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Acta Physica Sinica

Preparation of controllable three-mode entangled coherent states

Qu Zhao-Jun, Xiao‐Guang Ma, Xu Xiu-Wei, Chuan‐Lu Yang

Published Jan 1, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.61.034206

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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.
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.
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 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.
Cavity quantum electrodynamics is the intersection of quantum physics and microcavity optics research. In this paper, we presented a two-mode cavity coupled to a classical field driven by N three-level atoms to prepare entangled coherent states based on cavity QED. In this scheme, we adopt the interaction between the three-level atoms and the two-mode optical cavity, The initial state of one optical field is an odd-even coherent state, while the initial state of another optical field is a coherent state. After considering the time evolution of the initial states with the system, we obtained the specific form of the time evolution of the quantum states and prepared the entangled coherent state successfully. We discussed and analysed some of the nonclassical properties of the optical field and quantum states, including the second-order correlation function and the Wigner function. The results show that when calculating the second-order correlation function, the photons are found to exhibit a sub-Poisson distribution at some points in time. In addition, when observing the Wigner function of the quantum states evolving with time, it is found that there is a negative part of the Wigner distribution at some moments, which implies that the quantum state exhibits nonclassical properties at these certain moments.