atomic ensemble ensures a strong light–matter coupling and the dipole–dipole interactions between Rydberg states enable strong, tunable nonlinearities. For a sufficiently dense ensemble and at sufficiently high quantum number of the Rydberg state (n≥60), nonlinear response at the single-photon level has been already demonstrated^{15,16,17,18,19,20} and has been exploited to implement a number of operations with weak coherent states (WCSs)^21,22,23,24. Entanglement between a light field and a highly excited Rydberg state²⁵ has also been recently demonstrated.

While single-photon nonlinearities have been demonstrated with WCSs, efficient quantum information processing using this system requires two additional steps. First, a single-photon source that matches the frequency and the sub-MHz spectral bandwidth of the Rydberg excitation, and, second, the ability to store and retrieve the input single photon. The latter is of key importance for implementing high-fidelity photonic quantum operations using excited Rydberg states^23,26,27, and, in addition, it has been shown to be beneficial to enhance the nonlinear response of this kind of systems²⁸. While storage and retrieval of a single photon transmitted between remote atomic ensembles has been achieved in ground states^{29,30,31,32,33} or low-lying Rydberg states³⁴, storing it in a highly nonlinear Rydberg ensemble presents additional experimental challenges, such as high sensitivity to stray fields, stronger motional-induced dephasing due to the large wavelength mismatch between the single photon and the coupling laser, weak oscillator strength requiring higher intensity of the coupling beam, as well as strong focusing of the single-photon needed to achieve nonlinearity at low light power. These challenges make it more difficult to achieve the required signal-to-noise ratio (SNR) to preserve the quantum character of the stored and retrieved field.

Here we demonstrate storage and retrieval of a paired and synchronizable single photon in a highly nonlinear medium based on excited Rydberg atomic states of a cold atomic ensemble. This is realized by using a photon source based on a read-only cold atomic ensemble QM³⁵ with which we can generate pairs of non-classically correlated photons that fulfil the frequency and the narrow bandwidth requirement of the Rydberg medium. In the generation stage (site A in Fig. 1), after a successful heralding event a single photon is emitted at a programmable delay time t_A allowing for potential synchronization between different pair sources. The photon is then collected into an optical fibre and sent to a remote atomic ensemble (site B in Fig. 1) where it is stored as a collective Rydberg excitation and retrieved after a storage time t_B The storage and retrieval in high-lying Rydberg states is realized with sufficiently high SNR (>20) to enable the demonstration of highly non-classical correlations between the heralding photon and the highly excited Rydberg collective excitation, and preservation of the single-photon character of the retrieved field. Finally, we also demonstrate the highly nonlinear response of our medium with WCSs containing tens of photons. The last result is obtained in a cloud with moderate density and can be easily improved to reach single-photon nonlinearity via well-known atom trapping techniques. Combining a source of narrow-band correlated single photons with a highly nonlinear medium at high SNR, our system is a building block for future quantum networks with deterministic operations.

Figure 1: Experimental set-up with relevant atomic transitions and pulse sequence.

Following the numbering in the pulse sequence, in site A, we (1) send a series of write pulses (red solid arrow), (2) probabilistically detect a write photon (orange dashed line) by single-photon detector (SPD)) D1, (3) send an intense read pulse (orange solid arrow) after a storage time t_A generating deterministically (4) a read photon (red dashed line) that is sent to site B through a single-mode fibre (SMF). In site B, a counterpropagating, coupling beam (blue arrow) converts the read photon into a slowly propagating dark-state polariton. Here we (5) switch-off the coupling beam, storing the read photon and (6) switch it on again after a storage time t_B retrieving the photon that is detected by SPD D2. The coupling beam and the read photon are both focused by the same pair of aspheric lenses and are combined and separated by dichroic mirrors (DMs). Hanbury Brown–Twiss (HBT) set-up is shown in another box. The field to be analysed emerges from the SMF at position C₃, it is split by a 50:50 beam splitter (BS) and detected by two detectors, D3 and D4 afterwards. To analyse the photon statistic before and after storage in the Rydberg state, we connect the HBT set-up either at position C₁ or at C₂.

Results

Experimental set-up

A schematic of the experiment is shown in Fig. 1. In site A, we implement a photon-pair source with controllable delay, using a cold atomic QM based on the Duan–Lukin–Cirac–Zoller (DLCZ) scheme^35,36. We use a cold atomic ensemble of ⁸⁷Rb atoms. Atoms initially prepared in the ground state are illuminated with a series of weak coherent pulses at 780 nm (write pulses) red detuned by Δ=40 MHz with respect to the transition so that a write photon is probabilistically created via Raman scattering and detected by single-photon detector (SPD) D1. This heralds a single collective excitation in the state (Supplementary Note 1). The excitation can be deterministically readout after a controllable storage time t_A by means of a strong, counterpropagating read pulse on resonance with the transition. The read pulse creates a 350 ns-long (full width at half maximum, FWHM) read photon in a well-defined spatiotemporal mode resonant with the transition. The read photon is collected and sent through a 10 m single-mode fibre to site B, where a separate ensemble of cold ⁸⁷Rb atoms is prepared in the state . We estimate that the probability to obtain a single photon in front of ensemble B conditioned on the detection of a write photon (the heralding efficiency) is η_H=0.27. At site B, a coupling beam at 480 nm resonant with the , transition creates the condition for electromagnetically induced transparency (EIT)^37,38,39 (Supplementary Note 3; Supplementary Fig. 2), where and . This converts the read photon into a slow-propagating Rydberg dark-state polariton (see Supplementary Note 4). By adiabatically switching off the coupling beam, the read photon is stored as single collective Rydberg atomic excitation⁴⁰ and the state of the ensemble reads:

where N_B is the number of atoms in the interaction region, and k_p and k_c the wavevector of the single photon and coupling beam, respectively. The stored excitation is retrieved after a storage time t_B by switching the coupling beam back on and detected by a SPD D2 (Supplementary Fig. 3). The read photon waveform in ensemble A can be tailored by shaping the read pulse⁴¹ to maximize the SNR of the storage in site B. Notice that to match the frequency of the single photon emitted at site A, we have to employ at site B the instead of the most commonly used and stronger transition^{15,18,19,23,24}. This makes it more challenging to reach high storage efficiency of the single photon into the collective Rydberg state.

DLCZ QM

First, at fixed t_A∼1 μs, we characterize the DLCZ memory in site A as a source of high-quality synchronizable single photons when no storage in site B is performed, as shown in Fig. 2. The read single-photon quality is inferred by measuring its heralded anti-bunching parameter α=p(r₃, r₄|w)/p(r₃|w)p(r₄|w) via Hanbury Brown–Twiss (HBT) measurement before the 10 m single-mode fibre. We also measure the second-order, cross-correlation function =p₀(w, r₂)/p(w)p₀(r₂) of the paired write and read photons without loading the atoms in site B. Here p(w) (p(r_i)) is the probability to detect a write (read) photon by SPD D1 (Di, with i=2, 3, 4), while p(x, y) is the probability of coincident detection event x and y and p(x|y) is the conditional probability of event x conditioned on y. The subscript 0 indicates that no atoms are loaded in site B. At low p(w), a successful detection of a write photon projects the read mode into a high-quality single-photon state, with measured values as low as α=0.11±0.02 at p(w)=0.04%, shown in Fig. 2a. In the same condition strong non-classical correlations are found, being well above the classical bound of two for a state emitted by a DLCZ QM (assuming thermal statistics for the write and read fields, see Supplementary Note 1). At higher p(w), multiple excitations are created in the atomic ensemble and the classical bounds for α and for are recovered (Supplementary Note 1).

Figure 2: Anti-bunching parameter and cross-correlation function without storage in site B.

(a) Anti-bunching parameter α measured before site B and (b) cross-correlation function measured after site B without loading the atomic ensemble. Data are taken at t_A∼1 μs. For low p(w) high-quality heralded single photon in the read mode as well as non-classical correlations are created, beating the classical bounds (indicated by the dashed line). The solid lines are fits with a model described in Supplementary Note 2. The error bars are the propagated Poissonian error of the photon counting probabilities.

Storage in the Rydberg ensemble

We then store the emitted single photon in a collective high-lying Rydberg atomic excitation (Fig. 3a). Keeping a fixed t_A∼1 μs, we load the atoms in site B and we store the read photon as atomic coherence between states and by switching off the coupling beam while the photon is propagating through the ensemble. After a storage time t_B, we retrieve the stored excitation by switching the coupling beam back on. At t_B=500 ns, we achieve a storage and retrieval efficiency of η_B=3.4±0.4%, where η_B is defined as η_B=p(r₂|w)/p₀(r₂|w). We also measure =p(w, r₂)/p(w)p(r₂) after storage and retrieval (Fig. 3b). Our data show that for low p(w) demonstrating the persistence of non-classical correlations between the write photon and the collective Rydberg atomic excitation after storage. At t_B=500 ns, we explicitly violate the Cauchy–Schwarz (CS) inequality by three to four s.d.’s (Table 1), which states that a pair of classical light fields must satisfy (see ref. 36) , where and are the unheralded second-order autocorrelation functions of the write and read photon, for which a similar expression as for holds (Supplementary Note 1). For the same storage time, we also measured the anti-bunching parameter of the stored and retrieved read photon by a HBT measurement after site B and we found =1.2±0.2 at p(w)=3.98% and =0.0±0.35 at p(w)=0.59%, the latter confirming that the single-photon statistics are preserved after storage and retrieval (see Methods).

Figure 3: Single-photon storage sample and cross-correlation.

(a) Example of single-photon storage for t_A∼1 μs and p(w)=2.7%. Detected counts of single-photon detector D2 per trial and per temporal bin, conditioned on a detection of a write photon, as a function of the detection time t when no atoms are loaded in site B (red area), when the read photon is slowed by the presence of the coupling beam (that is, when the coupling beam is kept on, blue area) and when the read photon is stored and retrieved for t_B=500 ns (orange area). We attribute the dip at t∼0 μs observable in the slow light pulse to the fast switch-off of the trailing edge of the input read photon (see refs 44, 45)). The solid black line represents a leakage of the slowed read photon due to low optical depth of the ensemble in site B. The solid light blue line is a pictorial representation of the coupling beam power. The vertical dashed lines shows the 600 ns temporal window chosen for measuring p(w, r₂). In this example, the storage efficiency is η_B=3.4%. We refer the reader to Supplementary Note 5 and Supplementary Fig. 4 for a description of the cross-correlation function across the slowed-down pulse. (b) as a function of p(w) after storage and retrieval of the read photon for t_B=500 ns. The error bars represent the propagated Poissonian error of the photon counting probabilities. The solid line is a fit with a model given in Supplementary Note 2, from which we extract the intrinsic retrieval efficiency of the DLCZ source η_A=38.5%. Dashed horizontal line shows the classical bound =2.

Table 1 Reported value of the R parameter for the Cauchy–Schwarz inequality.

The memory capabilities of the Rydberg ensemble and of the DLCZ QM are studied in Fig. 4a) for p(w)=0.16±0.02%. First, we show p(r₂|w) and as a function of t_B (Fig. 4a,b) keeping a fixed t_A∼1 μs. p(r₂|w), along with , decreases when increasing the storage time, due to atomic motion and external residual fields that dephase the collective Rydberg state of equation (1). We also observe a oscillatory revival that we attribute to the hyperfine splitting ΔF of the Rydberg state resulting in a beating of p(r₂|w) with a period T=1/ΔF. The non-classical correlations between a photon and a stored Rydberg excitation are preserved up to around t_B∼6 μs. Fitting p(r₂|w) and with a model shown in Supplementary Notes 2 and 4, we extract the 1/e decay time of the storage efficiency, =3.3±0.3 μs as well as ΔF=170±16 kHz, the latter being compatible with the theoretical value of ΔF_theo=182.3 kHz.

Figure 4: Coincidence detection probability and cross-correlation functions.

Coincidence detection probability p(r₂|w) and as function of t_B for t_A∼1 μs (a,b) and as a function of t_A for t_B=500 ns (c,d). In a, the measured p(r₂|w) at t_B=500 ns corresponds to a storage and retrieval efficiency η_B=3.8±0.4%. The solid lines are a fit with the model described in the Supplementary Notes 2 and 4, from which we extract the 1/e decay times of p(r₂|w) being =3.3±0.3 μs and =24±2 μs for a,b, respectively. The error bars represent the propagated Poissonian error of the photon counting probabilities.

We also verify that we can generate the write and the read photon with long, controllable delay in site A, maintaining the non-classical correlation between them after storage and retrieval in site B. This result is shown in Fig. 4c,d where we change the read-out time t_B of the stored ground-state spin-wave while keeping a fixed t_B=500 ns. Here the ground-state storage ensures a storage time longer than in the Rydberg state. In this case, the 1/e decay time is =24±2 μs and we observe non-classical correlations between the write and the stored and retrieved read photon in site B up to t_A∼30 μs.

Nonlinear response of the Rydberg ensemble

Finally, we prove the highly nonlinear response of the Rydberg ensemble. This is demonstrated by storing for 4 μs WCSs with varying mean number of input photon N_in and measuring the mean number of photons in the retrieved pulse after storage N_out, in a way presented in ref. 28. For a linear medium, N_out=TN_in, where T is the storage efficiency, while here we show (Fig. 5) strong nonlinear dependence. Dipole–dipole interactions prevent many excitations to be stored and retrieved in the medium, which can therefore sustain no more than N_max photons. As a consequence N_out becomes ²². Our result shows (see Methods) N_max=68±8, although the nonlinear dependence of N_out with respect to N_in appears at a lower number of photons. It should be noted that this result is obtained with a standard magneto-optical trap with a moderate atomic density, and that this result shows a nonlinearity six times stronger than the one reported in ref. 28. As demonstrated in refs 15, 18, 19, increasing the density of atomic ensemble with known atomic trapping techniques will allow us to achieve nonlinearity at the single-photon level, as required for applications in quantum information science.

Figure 5: Nonlinear response of the Rydberg blockaded ensemble in site B.

We store weak coherent states with a varying mean number of photon N_in into the Rydberg state for a storage time t_A=4 μs and we measure the mean number of output photon N_out. We plot N_out normalized by the storage efficiency at low number of photons T as a function of N_in. Due to Rydberg induced photon blockade, the medium can stand a maximum of N_max=68±8. The solid line is a fit with the model described in the Supplementary Note 4. In this example, T=0.44±0.02%. The error bars are the propagated Poissonian error of the photon counting probabilities.

To summarize, we have demonstrated for the first time storage and retrieval of a paired single photon on a highly nonlinear medium based on an atomic ensemble. The nonlinearity relies on highly excited Rydberg states where the capability of successfully storing a single photon is of particular importance for implementing high-fidelity quantum gates. The source is based on an emissive QM with multimode capability⁴², which is particularly suitable for quantum networking applications. Connecting this type of source with a highly nonlinear medium represents a building block for quantum networks where the entanglement can be deterministically shared over long distance by deterministic BSMs.

Methods

DLCZ ensemble

In site A, the measured optical depth is OD∼5 on the transition. A bias magnetic field B=110 mG along the read and write photon direction defines the quantization axes. Write and read pulses are opposite circularly polarized σ− and σ₊, respectively. The write pulses have a Gaussian temporal shape of duration FWHM∼20 ns. The power and the temporal shape of the read pulses have been tailored to optimize the SNR of the stored and retrieved read photon which results in a Gaussian shape of FWHM∼350 ns. The angle between the write/read pulses and the write/read photon is θ=3.4°. From θ and from the Gaussian decay time extracted from the fit shown in Fig. 4c,d, we calculate an atomic temperature of T_A=77 μK (Supplementary Note 1). An optical cavity of finesse F=200 resonant with the write photons is used in front of detector D1 as a frequency filter in combination with a polarizing beam splitter, a quarter-wave plate and a half-wave plate that serve as polarization filtering.

Rydberg ensemble

In site B, the measured OD on the is OD∼5.5. The Rabi frequency of the coupling beam is Ω_c=2.66±0.06 MHz, which results in a width of the EIT line of FWHM∼0.7 MHz. The magnetic field is nulled via microwave spectroscopy. The read photon and the coupling beam are focused to waists radii , respectively. From the Gaussian decay , we extracted an atomic temperature of T_B=38±6 μK (Supplementary Note 4). The overall detection efficiency including fibre coupling losses and efficiency of the SPD D2 is η_det=15.2%

Measurement of coincidences

To measure coincidences, we use a temporal window of 600 ns around the stored and retrieved read photon and a temporal window of 60 ns around the detected write photon. The measured value of the anti-bunching parameter after t_B=500 ns, =0.00±0.35, at p(w)=0.59% corresponds to zero counts in the coincidence windows after 19 h of data acquisition.

Single-photon Rydberg memory linewidth

The single-photon Rydberg memory linewidth is set by the width of the EIT line in combination with the single-photon bandwidth. In Supplementary Fig. 5, we show p(r₂|w) after storage and retrieval of the read photon for t_B=500 ns in the Rydberg state , as a function of the coupling beam detuning δ_c with respect to the transition . We fit the result with a Gaussian function and we extract a width of FWHM=2.38±0.09 MHz, which is the convolution of the EIT linewidth and the read photon spectral width. From the measured EIT linewidth (FWHM_EIT=730 kHz), we find a read photon spectral width of . This proves that the heralded read photon can be generated in a DLCZ scheme with sub-natural linewidth in a given temporal mode, as demonstrated in ref. 41. Still, the spectral width of the read photon is slightly larger than the Fourier transform of its duration. We attribute this discrepancy to the long-term laser drift.

Characterization of the nonlinearity

Data for Fig. 5 are taken with an increased Rabi frequency of the coupling Ω_c=4.7±0.1 MHz, which results in a width of the EIT window of FWHM=1.3±0.04 MHz. Still the storage efficiency at low photon number T decreased with respect to data in Fig. 4. We attribute this decrease to an external stray electric field that fluctuates during time.

Measurement of the cross-correlation function

As shown in Supplementary Fig. 1, we build a start-stop histogram where the start is a write photon detection and the stop is a read photon detection and we measure the number coincidence detection events in the SPDs D1 and D2, C_D1,D2. We then compare C_D1,D2 with the coincidences due to accidental uncorrelated detections, . To measure C_D1,D2, we count the coincidences in a 60 ns-long temporal window in D1 and in a 600 ns-long temporal window in D2. The two detection windows are temporally separated by a time t_A+t_B, to take into account the storage time in the two ensembles. is measured by counting the coincidences between a fist write photon and a read photon detection coming from a successive uncorrelated trial. We then measure the cross-correlation via:

where is the average number of coincidences in the extra trials, that is, second to seventh peak in Supplementary Fig. 1.

Data availability

The data appearing in Figs 2, 3b and 4 are available in Zenodo with the identifier doi:10.5281/zenodo.165760⁴³. Other data may be available upon reasonable request.