Quantum memory with strong and controllable Rydberg-level interactions

Abstract

Realization of distributed quantum systems requires fast generation and long-term storage of quantum states. Ground atomic states enable memories with storage times in the range of a minute, however their relatively weak interactions do not allow fast creation of non-classical collective states. Rydberg atomic systems feature fast preparation of singly excited collective states and their efficient mapping into light, but storage times in these approaches have not yet exceeded a few microseconds. Here we demonstrate a system that combines fast quantum state generation and long-term storage. An initially prepared coherent state of an atomic memory is transformed into a non-classical collective atomic state by Rydberg-level interactions in less than a microsecond. By sheltering the quantum state in the ground atomic levels, the storage time is increased by almost two orders of magnitude. This advance opens a door to a number of quantum protocols for scalable generation and distribution of entanglement.

Introduction

Atomic systems involving highly excited Rydberg states are an attractive system for the continuing quest to realize large-scale quantum networks^1,2,3,4,5,6. An ultra-cold atomic ensemble in a quantum superposition of a ground and a Rydberg state features both rapid and deterministic preparation of quantum states and their efficient transfer into single-photon light fields^7,8. Notable achievements include the demonstration of deterministic Rydberg single-photon sources^9,10, atom-photon entanglement¹¹, many-body Rabi oscillations^12,13,14,15, photon anti-bunching and interaction-induced phase shifts^16,17 and single-photon switches^18,19,20. In parallel to these efforts, significant advances have been made in employing Rydberg interactions for entanglement of pairs of neutral atoms^21,22,23 and many-body interferometry²⁴.

All these experimental demonstrations relied critically on the strong interactions between Rydberg atoms. The interactions prevent more than one atom from being excited into a Rydberg state within a volume called the blockade sphere, if excitation into the Rydberg state is slow⁷. In the opposite limit of fast excitation to the Rydberg state, the interactions between the atoms act by dephasing the collective multi-atom states, thereby removing quantum state components with more than one excited atom from the observed Hilbert subspace²⁵. Both Rydberg blockade and dephasing mechanisms contribute to the sub-Poissonian statistics of the output light fields in experiments of refs 9, 10, 12, 16.

However, the large values of the electric dipole transition elements between Rydberg states also translate into a magnified sensitivity of these states to black-body radiation and ambient electric fields, leading to their relatively short lifetimes^1,26. Spontaneous emission, atomic motion and collisions further limit storage times for the ground-Rydberg atomic coherence^9,18. In contrast, ground atomic states are ideal for preserving quantum coherence²⁷, but implementation of fast and deterministic quantum operations is challenging due to their weak interactions. For example, deterministic single photons can be produced using measurement and feedback of Raman-scattered light fields²⁸, but the generation times are ∼1 ms—three orders of magnitude longer than in Rydberg approaches. Such considerations suggest to employ Rydberg levels for interactions and ground levels for storage to achieve both fast quantum operations and long-lived memory. In this work, we demonstrate a quantum memory where a non-classical polariton state created by Rydberg interactions is sheltered in the ground hyperfine sublevels for long-term storage.

Results

Experimental set-up

Our experimental approach is illustrated in Fig. 1: two 795 nm Raman fields (Ω_p and Ω_c) are applied to create an approximately coherent state of a spin-wave between the ground hyperfine states |a> and |b> in an ultra-cold ensemble of ⁸⁷Rb. Next, a 297 nm laser pulse Ω₁ couples state |b> directly to state |r> (np_3/2) creating a Rydberg polariton state. Subsequently, another 297 nm laser pulse Ω₂ transfers the excitation from the Rydberg state into state |b> for storage. After a storage period T_g in the ground states memory, the read-out field Ω_r converts the atomic excitation into the retrieved light field. The latter is directed onto a beam splitter and is subsequently detected by single-photon detectors D₁ and D₂. Additional details of the experimental protocol are given in Supplementary Notes 1 and 2.

Figure 1: Overview of the experiment.

(a) Essential elements of the experimental set-up. An ultra-cold ⁸⁷Rb gas is confined in a crossed dipole trap formed by two 1,064 nm fields. Two 795 nm beams (probe and control) and a 297 nm beam are focused on the atomic sample with waists (ω_p, ω_c, ω_1,2)=(5, 25, 18) μm, respectively. The probe and control beam are aligned with an angle 3°, while the 297 beam counter propagates with the probe beam. Probe Ω_p and control Ω_c laser fields are orthogonally circularly polarized. To avoid the dephasing of Rydberg state induced by inhomogeneous light shifts, the dipole trap is turned off before the Rydberg excitation field Ω₁ and switched back on after the Rydberg transfer field Ω₂. (b) Level diagram and experimental protocol. (i) Atoms are initially prepared in state |a> by means of optical pumping. The atomic ensemble is driven from |a> to |b> by the probe field Ω_p and control field Ω_c. Next, the 297 nm field Ω₁ couples |b> directly to the Rydberg state |r>, creating a singly excited Rydberg state. (ii) By applying the 297 nm field Ω₂, the short-lived Rydberg excitation is mapped into the ground state |b> for storage. (iii) The ground-state excitation is retrieved by the read field Ω_r and measured at D₁ and D₂. The atomic levels involved are |a>=|5s_1/2, F=1, m_F=0>, |b>=|5s_1/2, F=2, m_F=−2>, |e>=|5p_1/2, F=1, m_F=−1> and |r>=|np_3/2, m_J=−3/2>.

Rydberg excitation

Single-photon excitation from the ground state |b> to the Rydberg state |r> (62p_3/2) is studied in Fig. 2. The normalized sum S_n of the D₁ and D₂ detection rates is shown in Fig. 2a as a function of single-photon detuning δ_r from the |b>←|r> resonance. The measured (fwhm) width of the spectrum γ/2π=1.3 MHz is largely determined by the 0.7 μs duration of the excitation pulse Ω₁. The population of single excitation prepared in |b>, N (at δ_r=0) is shown in Fig. 2b as a function of Raman excitation population N_R in |b> (no coupling to the Rydberg state). N and N_R are obtained by normalizing the corresponding probabilities of photoelectric detection by the retrieval, transmission and detection efficiencies (Supplementary Note 3). The data are fit with a function of N=ζχN_R exp(−χN_R), where ζ=0.20(1) and χ=0.87(4) are adjustable parameters. The fit is suggested by the dephasing mechanism of multi-particle Rydberg excitations put forward in ref. 25. Here ζ corresponds to the population transfer efficiency of the |b>→|r>→|b> process in the absence of loss due to multi-particle dephasing, whereas the maximum single excitation preparation efficiency (including multi-particle dephasing loss) in state |b> is ξ_m=ζ/e.

Figure 2: Single-photon excitation to Rydberg p state.

(a) Single-photon spectroscopy of |b>←|r>=|62p_3/2, m_J=−3/2> transition. The normalized photoelectric detection rate S_n of the retrieved field is shown as a function of detuning (δ_r). The data are fit with a Lorentzian profile. (b) N, the population of prepared single excitation (with Ω₁ and Ω₂ fields ) is shown as a function of Raman excitation population N_R. Error bars, ±1 s.d.

The coherence properties of the ground-Rydberg transition are investigated in Fig. 3a by measuring the retrieved signal as a function of storage time T_r in state |62p_3/2>. The fast signal decay (with 1/e lifetime =1.58(5) μs) is a result of the atomic motional dephasing. During the Rydberg excitation, a spin-wave with phase is imprinted on the ground-Rydberg coherence by the Ω₁ field, where k₁ is the wave-vector of Ω₁, r is the atomic position and the spin-wave period is Λ_r=2π/|k₁|=297 nm. For a gas of atoms of mass M at a temperature T, atomic motion smears the spin-wave phase grating and leads to a 1/e decoherence time of (refs 28, 29), from which the inferred atom temperature is T≃10 μK. A lower value of T≃7 μK is found by observing the thermal expansion of the atomic cloud. The difference between the two measurements is a possible indication of atomic heating by the repeated application of the memory protocol. The =1.58(5) μs coherence time for the |62p_3/2> state is nearly identical to the =1.58(2) μs found for the |29p_3/2> state (Supplementary Note 4), indicating the absence of Rydberg interaction-induced decoherence.

Figure 3: Temporal dynamics of atomic polariton.

(a) The normalized photoelectric detection rate S_n of the retrieved field is shown as a function of storage time T_r in the Rydberg state. The data are fit with a Gaussian function exp(−(T_r+T_d)²/), while T_d=1 μs is the delay between two 297 nm fields Ω₁ and Ω₂ for T_r=0 and =1.58(5) μs. (b) The normalized photoelectric detection rate S_n of the retrieved field is shown as a function of storage time T_g in the ground states coherence. The data are fit with function exp(−(T_g+T_d)²/), where T_d=6 μs is the delay between the Raman excitation and the readout for T_g=0 and =71(2) μs. Error bars, ±1 s.d.

Ground-state coherence

To achieve longer storage time, we apply the Ω₂ field to coherently transfer the excitation from the Rydberg state |r> to the ground state |b>, with the single-photon detuning δ_r=0. Due to the non-collinear geometry between the probe and control fields with respective wave-vectors k_p and k_c, the atomic excitation forms a ground states spin-wave, with phase , where the wave-vector mismatch is Δk=k_p−k_c and the spin-wave period is Λ_g=2π/|Δk|=15 μm. The stored excitations can be converted into a propagating field by applying a read-out field Ω_r. To study the temporal dynamics of the quantum memory, the retrieved signal is measured as a function of the storage time T_g in the ground hyperfine sublevels, as shown in Fig. 3b. The observed 1/e quantum memory lifetime is =71(2) μs, while the expected lifetime from the scaled value of the ground-Rydberg coherence is × (Λ_g/Λ_r)≈80 μs. Assuming the difference in the two values is due to diffusion of atoms out of the ensemble in the transverse (x and y) dimensions, we estimate the transverse waist (1/e²) of the atomic ensemble to be ≃6(1) μm, which agrees with the measured 5 μm waist of the probe field (Supplementary Note 4). In the future, the quantum memory lifetime can be extended into the minute range by employing a suitable state-insensitive optical lattice capable of atom confinement on a length scale smaller than the spin-wave period Λ_g (refs 27, 30).

Quantum statistics

To characterize the non-classical behaviour of our quantum memory, the atomic excitation is read out after a storage time of T_g=2 μs and a Hanbury Brown-Twiss measurement is performed on the retrieved field with a beam splitter followed by two single-photon detectors D₁ and D₂. The photoelectric detection events at detectors D₁ and D₂ are cross correlated, with the resulting second-order intensity correlation function g⁽²⁾() shown in Fig. 4, where is the time delay between the detection events. Panel (a) shows the measurement for an approximately coherent state created by the two Raman fields Ω_p and Ω_c. The measured second-order intensity correlation function at zero delay g⁽²⁾(0)=1.06(8) is consistent with unity. Panels (b–d) show the quantum statistics of a memory coupled to Rydberg levels np_3/2 for n=29, 62 and 70, respectively.

Figure 4: Quantum statistics.

Measured second-order intensity correlation function g⁽²⁾ as a function of delay . The data bins for g⁽²⁾(0) are highlighted. (a) g⁽²⁾() is measured with retrieved coherent light created by the two Raman fields Ω_p and Ω_c. (b–d) 297 nm fields (Ω₁ and Ω₂) couple state |b> to a Rydberg state |np_3/2>, and g⁽²⁾() is measured at n=29, 62 and 70, respectively. Error bars, ±1 s.d.

As a result of the chosen principal quantum numbers (n≲70) and sample size (∼10 μm) in our experiment, interactions between the most distant Rydberg atom pairs are in the van der Waals regime, which scale as ∼n¹¹ (ref. 1). For low values of n, the presence of multiple excitations is expected and the measured g⁽²⁾(0)=1.22(14) for n=29 is consistent with unity. When the interactions are not sufficiently strong for the blockade to be operational over the entire ensemble, more than one Rydberg atom can be excited. Van der Waals interactions lead to the accumulation of phase shifts between different atomic pairs, decoupling them from the phase-matched collective emission mode of the read-out stage. The observed suppression of two-photon events at zero delay for high-lying Rydberg states n=62 and 70 reflects Rydberg excitation blockade and interaction-induced dephasing between multiple excitations and demonstrates the single-photon character of the retrieved field. The transition from the classical statistics to the manifestly quantum regime is associated with an approximately four orders of magnitude increase in the interaction strength from n=29 to 70. The measured values of g⁽²⁾(0)=0.22(8) for n=62 and g⁽²⁾(0)=0(0.04) for n=70 confirm the preparation of single-quanta in the ground memory states. The quantum statistics of the retrieved light field as a function of storage time are shown in Fig. 5, with all the measured values for g⁽²⁾(0) well below unity for up to 42 μs-long storage.

Figure 5: Non-classical memory dynamics.

The single excitation generated with the 70p_3/2 state is mapped onto the retrieved field after being stored in the ground states memory for a time of T_g. The second-order intensity correlation function at zero delay g⁽²⁾(0) is measured at different storage times T_g. Error bars, ±1 s.d.

Discussion

We have demonstrated a quantum memory with 8% efficiency to prepare a single excitation in <1 μs, and a memory lifetime of 70 μs. The storage times can be further extended, conceivably up to and beyond several seconds, by adopting a state-insensitive optical lattice^27,30. The results presented here show that the two essential quantum network capabilities—fast quantum state generation and long-term storage—can be achieved at the same time in an atomic-ensemble-based system, opening a route toward a broad range of quantum information protocols. In particular, complex quantum states of atomic ensembles can be generated and stored in their ground states and subsequently converted into highly non-classical states of propagating light fields⁷.

Methods

Preparation of the ultra-cold atomic sample

To quickly create a dense sample of ⁸⁷Rb in a low background pressure environment, a 2D⁺ magneto-optical trap (MOT) is first loaded from the background gas. The 3D MOT is then loaded from the cold atomic beam generated by the 2D⁺ MOT and directed through a differential pumping opening for 300 ms. For the following 22 ms, the gradient of the 3D MOT is increased to 25 G/cm to compress and load the atoms into an optical dipole trap formed by two orthogonally polarized YAG laser beams, intersecting at an angle of 22°. Sub-Doppler cooling of the atoms is performed by increasing the cooling light detuning and decreasing the power of repumper light for 12 ms. The dipole trap beams have a total power of 5 W and transverse waists of 17 and 34 μm, resulting in a maximum trap depth of ≃560 μK. The depth of the dipole trap is adiabatically lowered to ≃30 μK during the 200 ms after the sub-Doppler cooling stage to further cool the atoms, with the atomic temperature of ∼7 μK inferred from the observed rate of thermal expansion. The peak atomic density is ρ∼2 × 10¹¹ cm⁻³. The atomic ensemble has ∼10 μm size in the longitudinal (z) dimension, while the ∼5 μm waist of the focused probe beam determines transverse (x− and y−) dimensions of the ensemble. A bias magnetic field of 3.5 G is switched on and atoms are optically pumped to the 5s_1/2, F=1, m_F=0 state.

Data acquisition

In each experimental trial, photoelectric events from detectors D₁ and D₂ are recorded within a time interval of 200 ns, determined by the length of the retrieved pulse. The photoelectric detection probability for both detectors is given by P=P₁+P₂=N₁/N₀+N₂/N₀, where N_1,2 are the numbers of detection events recorded by D₁ and D₂ and N₀ is the number of experimental trails. The probability for detecting double coincidences is given by P₁₂()=N₁₂()/N₀, where N₁₂() is the number of coincidences from the two detectors with time delay . The second-order intensity correlation function is calculated as g⁽²⁾()=P₁₂()/(P₁P₂).

Data availability

The data that support the findings of this study are available from the corresponding author on request.