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A phase transition from a classical thermal mixed state to a quantum-mechanical pure state of exciton polaritons is observed in a GaAs multiple quantum-well microcavity from the decrease of the second-order coherence function. Supporting evidence is obtained from the observation of a nonlinear threshold behavior in the pump-intensity dependence of the emission, a polariton-like dispersion relation above threshold, and a decrease of the relaxation time into the lower polariton state. The condensation of microcavity exciton polaritons is confirmed.

Recent developments of quantum information science [1] critically rely on entanglement, an intriguing aspect of quantum mechanics where parts of a composite system can exhibit correlations stronger than any classical counterpart [2]. In particular, scalable quantum networks require capabilities to create, store, and distribute entanglement among distant matter nodes via photonic channels [3]. Atomic ensembles can play the role of such nodes [4]. So far, in the photon counting regime, heralded entanglement between atomic ensembles has been successfully demonstrated via probabilistic protocols [5,6]. However, an inherent drawback of this approach is the compromise between the amount of entanglement and its preparation probability, leading intrinsically to low count rate for high entanglement. Here we report a protocol where entanglement between two atomic ensembles is created by coherent mapping of an entangled state of light. By splitting a single-photon [7,8,9] and subsequent state transfer, we separate the generation of entanglement and its storage [10]. After a programmable delay, the stored entanglement is mapped back into photonic modes with overall efficiency of 17%. Improvements of single-photon sources [11] together with our protocol will enable "on-demand" entanglement of atomic ensembles, a powerful resource for quantum networking.In the quest to achieve quantum networks over long distances [3], an area of considerable activity has been the interaction of light with atomic ensembles comprised of a large collection of identical atoms [4,12,13]. In the regime of continuous variables, a particularly notable advance has been the teleportation of quantum states between light and matter [14]. For discrete variables with photons taken one by one, important achievements include the efficient mapping of collective atomic excitations to single photons [15,16,17,18,19], the realization of entanglement between a pair of distant ensembles [5,20] In all these cases, progress has relied upon probabilistic schemes following the measurement-induced approach developed in the seminal paper by Duan, Lukin, Cirac and Zoller [4] (DLCZ ) and subsequent extensions. For the DLCZ protocol, heralded entanglement is generated by detecting a single photon emitted indistinguishably by one of two ensembles. Intrinsically, the probability p to prepare entanglement with only 1 excitation shared between two ensembles is related to the quality of entanglement, since the likelihood for contamination of the entangled state by processes involving 2 excitations scales as p [20], and results in low success probability for each trial. Although the degree of stored entanglement can approach unity for the (rare) successful trials [20], the condition p ≪ 1 dictates reductions in count rate and compromises in the quality of the resulting entangled state (e.g., as p → 0, processes such as stray light scattering and detector dark counts become increasingly important). Furthermore, for finite memory time, subsequent connection of entanglement become...

The effect of quantum statistics in quantum gases and liquids results in observable collective properties among many-particle systems. One prime example is Bose-Einstein condensation, whose onset in a quantum liquid leads to phenomena such as superfluidity and superconductivity. A Bose-Einstein condensate is generally defined as a macroscopic occupation of a single-particle quantum state, a phenomenon technically referred to as off-diagonal long-range order due to non-vanishing off-diagonal components of the single-particle density matrix. The wavefunction of the condensate is an order parameter whose phase is essential in characterizing the coherence and superfluid phenomena. The long-range spatial coherence leads to the existence of phase-locked multiple condensates in an array of superfluid helium, superconducting Josephson junctions or atomic Bose-Einstein condensates. Under certain circumstances, a quantum phase difference of pi is predicted to develop among weakly coupled Josephson junctions. Such a meta-stable pi-state was discovered in a weak link of superfluid 3He, which is characterized by a 'p-wave' order parameter. The possible existence of such a pi-state in weakly coupled atomic Bose-Einstein condensates has also been proposed, but remains undiscovered. Here we report the observation of spontaneous build-up of in-phase ('zero-state') and antiphase ('pi-state') 'superfluid' states in a solid-state system; an array of exciton-polariton condensates connected by weak periodic potential barriers within a semiconductor microcavity. These in-phase and antiphase states reflect the band structure of the one-dimensional polariton array and the dynamic characteristics of metastable exciton-polariton condensates.

Nearly one decade after the first observation of Bose-Einstein condensation in atom vapors and realization of matter-wave (atom) lasers, similar concepts have been demonstrated recently for polaritons: half-matter, half-light quasiparticles in semiconductor microcavities. The half-light nature of polaritons makes polariton lasers promising as a new source of coherent and nonclassical light with extremely low threshold energy. The half-matter nature makes polariton lasers a unique test bed for many-body theories and cavity quantum electrodynamics. In this article, we present a series of experimental studies of a polariton laser, exploring its properties as a relatively dense degenerate Bose gas and comparing it to a photon laser achieved in the same structure. The polaritons have an effective mass that is twice the cavity photon effective mass, yet seven orders of magnitude less than the hydrogen atom mass; hence, they can potentially condense at temperatures seven orders of magnitude higher than those required for atom Bose-Einstein condensations. Accompanying the phase transition, a polariton laser emits coherent light but at a threshold carrier density two orders of magnitude lower than that needed for a normal photon laser in a same structure. It also is shown that, beyond threshold, the polariton population splits to a thermal equilibrium Bose-Einstein distribution at in-plane wave number k ʈ > 0 and a nonequilibrium condensate at kʈ ϳ 0, with a chemical potential approaching to zero. The spatial distributions and polarization characteristics of polaritons also are discussed as unique signatures of a polariton laser. E xperimentally realized macroscopic degenerate boson systems, such as lasers, superfluid He 3 and He 4 , the Bardeen-CooperSchreiffer state in superconductors, and Bose-Einstein condensation (BEC) of atomic vapors, have deepened our fundamental understanding of macroscopic quantum orders and led to novel research tools as well as applications. A missing member from the family has been a macroscopically ordered state of weakly interacting bosons in condensed matter systems. Exciton and polariton BECs are the most promising candidates in this category. Since they were first proposed in the 1960s (1-3), tremendous efforts have been engaged in the search (4-13). Exciton and polariton BECs are attractive yet elusive because of the complications inherent to solid-state systems with strong Coulomb interactions. It is a formidable task to describe the excitations in solids in full detail. The common approach is to treat the stable ground state of an isolated system as a quasivacuum and to introduce quasiparticles as units of elementary excitation, which only weakly interact with each other. An exciton is a typical example of such a quasiparticle. As a result of optical excitation from the crystal ground state, an exciton consists of a bound pair of an electron and hole whose Coulomb interaction serves as the binding energy. Excitons have integral total spin, thus they behave like bosons, weakly interac...

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We demonstrate entanglement distribution between two remote quantum nodes located 3 meters apart [1]. This distribution involves the asynchronous preparation of two pairs of atomic memories and the coherent mapping of stored atomic states into light fields in an effective state of near maximum polarization entanglement. Entanglement is verified by way of the measured violation of a Bell inequality, and can be used for communication protocols such as quantum cryptography. The demonstrated quantum nodes and channels can be used as segments of a quantum repeater, providing an essential tool for robust long-distance quantum communication.In quantum information science [2], distribution of entanglement over quantum networks is a critical requirement, including for metrology [3], quantum computation [4,5] and communication [4,6]. Quantum networks are composed of quantum nodes for processing and storing quantum states, and quantum channels that link the nodes. Significant advances have been made with diverse systems towards the realization of such networks, including ions [7], single trapped atoms in free space [8,9] and in cavities [10], and atomic ensembles in the regime of continuous variables [11].An approach of particular importance has been the seminal work of Duan, Lukin, Cirac, and Zoller (DLCZ) for the realization of quantum networks based upon entanglement between single photons and collective excitations in atomic ensembles [12]. Critical experimental capabilities have been achieved, beginning with the generation of nonclassical fields [13,14] with controlled waveforms [15] and extending to the creation and retrieval of single collective excitations [16,17,18] with high efficiency [19,20]. Heralded entanglement with quantum memory, which is the cornerstone of networks with efficient scaling, was achieved between two ensembles [21]. More recently, conditional control of the quantum states of a single ensemble [22,23,24] and of two distant ensembles [25] has also been implemented, as are likewise required for the scalability of quantum networks based upon probabilistic protocols.Our interest is to develop the physical resources that enable quantum repeaters [6], thereby allowing entanglement-based quantum communication tasks over quantum networks on distance scales much larger than set by the attenuation length of optical fibers, including quantum cryptography [26]. For this purpose, heralded number state entanglement [21] between two remote atomic ensembles is not directly applicable. In- * Current address: Group of Applied Physics, University of Geneva, Geneva, Switzerland † Current address: Departamento de Física, Universidade Federal de Pernambuco, Recife-PE, 50670-901, Brazil stead, DLCZ proposed to use pairs of ensembles (U i , D i ) at each quantum node i, with the sets of ensembles {U i }, {D i } separately linked in parallel chains across the network [12]. Relative to the state of the art in Ref.[21], the DLCZ protocol requires the capability for the independent control of pairs of entangled ensembles...

Heralded entanglement between collective excitations in two atomic ensembles is probabilistically generated, stored, and converted to single-photon fields. By way of the concurrence, quantitative characterizations are reported for the scaling behavior of entanglement with excitation probability and for the temporal dynamics of various correlations resulting in the decay of entanglement. A lower bound of the concurrence for the collective atomic state of 0:9 0:3 is inferred. The decay of entanglement as a function of storage time is also observed, and related to the local dynamics. DOI: 10.1103/PhysRevLett.99.180504 PACS numbers: 03.67.Mn, 03.65.Yz, 03.67.Hk, 42.50.Dv Beyond a fundamental significance, quantum control of entanglement between material systems is an essential capability for quantum networks and scalable quantum communication architectures [1,2]. In recent years, significant advances have been achieved in the control of the quantum states of atomic systems, including entanglement of trapped ions [3,4] and between macroscopic spins [5]. By following the seminal paper of Duan, Lukin, Cirac, and Zoller (DLCZ) [6], entanglement between single collective excitations stored in two remote atomic ensembles has also been demonstrated [7]. In the DLCZ protocol, entanglement is created in a probabilistic but heralded way from quantum interference in the measurement process [8][9][10]. The detection of a photon from one or the other atomic ensemble in an indistinguishable fashion results in an entangled state with one collective spin excitation shared coherently between the ensembles. Such entanglement has been critical for the initial implementation of functional quantum nodes for entanglement distribution [11], for the investigation of entanglement swapping [12] and for lightmatter teleportation [13].Because of the relevance to quantum networking tasks, it is important to obtain detailed characterizations of the physical processes related to the creation, storage, and utilization of heralded entanglement. Towards this end, significant advances have been demonstrated in the generation of photon-pairs [14,15] and the efficient retrieval of collective excitation [16,17]. Moreover, decoherence processes for a single atomic ensemble in the regime of collective excitation have been investigated theoretically [18] and a direct measurement of decoherence for one stored component of a Bell state recently performed [19]. However, to date no direct study has been reported for the decoherence of an entangled system involving two distinct atomic ensembles, which is a critical aspect for the implementation of elaborate protocols [20 -22]. The decoherence of entanglement between ensembles has been shown in recent setups, through the decay of the violation of a Bell inequality [11] and the decay of the fidelity of a teleported state [13]. However, a quantitative analysis was not provided since these setups involved many others parameters, such as phase stability over long distances.In this Letter, we report measurements ...