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Chinese Journal of Quantum Electronics

Preparation of Schr dinger cat states in a cavity with medium and a moving mirror

Qu Zhao-Jun, Liu Sheng-dian, Chuan‐Lu Yang, Xiao‐Guang Ma

Published Jan 1, 2010• 0 citations
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Abstract

For a system composed of a cavity with Kerr medium, a movable mirror (treated as a quantum harmonic oscillator with frequencyω_m and a single mode field in the cavity, the time evolution operator and its transformation of the system are given. Time evolution of the system state is obtained with full quantum theory. State of the cavity field at the time of the mirror back to its original state is discussed, and a variety of multicomponent Schrdinger cat states which are different from those in the published literature are obtained, which is significant for the investigation of the nature and applications of the Schrdinger cat states.

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Journal of Guangxi Normal University•Jan 1, 2015•0 citations
For a system composed of a cavity with Kerr medium, a movable mirror (treated as a quantum harmonic oscillator with frequencyω_m and a single mode field in the cavity, the time evolution operator and its transformation of the system are given. Time evolution of the system state is obtained with full quantum theory. State of the cavity field at the time of the mirror back to its original state is discussed, and a variety of multicomponent Schrdinger cat states which are different from those in the published literature are obtained, which is significant for the investigation of the nature and applications of the Schrdinger cat states.
For a system composed of a cavity with a movable mirror(treated as a quantum harmonic oscillator with frequency ωm) and a single mode field in the cavity,the time evolution operator of the system is given,which is obtained by means of full quantum theory in the Schrdinger picture. The result shows that the state of the cavity field at the moment can give a variety of multicomponent Schrdinger cat states when the mirror returns to its original state,which are different from those in the published literature,and the desired Schrdinger cat state can be chosen by adjusting the frequency of the single mode cavity field.
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.
It has great meaning to study the effect of a moving mirror in a cavity on the dynamic behavior of a two-level atom injected in the cavity. In this paper, for a system composed of a two-level injected atom and a single-mode field and a moving mirror in the cavity (the moving mirror to be regarded as a quantum harmonic oscillator with frequency ωm), the time-evolution of its state is obtained by means of complete quantum theory in the interaction picture. The time-evolution of the atomic population is derived on the basis of former investigations. It is found that the atomic population oscillates near its initial value. The result shows that the periodic motion of the mirror has a periodic effect on the atomic population.
For a system composed of a three-mode cavity field interacting with a movable mirror, the time evolution operator of the system and its transformation are given, and the time evolution of the system state is obtained by means of quantum theory. The result shows that the state of the three-mode cavity field is in an entangled coherent state when the mirror returns to its original state, and the preparations of different entangled coherent states can be controlled. Nine different three-mode entangled coherent states are given, and the different phase factors of these states indicate the different reactions between the field and the movable mirror, which provides an important theoretical basis for the experimental preparations of controllable entangled coherent states.
This paper investigates a coupled cavity optomechanical system consisting of two Fabry-Perot cavities and the two cavities are coupled via an optical fiber.Every cavity is made of one fixed mirror and a movable mirror,and the movable mirror can be regarded as a mechanical oscillators.Meanwhile,the two cavity modes are driven by classical laser fields.So,the interaction is inevitable between cavities,cavity and moving mirror,cavity and classical field.Firstly,in order to eliminate the two cavity fields,an effective Hamiltonian of the two phonon modes is derived by means of picture transformation,adiabatic eliminating,and rotating wave approximation ignoring the high frequency items,etc.Secondly,if the two mechanical oscillators initially are in coherent states,the coupled mechanical oscillators can be used to transmit state.Finally,in order to verify the analytical result,the fidelity of quantum state is numevically simulated,the result shows that the quantum state can be transferred periodically between the two mechanical oscillators,which is the same as the analytical result.