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Chinese Physics B

Nonlinear interactions and quantum entanglement for collective fields in near-resonantly driven systems

Xiu Zhang, Xiangming Hu, Xuehua Zhang, Fei Wang

Published Dec 1, 2010• 1 citation
Publisher

Abstract

This paper proposes a novel form of multimode nonlinear interactions by using a near-resonantly dressed atomic ensemble in an optical cavity. Due to quantum interference, a pair of collective fields come into the bilinear interactions, whose strengths are proportional to the population difference between dressed states which are coupled to the collective fields. By such an interaction, it is possible to obtain perfect multimode squeezing and collective Einstein-Podolsky-Rosen (EPR) entanglement in the cavity output.

DOI
10.1088/1674-1056/19/12/124204

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This paper proposes a novel form of multimode nonlinear interactions by using a near-resonantly dressed atomic ensemble in an optical cavity. Due to quantum interference, a pair of collective fields come into the bilinear interactions, whose strengths are proportional to the population difference between dressed states which are coupled to the collective fields. By such an interaction, it is possible to obtain perfect multimode squeezing and collective Einstein-Podolsky-Rosen (EPR) entanglement in the cavity output.
Parametric interaction of a pair of cavity fields in a near-resonantly driven atomic system is described by a bilinear Hamiltonian that decouples from atomic flip operators and is proportional to the population difference between dressed states. For proper choice of parameters, the parametric interaction is enhanced by at least two orders compared to the dispersively dressed cases. Although spontaneous emission is fed into the cavity fields, destructive interference occurs in the fluctuations of a pair of collective modes. As a result of the two factors, perfect squeezing and Einstein–Podolsky–Rosen entanglement in the output occur when the cavity relaxation rates are much larger than in the dispersive case. The mechanism is applicable to a great variety of multilevel systems and has experimental advantages in the cavity QED generation of squeezed and entangled states of light.
We show that Einstein–Podolsky–Rosen (EPR) light entanglement is obtainable via the resonant nonlinear interactions enhanced by electromagnetically induced transparency. A three-level system is used as a unified model, where two metastable states are coupled to each other via microwave, or Raman, or two-photon transition, and the upper metastable state is coupled to the excited state. A pair of inner sidebands is amplified as optical cavity modes via the transition from the excited state to the other metastable state. The analysis is presented by using the dressed-atom squeezed-transformed-mode approach. For a proper ratio of the amplitudes of the applied fields, the sum of the variances for two EPR-like operators approaches zero, which corresponds to EPR entanglement.
We propose an efficient scheme for realizing two-mode squeezing for two cavity modes with an atomic ensemble trapped in the cavity and driven by two classical fields. Through a suitable choice of the driving classical fields, the evolution dynamics of the two cavity modes is decoupled with the atomic system and described by a two-mode squeezing operator. We show that a highly squeezed state can be obtained at the output even with a bad cavity. The required experimental techniques are within the scope of what can be obtained in the BEC-cavity setup.
We explore the quantum entanglement between two collective fields via atomic coherence effects. For three-level atoms in V\mathsf{V}V configuration driven by two applied fields on two-photon resonance, one coherent superposition of the excited states is not excited, which is the counterpart of coherent population trapping. The coherence-induced depopulation makes two cavity fields in each collection combine into a quantum-beat, i.e., equivalently, the difference mode of the two components decouples from the driven atoms. The two sum modes, when they are arranged in the four-wave mixinglike interactions, can be prepared in Einstein-Podolsky-Rosen entangled state. Correspondingly, any two individual fields from different collective modes are entangled with each other. Furthermore, the effects of thermal reservoir and laser linewidths are discussed, and a generalization is given to the case in which each quantum beat involves more than two modes.
We present a scheme to generate unitarily two-mode and four-mode field squeezing in optical cavities with the near-resonantly dressed three-level atoms in the $\mathrm{\ensuremath{\Lambda}}$ configuration. The dressing fields open two coherent population trapping (CPT) windows, within which the atoms stay predominantly in the dark state and yield strong nonlinearities for both the dressing fields themselves and the other applied fields. The two-mode squeeze operator is separated from degrees of freedom of atoms in a common CPT window, and the multimode squeeze operator is segregated in different CPT windows. The resulting two-mode and multimode interaction strengths are at least one order higher than in the previous dispersive schemes, where all fields are far off resonant with the atoms. The present near-resonant scheme is robust to spontaneous emission since atoms are nearly trapped in a long-lived superposition state.
We study multipartite entanglement, the generation of Einstein-Podolsky-Rosen (EPR) states, and quantum steering in a three-mode optomechanical system composed of an atomic ensemble located inside a single-mode cavity with a movable mirror. The cavity mode is driven by a short laser pulse, has a nonlinear parametric-type interaction with the mirror and a linear beam-splitter-type interaction with the atomic ensemble. There is no direct interaction of the mirror with the atomic ensemble. A threshold effect for the dynamics of the system is found, above which the system works as an amplifier and below which as an attenuator of the output fields. The threshold is determined by the ratio of the coupling strengths of the cavity mode to the mirror and to the atomic ensemble. It is shown that above the threshold, the system effectively behaves as a two-mode system in which a perfect bipartite EPR state can be generated, while it is impossible below the threshold. Furthermore, a fully inseparable tripartite entanglement and even further a genuine tripartite entanglement can be produced above and below the threshold. In addition, we consider quantum steering and examine the monogamy relations that quantify the amount of bipartite steering that can be shared between different modes. It is found that the mirror is more capable for steering of entanglement than the cavity mode. The two-way steering is found between the mirror and the atomic ensemble despite the fact that they are not directly coupled to each other, while it is impossible between the output of cavity mode and the ensemble which are directly coupled to each other.