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Chinese Physics Letters

Two Methods to Dynamics of Cavityless Optomechanical Systems

Shao-Hua Xiang, Wen Wei

Published Aug 1, 2010• 3 citations
Publisher

Abstract

We present two methods to solve the equation of motion of the cavityless optomechanical system and obtain an explicit formula of the covariance matrix of the evolved state when the initial state is Gaussian. We study the entanglement dynamics of this system initially in the vacuum state. It is shown that bipartite entanglement behaves in a periodic manner. In particular, we can easily generate a genuine three-mode continuous-variable entanglement.

DOI
10.1088/0256-307x/27/8/080304

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We present two methods to solve the equation of motion of the cavityless optomechanical system and obtain an explicit formula of the covariance matrix of the evolved state when the initial state is Gaussian. We study the entanglement dynamics of this system initially in the vacuum state. It is shown that bipartite entanglement behaves in a periodic manner. In particular, we can easily generate a genuine three-mode continuous-variable entanglement.
We use the symplectic transformation of the known linear optical elements to investigate the dynamical evolution of a three-mode cavityless optomechanical system and give explicit formulas for the input and output covariance matrices of the three mode fields when the initial state is Gaussian. Unlike the conventional approaches, the present one does not necessitate solution of the equation of motion of such a system. We study the dynamical behavior of bipartite entanglement in this system when the mirror vibrational mode is initially in a single-mode squeezed vacuum state and each of the two reflected optical sideband modes is in the vacuum state. It is found that the entanglement configuration alternates between a fully separable state and a continuous-variable entangled state during evolution.
In this paper, we quantitatively study the dynamics of the tripartite entanglement of the three-mode Gaussian state in a cavity-free optomechanical system. After deriving the explicit form of the evolved state matrix covariance, we elucidate in detail the evidence of entanglement monogamy in different mode partitions, based on Coofman–Kundu–Wotters inequalities, using the Gaussian Contangle quantifying bipartite entanglement. Next, we focus on the genuine tripartite entanglement quantified by means of the Residual Gaussian Contangle.
We discuss the generation and evolution of entangled light in a correlated spontaneous emission laser. The master equation for the two-mode field in a cavity is derived and solved analytically. The time-dependent characteristic function in the Wigner representation for the two-mode field is obtained. It shows that the two-mode field in the cavity evolves in a two-mode Gaussian state. The entanglement degree of the two-mode field in the cavity increases initially, then decreases, and finally vanishes as the field evolves from an initial vacuum. The period of the entanglement is extended as the intensity of the driving field is increased. It is found that the entanglement still exists even when the two-mode squeezing disappears. During the entanglement period, the intensity of the field is amplified. The entanglement for the initial field being a two-mode squeezed vacuum and the entanglement of the output field are also discussed.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment. Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the generation and evolution of entanglement in terms of the covariance matrix for an arbitrary Gaussian input state. For some values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation or entanglement collapse (entanglement sudden death) take place or even a periodic collapse and revival of entanglement. We show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, a description of the continuous-variable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment was given. Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, the generation and evolution of entanglement in terms of the covariance matrix for an arbitrary Gaussian input state was described. For some values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation, entanglement sudden death or a periodic collapse and revival of entanglement take place. The time evolution of the logarithmic negativity, which characterizes the degree of entanglement of the quantum state was analyzed.
Abstract Nonclassical states are an important class of states in quantum mechanics, particularly for applications in quantum information theory. Optomechanical systems are invaluable platforms for exploring and harnessing these states. In this study, we focus on a mirror-in-the-middle optomechanical system. In the absence of losses, a separable state, composed of the product of coherent states, evolves into an entangled state. Furthermore, we demonstrate that generating a two-mode Schrödinger-cat state depends on the optomechanical coupling. Additionally, when the optical modes are uncoupled from the mechanical mode, we find no entanglement for certain nonzero optomechanical coupling intensities. We exactly solve the Gorini–Kossalokowinki–Sudarshan–Lindblad master equation, highlighting the direct influence of the reservoir on the dynamics when mechanical losses are considered. Then, we discuss vacuum one-photon superposition states to obtain exact entanglement dynamics using concurrence as a quantifier. Our results show that mechanical losses in the mirror attenuate the overall entanglement of the system.