In this letter we present an experimental study of the collective dipole oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. Dynamics of the center-of-mass dipole oscillation is studied in a broad parameter region, as a function of spin-orbit coupling parameters as well as oscillation amplitude. Anharmonic properties beyond effective-mass approximation are revealed, such as amplitude-dependent frequency and finite oscillation frequency at place with divergent effective mass. These anharmonic behaviors agree quantitatively with variational wave-function calculations. Moreover, we experimentally demonstrate a unique feature of spin-orbit coupled system predicted by a sum-rule approach, stating that spin polarization susceptibility-a static physical quantity-can be measured via dynamics of dipole oscillation. The divergence of polarization susceptibility is observed at the quantum phase transition that separates magnetic nonzero-momentum condensate from nonmagnetic zero-momentum phase. The good agreement between the experimental and theoretical results provides a bench mark for recently developed theoretical approaches.Many interesting quantum phases can emerge in solid state materials when electrons are placed in a strong magnetic field or possess strong spin-orbit (SO) coupling, such as the fractional quantum Hall effect [1] and the topological insulator [2]. In cold atom systems, albeit neutral atoms have neither charges nor SO coupling, the recent exciting experimental progress demonstrates that artificial gauge potentials can be synthesized in laboratory by laser control technique [3][4][5][6][7][8][9][10]. Synthetic gauge potential is becoming a powerful tool for simulating real materials with cold atoms. Moreover, the system of SO coupled bosons does not have an analogy in conventional condensed matter systems, and can exhibit many novel phases [11] such as striped superfluid phase [12,13] and half vortex phase [14][15][16][17].Collective excitations play an important role in studying physical properties of trapped atomic Bose-Einstein condensates (BEC) and degenerate Fermi gases. Collective dipole oscillation is a center-of-mass motion of all atoms. For a conventional condensate, the dipole oscillation is trivial: the frequency is just the harmonictrap frequency, independent of oscillation amplitude and interatomic interaction. This is known as Kohn theorem [18,19]. For a SO coupled condensate, however, it was found [4] that the dipole-oscillation frequency deviates from the trap frequency and the experimental data thereby can be explained by effective-mass approximation. Recently, much theoretical effort has been taken to understand dynamics of a SO coupled BEC [20][21][22][23][24][25], and many predicted unconventional properties remain to be experimentally explored. In particular, the so-called sum-rule approach predicts [25] a unique feature of SO coupled condensate: spin polarization susceptibility-a static physical quantity-can be measured via dynamics of dipole oscillatio...

Quantum communication is a method that offers efficient and secure ways for the exchange of information in a network. Large-scale quantum communication (of the order of 100 km) has been achieved; however, serious problems occur beyond this distance scale, mainly due to inevitable photon loss in the transmission channel. Quantum communication eventually fails when the probability of a dark count in the photon detectors becomes comparable to the probability that a photon is correctly detected. To overcome this problem, Briegel, Dür, Cirac and Zoller (BDCZ) introduced the concept of quantum repeaters, combining entanglement swapping and quantum memory to efficiently extend the achievable distances. Although entanglement swapping has been experimentally demonstrated, the implementation of BDCZ quantum repeaters has proved challenging owing to the difficulty of integrating a quantum memory. Here we realize entanglement swapping with storage and retrieval of light, a building block of the BDCZ quantum repeater. We follow a scheme that incorporates the strategy of BDCZ with atomic quantum memories. Two atomic ensembles, each originally entangled with a single emitted photon, are projected into an entangled state by performing a joint Bell state measurement on the two single photons after they have passed through a 300-m fibre-based communication channel. The entanglement is stored in the atomic ensembles and later verified by converting the atomic excitations into photons. Our method is intrinsically phase insensitive and establishes the essential element needed to realize quantum repeaters with stationary atomic qubits as quantum memories and flying photonic qubits as quantum messengers.

. Here we present an experimental investigation into extending the storage time of quantum memory for single excitations. We identify and isolate distinct mechanisms responsible for the decoherence of spin waves in atomic-ensemble-based quantum memories. By exploiting magnetic-field-insensitive statesso-called clock states-and generating a long-wavelength spin wave to suppress dephasing, we succeed in extending the storage time of the quantum memory to 1 ms. Our result represents an important advance towards long-distance quantum communication and should provide a realistic approach to large-scale quantum information processing.The quantum repeater with atomic ensembles and linear optics has attracted broad interest in recent years, as it holds promise to implement long-distance quantum communication and the distribution of entanglement over quantum networks. Following the protocol proposed in ref. 3 and the subsequent improved schemes 4-7 , significant experimental progress has been accomplished, including the coherent manipulation of the stored excitation in one 10,11 or two 14-16 atomic ensembles, the demonstration of memory-built-in quantum teleportation 17 and the realization of a building block of the quantum repeater 13,18 . In these experiments, the atomic ensembles serve as the storable and retrievable quantum memory for single excitations.Despite the advances achieved in manipulating atomic ensembles, long-distance quantum communication with atomic ensembles remains challenging owing to the short storage time of the quantum memory for single excitations. For example, for direct generation of entanglement between two memory qubits over a few hundred kilometres, we need a memory with a storage time of a few hundred microseconds. However, the longest storage time reported so far is of the order of only 10 µs (refs 10-13).It has long been believed that the short coherence time is mainly caused by the residual magnetic field 19,20 . Thereby, storing the collective state in the superposition of the first-order magnetic-field-insensitive states 21 , that is, the 'clock states', is suggested to inhibit this decoherence mechanism 19 . A numerical calculation shows that the expected lifetime is of the order of seconds in this case.Here we report on our investigation of prolonging the storage time of the quantum memory for single excitations. In the experiment, we find that using only the 'clock state' is not sufficient to obtain the expected long storage time. We further analyse, isolate and identify the distinct decoherence mechanisms, and thoroughly investigate the dephasing of the spin wave (SW) by varying its wavelength. We find that the dephasing of the SW is extremely sensitive to the angle between the write beam and detection mode, especially for small angles. On the basis of this finding, by exploiting the 'clock state' and increasing the wavelength of the SW to suppress the dephasing, we succeed in extending the storage time from 10 µs to 1 ms.The illustration of our experiment is depicted in Fig. 1a,b....

In this Letter we propose a robust quantum repeater architecture building on the original Duan-Lukin-Cirac-Zoller (DLCZ) protocol [L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Nature (London) 414, 413 (2001)10.1038/35106500]. The architecture is based on two-photon Hong-Ou-Mandel-type interference which relaxes the long-distance stability requirements by about 7 orders of magnitude, from subwavelength for the single photon interference required by DLCZ to the coherence length of the photons. Our proposal provides an exciting possibility for robust and realistic long-distance quantum communication.

Quantum memories are regarded as one of the fundamental building blocks of linear-optical quantum computation [1] and long-distance quantum communication [2]. A long standing goal to realize scalable quantum information processing is to build a long-lived and efficient quantum memory. There have been significant efforts distributed towards this goal. However, either efficient but short-lived [3,4] or long-lived but inefficient quantum memories [5][6][7] have been demonstrated so far. Here we report a high-performance quantum memory in which long lifetime and high retrieval efficiency meet for the first time. By placing a ring cavity around an atomic ensemble, employing a pair of clock states, creating a longwavelength spin wave, and arranging the setup in the gravitational direction, we realize a quantum memory with an intrinsic spin wave to photon conversion efficiency of 73(2)% together with a storage lifetime of 3.2(1) ms. This realization provides an essential tool towards scalable linearoptical quantum information processing.A high-performance quantum memory is of crucial importance for large-scale linear-optical quantum computation[1], distributed quantum computing, and long-distance quantum communication [2]. The lifetime and the retrieval efficiency of a quantum memory are two important quantities that determine the scalability of realistic quantum information protocols. For a certain quantum information task, e.g. creating a large-scale cluster state [8] or distributing entanglement through the quantum repeater protocol [9-12], the time overhead T r is inversely proportional to a power law of the retrieval efficiency R, T r ∝ R −n , where n is determined by the scale of the quantum computation or the communication distance. In order to implement one of those tasks, the lifetime of the quantum memory must be larger than this time overhead. To satisfy this condition, one has to improve the lifetime of the quantum memory and reduce the time overhead by improving the retrieval efficiency. Besides, different protocols also set thresholds on the retrieval efficiency and lifetime. For example, in loss-tolerant linear-optical quantum computation the minimum retrieval efficiency required is 50% [13] and in long-distance quantum communication distributing en-tanglement over 1000 km requires a communication time of at least 3.3 ms.Quantum memories for light have been demonstrated with atomic ensembles [14][15][16], solid state systems [17,18], and single atoms [19]. With these quantum memories, the principle of some quantum information protocols have been demonstrated, e.g., functional quantum repeater nodes were realized with atomic ensembles [20,21]. However, due to the low retrieval efficiency and short lifetime, the implementation of further steps is extremely difficult. Therefore, in recent years, many efforts have been devoted towards improving the retrieval efficiency and the lifetime of the quantum memories and significant progress has been achieved. However, an efficient and long-lived quantum memory remai...