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Australian Journal of Physics

Preparation of Motion Entangled Coherent States of Two Cavity Mirrors

Shi‐Biao Zheng

Published Apr 27, 2001• 0 citations
Publisher

Abstract

A scheme is proposed for the generation of entangled coherent states of two spatially separated cavity mirrors. In the scheme, a two-level atom is sent through two cavities, each having a movable mirror, to produce an entangled photon state for the cavity fields. Then the optomechanical effects further entangle the mirror motions with the cavity fields. A second two-level atom, passing through the cavities, is state-selectively measured, which reduces the mirror motions to an entangled coherent state.We also show how to distinguish such an entangled state from a classical mixture.

DOI
10.1071/ph00017

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A scheme is proposed for the generation of entangled coherent states of two spatially separated cavity mirrors. In the scheme, a two-level atom is sent through two cavities, each having a movable mirror, to produce an entangled photon state for the cavity fields. Then the optomechanical effects further entangle the mirror motions with the cavity fields. A second two-level atom, passing through the cavities, is state-selectively measured, which reduces the mirror motions to an entangled coherent state.We also show how to distinguish such an entangled state from a classical mixture.
We describe how a quantum system composed of a cavity field interacting with a movable mirror can be utilized to generate a large variety of nonclassical states of both the cavity field and the mirror. First we consider state preparation of the cavity field. The system dynamics will prepare a single mode of the cavity field in a multicomponent Schr\"odinger-cat state, in a similar manner to that in a Kerr medium. In addition, when two or more cavity modes interact with the mirror, they can be prepared in an entangled state, which may be regarded as a multimode generalization of the even and odd coherent states. We show also that near-number states of a single mode may be prepared by performing a measurement of the position of the mirror. Second we consider state preparation of the mirror and show that this macroscopic object may be placed in a Schr\"odinger-cat-like state by a quadrature measurement of the light field. In addition, we examine the effect of the damping of the motion of the mirror on the field states inside the cavity and compare this with the effect of cavity field damping.
We propose a scheme for the generation of two-mode entangled states between two spatially separated cavities. It utilizes a two-level atom sequentially coupling to two high-Q cavities with strong classical driving fields. By suitably choosing the intensities and detunings of the fields and precisely controlling the dynamics, entangled coherent states and Bell states can be produced between the modes of the two cavities. These entangled states should have applications in quantum information processing.
We propose a novel scheme for generating the entanglement of two oscillating mirrors in an optomechanical system via a flying atom. In this scheme, a two-level atom, in an arbitrary superposition state, passes through an optomechanical system with two oscillating cavity-mirrors, and then its states are detected. In this way, we can generate the entangled states of the two oscillating mirrors. We derive the analytical expressions of the entangled states and make numerical calculations. We find that the entanglement of the two oscillating mirrors can be controlled by the initial state of the atom, the optomechanical coupling strength, and the coupling strength between the atom and the cavity field. We investigate the dynamics of the system with dissipations and discuss the experimental feasibility.
Quantum entanglement and quantum superposition are fundamental properties of quantum mechanics, which underline quantum information and quantum computation. Preparing quantum states in the macroscopic level is both conceptually interesting for extending quantum physics to a broader sense and fundamentally important for testing the validity of quantum mechanics. In this dissertation, schemes of preparing macroscopic entanglement and macroscopic superposition states in cavity optomechanics are studied using the unitary evolution method in the nonlinear regime or Lyapunov equation in the linearized regime. Quantum entanglement and quantum superposition states can be realized using experimentally feasible parameters with the proposals in this dissertation.\nFirstly, a scheme of entangling two movable end mirrors in a Fabry-Perot cavity that are coupled to a common single photon superposition state is studied. It is shown that strong entanglement can be obtained either in the single-photon strong coupling regime deterministically or in the single-photon weak coupling regime conditionally.\nSecondly, a scheme of entangling two movable end mirrors, that are coupled to two-mode entangled fields generated from a correlated-emission laser is investigated. By tuning the input driving laser frequencies at the Stokes sidebands of the cavity, the radiation-pressure coupling can be linearized as an effective beam-splitter-like interaction. Hence entanglement can be transferred from the two-mode fields to the two mechanical mirrors. Macroscopic entanglement between macroscopic mirrors persists at temperature ~ 1K.\nThirdly, a scheme of creating macroscopic quantum superpositions of a mechanical mirror via periodically flipping a photonic qubit is proposed. Quantum superposition states of a mechanical mirror can be obtained via the nonlinear radiation coupling with a single-photon superposition state. However, the difference between two superposed mechanical states is very small due to the weak single-photon coupling rate available in experiment. By periodically flipping the photonic qubit state, the difference can be magnified. It is shown in detail that this scheme is experimentally feasible under current technology.