Heralding Quantum Entanglement between Two Room-Temperature Atomic Ensembles

Establishing quantum entanglement between individual nodes is crucial for building large-scale quantum networks, enabling secure quantum communication, distributed quantum computing, enhanced quantum metrology and fundamental tests of quantum mechanics. However, the shared entanglements have been merely observed in either extremely low-temperature or well-isolated systems, which limits the quantum networks for the real-life applications. Here, we report the realization of heralding quantum entanglement between two atomic ensembles at room temperature, where each of them contains billions of motional atoms. By measuring the mapped-out entangled state with quantum interference, concurrence and correlation, we strongly verify the existence of a single excitation delocalized in two atomic ensembles. Remarkably, the heralded quantum entanglement of atomic ensembles can be operated with the feature of delay-choice, which illustrates the essentiality of the built-in quantum memory. The demonstrated building block paves the way for constructing quantum networks and distributing entanglement across multiple remote nodes at ambient conditions.

atomic ensembles at room temperature, where each of them contains billions of motional atoms. By measuring the mapped-out entangled state with quantum interference, concurrence and correlation, we strongly verify the existence of a single excitation delocalized in two atomic ensembles. Remarkably, the heralded quantum entanglement of atomic ensembles can be operated with the feature of delay-choice, which illustrates the essentiality of the built-in quantum memory. The demonstrated building block paves the way for constructing quantum networks and distributing entanglement across multiple remote nodes at ambient conditions.

Introduction.
The development of quantum mechanics has built strong foundations for quantum entanglement in fundamental principles and experiments. Establishing a heralded quantum entanglement between two macroscopic objects is not only of prime importance to the verification of quantum theories [1,2], but also a critical ability for constructing large-scale quantum networks [3].
As the conceptual graph shows in Fig. 1a, the heralded entanglement of individual quantum nodes together with the built-in quantum memory, used to store quantum states, is an essential ingredient for building quantum networks. Together with the local operations and classical communication, quantum resources can be disseminated among the whole quantum networks, which have wide applications for quantum information processing [4,5,6,7,8,9], quantum computation [10] and quantum metrology [11,12,13].
So far, several seminal experimental achievements of heralding entanglement between two individual nodes have been accomplished in various systems, such as cold atomic ensembles [14], trapped ions [15], solid-state crystals doped with rare-earth ions [16] and macroscopic diamonds [17].
Furthermore, much experimental efforts have been paid to build scalable quantum repeaters based on heralded entanglement in cold atomic ensembles [8,18]. The achieved heralded quantum entanglements between two quantum nodes, however, have to be prepared and detected in the systems that are maintained at extremely low temperature and well isolated with environment. These rigorous conditions for being avoid of strong decoherence effects limit the efficient physical scalability for quantum networks.
Apart from successful sharing quantum entanglement, quantum memories, as the stationary nodes of quantum networks [19], should satisfy some key features to efficiently deliver the promised quantum advantages, including the capacities of operating at room temperature, low noise level and large time bandwidth product (the storage lifetime of entanglement divided by pulse duration). However, these capacities have been proven not compatible to each other in practice and very challenging to achieve at the same time [20,21]. Until recently, the Duan-Lukin-Cirac-Zoller protocol operating at far off-resonance configuration has been found capable of accessing all the capacities simultaneously, especially the intrinsic low-noise mechanism [22,23,24].
Here, we experimentally realize the heralding quantum entanglement between two atomic ensembles and achieve quantum network nodes simultaneously at low-noise, broadband and room-temperature regime. Billions of motional atoms collectively carry the entangled state and are separated by two centimeter-size glass cells. By mapping the stored state to photonic state, we are able to verify the heralded quantum entanglement rigorously, and more remarkably, to test the delay-choice gedanken experiment with built-in quantum memories.
Experimental implement and results.
The time sequence and energy levels for the generation and verification of the heralded entanglement are illustrated in Fig. 1b. For establishing entanglement between the two atomic ensembles (labels L, R), the optical pump pulse is split into two equal parts by controlling the incident polarization to symmetrically excite the L and R ensembles. Due to the sufficiently weak intensity of each pulse, the probability of simultaneously generating two excitations resulting from spontaneous Raman scattering in both ensembles is extremely low [4,25]. No matter which atomic ensemble has been excited, there will be a single collective excitation, called spin wave, shared by billions of motional atoms [26]. Accompanying with the generation of the atomic spin wave, a correlated Stokes photon will be scattered from the ensemble with different polarization from the optical pump light. If we can erase the "which-way" information (scattering from L or R ensemble), a spin wave will be heralded and delocalized in the two atomic ensembles. As shown in Fig. 2, we use the half-wave plate and polarizer to mix the polarization information to realize the indistinguishable detection of the Stokes photon, the resulted joint state can be written as [14] where |1 L,R , |0 L,R represent whether there is a spin wave in L or R ensemble, ϕ S is the phase difference before detecting of the Stokes photon, and ± depends on which detector receive the Stokes photon.
For verifying the existence of the heralded entanglement, we need to reconstruct the density matrix ρ L,R for the entangled state (1). However, the direct measurement of spin wave is an unaccessible task. Alternatively, the quantum coherence between spin waves can be transformed into the interference of anti-Stokes photon, and measured by single-photon detectors. We apply another optical probe pulse for mapping the delocalized spin wave into an anti-Stokes photon (as Figure 1b shows) after a storage time of 100ns. Similar with equation (1), the entangled state of spin wave distributed by two ensembles will be transformed into the entangled state of two spatial modes (L and R) for anti-Stokes photon, i.e. Ψ AS where |1 AS L,R , |0 AS L,R have the same meaning as equa-tion (1), ϕ AS is the phase difference for the anti-Stokes photon. In other words, the entanglement of photon retrieved from the ensembles, represented by state Ψ AS L,R , is also heralded by the detection of a single Stokes photon, whose density matrix ρ AS L,R can be reconstructed by the measured statistics of correlated photons.
The experimental realization of above scheme in room-temperature atomic ensembles is organized in Fig. 2. The scattered Stokes and anti-Stokes photons with orthogonal polarizations are combined in a polarizing beam splitter, which forms a Mach-Zehnder interferometer together with the part of separating the control light. Then, the correlated scattering photons pair is redirected to individual measurement blocks according to their different time sequences. It is worth noting that the phase of the interferometer must be stabilized, which is vital to observe the interference phenomenon of the heralded anti-Stokes photon, i.e. the phase ϕ S and ϕ AS must be kept constant. Therefore, an auxiliary field with feedback control has been directed into the interferometer for phase locking (see Methods). In addition, the adopted far off-resonance configuration is insensitive to the Doppler effects of motional atoms meanwhile endows the broadband feature, which allows the detections of the heralded entangled photon modes at high data rate.
Before verifying the genuine entanglement between the two atomic modes, we firstly evaluate the coherence of the two modes of atomic entangled state, which can be inferred from the interference of the anti-Stokes photon. Due to that the single spin wave is distributed between L and R ensembles, the retrieved anti-Stokes photon is also delocalized in two spatial modes with different polarizations combined by the polarizing beamsplitter in Fig. 2. By adding an extra Pancharatnam-Berry's phase [17,27,28] (tuning the phase item ϕ AS , see Methods) between the different polarization modes, we can observe the interference of anti-Stokes photon after the projection measurement in the two output ports D 3 and D 4 . The interference results N ± with phase variations (the coincidence counts of D 1 and D 3,4 ) are shown in Fig. 3a. The experimen-tally measured results of N ± can be fitted by sinusoidal oscillations, whose theoretical forms are proportional to sin 2 [(ϕ S + ϕ AS + π ± π) /2] [17]. The high fringe visibility of anti-Stokes photon between the two spatial modes implies that the quantum coherence between the L and R ensembles can be well preserved in a certain storage time.
To quantitatively evaluate the entanglement between L and R ensemble, we map it into the entanglement of anti-Stokes photon between two spatial modes and measure its concurrence (a monotonic measure of entanglement, which is positive for entangled state and zero for separable state). Due to that this transformation is local operation, it does not increase entanglement amount. Therefore, the concurrence of the photonic entanglement sets a lower bound for the atomic entanglement [14]. The density matrix of the entanglement of a single anti-Stokes photon distributed in two spatial modes, represented by ρ AS L,R = Ψ AS L,R Ψ AS L,R , can be expressed as a matrix in the representation of photonic Fock state basis. The correlation of the concurrences for the density matrix ρ AS L,R and ρ L,R can be read as [29,30] C a ≥ C p = 2 max(0, |d| − √ p 00 p 11 ) where C a , C p are the concurrence of the entanglement of atomic ensembles and anti-Stokes photon respectively, d is the off-diagonal coherence of ρ AS L,R , p ij is the heralded probability of registering i ∈ {0, 1} photon in the L mode and j ∈ {0, 1} photon in the R mode.
The density matrix of the heralded entanglement of anti-Stokes modes ρ AS L,R can be deduced from the measurement results of the correlated photons statistics, whose specific form is shown in Fig. 3b. The off-diagonal item d, standing for the coherence of two anti-Stokes modes, can be evaluated by the visibility V of interference fringe in Fig. 3a, i.e. d = V (p 01 + p 10 )/2.
where |H S,AS , |V S,AS represent the orthogonal polarization modes of the Stokes and anti-Stokes photons. We compensate the extra Pancharatnam-Berry's phase of ϕ S or ϕ AS to make ϕ S + ϕ AS = 0, forming the maximal entangled state. By performing the quantum state tomography measurement of two-qubits [31], the reconstructed state of our experimental state is shown in Fig. 4b.

Discussion and Conclusion.
In conclusion, we have reported the experimental realization of heralding quantum entanglement among billions of motional atoms separated by two glass cells, at low-noise, broadband and room-temperature regime. The achieved low-noise level delivers a high visibility of the quantum interference of the heralded entanglement between different anti-Stokes modes, as well as a tomography results of the joint entangled state of the two photonic qubits with high concurrence and fidelity. Furthermore, the broadband feature may enable future quantum networks being operated at high data rates, providing the accessibilities for overcoming the losses and inefficiency to generate and analyze the quantum entanglement. We also harness the memorybuilt-in feature to test delay-choice gedanken experiment, beside fundamental interest, which illustrates the capacities of quantum networks with shared quantum entanglement and quantum memory.
The demonstrated low-noise, broadband and room-temperature building block is key to con-struct future scalable and environment-friendly quantum networks. Along this way, a few milestone works can be done for developing entirely new capacities of engineering quantum systems towards real-applications, while pushing the boundaries of quantum-classical transition. One may teleport arbitrary qubit to separated atomic ensembles consisted of motional atoms at ambient environment. One may build broadband and room-temperature quantum repeaters [5,6,8] capable of distributing quantum resources at high-speed fashion. The room-temperature atomic ensemble has the advantages of being cost-effective and easily miniaturized compared with other systems, which may exert great superiorities in building practical quantum networks, especially for the scenery of outer space. In addition, it is quite promising to prolong the lifetime of the heralded quantum entanglement among nodes, for instance, to preserve the coherence by the anti-relaxation coating in the vapor cell [36,37], to transfer the spin wave of alkaline metal atoms to noble-gas nuclear spins in the regime of spin exchanging [38,39], etc.
a large optical depth. In order to alleviate the collisions between cesium atoms, we have injected 10 T orr Ne buffer gas into the vapor cell. Benefit from the developed precise frequency locking system, the frequency of the optical control light can be locked to a fixed detuning and conveniently tuned on demand, which helps to create and verify the quantum entanglement precisely. The pump light, being resonated to the |e → |s transition, is directed from one port of Wollaston prism (WP), which propagates along the same path of the optical control light but with opposite direction and is employed to initialize the state of atoms. The creation of the pump and control light is generated in a programable fashion. To be specific, the optical control light pulse is 2ns generated by a high speed light modulator and the pump light pulse is 2us propagating along the diffraction path of an acousto-optical modulators (AOM).
The Stokes and anti-Stokes photons generated via spontaneous Raman scattering process are orthogonally polarized with the optical pump and probe light [40]. We separate the control photons) will suffer from dramatic variations. In order to observe and verify the genuine entanglement between the two room-temperature ensembles from trial to trial, we should stabilize the interferometer loop in Fig. 2 at a fixed phase.
The auxiliary light field for phase locking of the interferometer loop in Fig. 2 has the same frequency as optical pump and probe pulse, but in the form of continuous wave. Due to the orthogonal polarization between the optical control light and scattering photons, it seems impossible to make the auxiliary light field propagating through the same path as the original interferometer loop, because the Glan-Taylor prism used for purifying the polarization of control light only allows one polarized light pass through, and blocks the orthogonal one with a extinction rate up to 10 5 . As the inset of Figure 2 shows, we employ a special half-wave plate with a hole in the center to change the polarization of auxiliary light field while keep the polarization of the optical control light unaffected. According to the interference results of the auxiliary field, the feedback electric controlling signal will be sent to the Piezoelectric ceramics to compensate the optical path.
Quantum interference for the heralded entanglement of anti-Stokes modes: For evaluating the coherence of the heralded entangled modes between the orthogonal polarization of anti-Stokes photon (can be written as 1 , we need to control the phase ϕ AS to acquire the interference results by means of the projection measurements (made up of the half-wave plate and polarizing beamsplitter shown in Fig. 2). The manipulation of this phase is achieved in the way of Pancharatnam-Berry's phase [17,27,28], which is realized by using two quarter-wave plates and a half-wave plate labelled by the component phase shifter in the verifying module shown in Fig. 2. i.e. initializing, heralding and verifying processes, which form a single experimental trial. The atomic ensembles in each node has equal probability to contain a single excitation shared by all the atoms when the entanglement has been established, which is symbolized by spin-up in the graph. The atomic entanglement is heralded by the single Stokes photon which is also entangled between two different polarization modes. In the energy levels of the heralding and verifying processes, the solid lines represent three-level Λ-type configuration of atoms: the two ground states label |g (6S 1/2 , F = 3) with electronic spin down and |s (6S 1/2 , F = 4) with electronic spin up, which are hyperfine ground states of cesium atoms; the excited state labels |e (6P 3/2 , F = 2, 3,4,5). The shaded area between energy levels represent broad virtual energy levels induced by the short optical pump and probe laser pulse. Figure 2: Experimental setup. The optical control pulse is directed into the Mach-Zehnder interferometer to generate the entanglement between the L and R ensembles. For combine photons from two ensembles at the PBS, the polarization of the control light in the left arm is transformed into being orthogonal to the right arm by the HWP after the GTP. The continuous auxiliary light field for phase locking is paralleled to the path of the control light, but has a small spatial shift to go thorough the hollow HWP for changing its polarization. This design is mainly due to the orthogonal polarizations between the control light passing through the GTP and the scattered signal photons passing the port of WP. The interference results of the auxiliary light field will be input to the processor, and then a feedback electric signal will be given to drive PZT to actively lock the phase of the interferometer. We utilize the time difference between the Stokes and anti-Stokes photons to separate their paths by applying a 100 ns control signal to the AOM. By this way, the two photons are directed into different analyzing modules, i.e. the heralding part and verifying part. The PS is used to adjust the Pancharatnam-Berry's phase to acquire the interference results of the heralded anti-Stokes photon. PBS: polarization beam splitter, WP: Wollaston prism, GTP: Glan-Taylor prism, FPC: Fabry-Pérot cavity, HWP: half wave plate, PS: phase shifter, PZT: piezoelectric ceramics, AOM: acousto-optical modulators, APD: avalanche photodiode detector. The density matrix elements are p 01 = 3.1 × 10 −3 , p 10 = 3.5 × 10 −3 , d = V × (p 01 + p 10 )/2 = 2.9 × 10 −3 , p 11 = 5.5 ± 1.1 × 10 −7 . The p 11 indicates the high-order excitation events, which has been much smaller than the events of single excitation, so we can neglect the higher-order excitation events contributing to the density matrix.