Entanglement is considered to be one of the most profound features of quantum mechanics 1,2 . An entangled state of a system consisting of two subsystems cannot be described as a product of the quantum states of the two subsystems 9,10,16,17 . In this sense the entangled system is considered inseparable and nonlocal. It is generally believed that entanglement manifests itself mostly in systems consisting of a small number of microscopic particles. Here we demonstrate experimentally the entanglement of two objects, each consisting of about 10 12 atoms. Entanglement is generated via interaction of the two objects -more precisely, two gas samples of cesium atoms -with a pulse of light, which performs a non-local Bell measurement on collective spins of the samples 14 . The entangled spin state can be maintained for 0.5 millisecond. Besides being of fundamental interest, the robust, long-lived entanglement of material objects demonstrated here is expected to be useful in quantum information processing, including teleportation 3-5 of quantum states of matter and quantum memory. In this Letter we describe an experiment on the generation of entanglement between two separate samples of atoms containing 10 12 atoms each, along the lines of a recent proposal 14 . Besides the fact that we demonstrate a quantum entanglement at the level of macroscopic objects, our experiment proves feasible a new approach to the quantum interface between light and atoms suggested in 14,15 and paves the road towards the other protocols proposed there, such as the teleportation of atomic states and quantum memory. The entanglement is generated through a non-local Bell measurement on the two samples' spins performed by transmitting a pulse of light through the samples.The ideal EPR entangled state of two sub-systems described by continuous non- . Recently in 16,17 , the necessary and sufficient condition for the entanglement or inseparability for such Gaussian quantum variables has been cast in a form of an inequality involving only the variances of variables:

We propose an efficient method for mapping and storage of a quantum state of propagating light in atoms. The quantum state of the light pulse is stored in two sublevels of the ground state of a macroscopic atomic ensemble by activating a synchronized Raman coupling between the light and atoms. We discuss applications of the proposal in quantum information processing and in atomic clocks operating beyond quantum limits of accuracy. The possibility of transferring the atomic state back on light via teleportation is also discussed. 42.50.Lc, 42.50.Dv, 42.50.Ct, 06.30.Ft Light is an ideal carrier of quantum information, but photons are difficult to store for a long time. In order to implement a storage device for quantum information transmitted as a light signal, it is necessary to faithfully map the quantum state of the light pulse onto a medium with low dissipation, allowing for storage of this quantum state. Depending on the particular application of the memory, the next step may be either a (delayed) measurement projecting the state onto a certain basis, or further processing of the stored quantum state, e.g., after a read-out via the teleportation process. The delayed projection measurement is relevant for the security of various quantum cryptography and bit commitment schemes [1]. The teleportation read-out is relevant for full scale quantum computing.In this Letter we propose a method that enables quantum state transfer between propagating light and atoms with an efficiency up to 100% for certain classes of quantum states. The long term storage of these quantum states is achieved by utilizing atomic ground states. In the end of the paper we propose an atom-back-to-light teleportation scheme as a read-out method for our quantum memory.We consider the stimulated Raman absorption of propagating quantum light by a cloud of Λ atoms. As shown in the inset of Fig.1, the weak quantum field and the strong classical field are both detuned from the upper intermediate atomic state(s) by ∆ which is much greater than the strong field Rabi frequency Ω s , the width of an upper level γ i and the spectral width of the quantum light Γ q . The Raman interaction "maps" the non-classical features of the quantum field onto the coherence of the lower atomic doublet, distributed over the atomic cloud.In our analysis we eliminate the excited intermediate states, and we treat the atoms by an effective two-level approximation. We start with the quantum Maxwell-Bloch equations in the lowest order for the slowly varying operatorQ:Q =σ 31 e −i(ωq−ωs)t+i(kq −ks)z (it will be assumed, that (k q − k s )L ≪ 1, where L is the length of the atomic cloud, z is the propagation direction, and ω q,s and k q,s are frequencies and wavevectors of "quantum" and "strong" fields respectively) [2,3]Γ is the dephasing rate of the 1 ↔ 3 coherence which also includes the strong field power broadening Γ s ≃ ω 3h κ 2 1 |E s | 2 /(3c 3 ) due to spontaneous Raman scattering [2],F (z, t) is the associated quantum Langevin force with correlation function F * (z,...

No abstract

We present hitherto unknown forms of soliton dynamics in the forbidden frequency gap of a Bragg reflector, modified by periodic layers of near-resonant two-level systems (TLS). Remarkably, even extremely low TLS densities create an allowed band within the forbidden gap. This spectrum gives rise, for any Bragg reflectivity, to a vast family of stable gap solitons, both standing and moving, having a unique analytic form, an arbitrary pulse area, and inelastic collision properties. These findings suggest new possibilities of transmission control, noise filtering or "dynamical cavities" (self-traps) for both weak and strong signal pulses. The study of light-matter interactions in periodic dielectric structures has developed into a vast research area. At the heart of this area is the interplay between the resonant reflections induced by the Bragg reflector, giving rise to photonic band gaps, and their dynamical modifications due to nonlinear light-matter interactions. The pulsed mode of propagation in such structures exhibits a variety of unique fundamentally and technologically interesting regimes: nonlinear filtering, switching, and distributed-feedback amplification [1]. Of particular interest are gap solitons (GS), i.e., moving or standing (quiescent) self-localized pulses, whose spectrum is centered in a gap induced by the grating. GS in Kerrnonlinear Bragg reflectors have been extensively analyzed [2] and experimentally observed [3]. Recently, GS have also been predicted in Bragg-reflecting second-harmonic generating media [4].This work is dedicated to a different mechanism supporting GS in periodic media, which is based on nearresonant field-atom interactions. The first step in this direction has been made in Ref. [5], where an exact moving GS solution has been found in a periodic structure composed of thin layers of resonant two-level systems (TLS) separated by half-wavelength non-absorbing dielectric layers, i.e., a resonantly-absorbing Bragg reflector (RABR). In the soliton solution obtained in Ref.[5], the combined area of the forward-and backward-propagating pulses is 2π, characteristic of self-induced transparency (SIT) solitons in uniform media [6]. The existence of this soliton stems from the cooperative resonant atomic polarizability, which compensates for the periodic modulation of the linear polarizability in the Bragg reflector [5,7]. The analysis presented in Ref. [5] leaves several open questions of fundamental and applied importance: (i) Can one overcome the basic restriction implicit in this solution, namely, that the cooperative length over which a SIT pulse is formed, must be shorter than the Bragg reflection length? If this restriction is essential, then the soliton would only exist in weakly-reflecting Bragg structures, which can hardly serve as efficient filters that block pulses other than GS. (ii) Are GS admitted in a RABR for weak pulses whose area is less than 2π? (iii) Is there a quiescent counterpart to the moving GS, which would imply complete dynamic confinement of light in the RAB...

Electromagnetic fields dressed by inverted two-level atoms become tachyonlike excitations with group velocities which are faster than c, infinite, or negative. Such excitations describe the stable modes of the medium when it is weakly probed off resonance. The launching of these tachyonlike excitations is discussed, along with a proposed experiment to observe them. Their existence does not violate Einstein causality. [S0031-9007(96)00891-5]