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Laser Physics

Entanglement and statistical properties in cavity optomechanics with a single atom

Ye‐Jun Xu, Shuangshuang Wang, Meng-Ran Chen, Qinghong Liao

Published Apr 11, 2019• 7 citations
Publisher

Abstract

Abstract We put forward a proposal to prepare tripartite interplay in a cavity optomechanical system with a two-level atom. We study the dynamical properties of the atomic linear entropy and find that the entanglement between the atom and the subsystem of the field and mechanical resonator can be effectively manipulated by atom coherence. The Mandel parameter is employed to reveal the sub-Poissonian statistics of the optical and mechanical modes. Moreover, we discuss the influence of the system dissipations, including atomic, optical and mechanical modes, on the temporal evolution of the linear entropy and the Mandel parameters.

DOI
10.1088/1555-6611/ab0c91

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Abstract In this paper the interaction of a three-level atom in V -configuration with a two-mode quantized field in cavity optomechanics is studied. To achieve the purpose, we first deduce the effective Hamiltonian and evaluate the explicit time-dependent form of the state vector of the whole system by choosing special initial conditions for atom, field and the oscillatory mirror. Interestingly, we can obtain the time evolution of atomic linear entropy, population inversion, quantum statistics and squeezing, both analytically and numerically. The results show that the entanglement between the atom and the subsystem of field and mirror, and all above-mentioned physical quantities can be appropriately controlled by the initial atom-field state condition, the parameters of cavity optomechanics as well as atom-field coupling strengths. In particular, the appearance of collapse-revival phenomenon in the entanglement and quantum photon statistics, also the full sub-Poissonian statistics in the two modes of field as well as in the mechanical mode of optomechanical system are noticeable features of the work.
We investigate the dynamics of entanglement between two remote, macroscopic, mechanical modes in a model consisting of two cavities, with each cavity containing a two-level atom and having one movable mirror. The results show that the time evolution of entanglement exhibits periodic behavior that does not depend on the atomic coherent angles and that the amount of entanglement increases with increasing atomic coherent angle. A maximally entangled state between mechanical modes can be prepared. We find a simple method for inferring the entanglement properties between two mechanical modes. We propose a potential way to control and manipulate the entanglement.
We have investigated a wide range of nonclassical behavior exhibited by a tripartite cavity optomechanical system comprising a two-level atom placed inside a Fabry–Perot type optical cavity with a vibrating mirror attached to one end. We have shown that the atom’s subsystem von Neumann entropy collapses to its maximum allowed value over a significant time interval during dynamical evolution. This feature is sensitive to the nature of the initial state, the specific form of intensity-dependent tripartite coupling, and system parameters. The extent of nonclassicality of the field is assessed through the Mandel Q parameter and Wigner function. Both entropic and quadrature squeezing properties of the field are quantified directly from optical tomograms, thereby avoiding tedious state reconstruction procedures.
Based on quantum theory, an investigation is conducted on the evolution characteristics of linear entropies of 1) atoms, 2) two cavities and 3) atom-cavity system in the interaction process of two entangled dissipative cavities and a single two-level atom which runs through one of cavities. The effect of the dissipative constant and the coupling strength of interaction between atom and cavity field on all three linear entropies is discussed for the resonant case.The results show that all three linear entropies strongly depend on the dissipative constant of cavity and the coupling strength between cavity field and atoms. Furthermore, the dissipative constant and the strength of interaction between atoms and cavity field affect not only the amplitude of the oscillation of field quantum entropy evolution but also its periodicity.
In the field of optomechanics, one typically studies the interaction of a single mechanical resonator and a single optical cavity mode. In this thesis, we investigate collective quantum effects in optomechanical systems with two or more optical and mechanical modes. First, we study the generation and destruction of entanglement between two mechanical resonators effected by optical cavity fields. We also describe how the optomechanical interaction can be employed to mediate strong coherent coupling and entanglement between a micromechanical membrane and a single atom. Secondly, we show that a configuration with two optical and a single mechanical mode can lead to enhanced nonlinear interactions, which can be exploited for quantum non-demolition measurements of the phonon and photon numbers. Finally, we explore the quantum many-body dynamics of optomechanical arrays. In particular, we research into the transition from a disordered state due to quantum noise to a state with phasecoherent mechanical oscillations. As an intermediate step towards this study, we also investigate the nonlinear classical dynamics of single- and multi-mode optomechanical setups and compare theoretical predictions to experimental data.