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Journal of Optics B Quantum and Semiclassical Optics

Macroscopic entangled states

В. Н. Горбачев, Alexander Ya. Kazakov, Andrew I. Trubilko

Published Oct 23, 2004• 1 citation
Publisher

Abstract

The interaction between an ensemble of two-level identical atoms and three-mode light when one of the modes is classical and its Rabi frequency far exceeds the effective Rabi frequencies of the remaining quantized modes is considered. An effective Hamiltonian that describes a process like non-degenerate down conversion is found and the statistics of the quantized modes is discussed with the use of an exact solution of the Schrodinger equation for a field in the Fock–Bargmann representation. It is found that the occupation number of each quantized mode can depend exponentially on the number of atoms and the light state may be squeezed. The squeezing obtained is nearly perfect and results in a continuous analogue of the maximally entangled Einstein–Podolski–Rosen state of the light with a macroscopically large number of photons.

DOI
10.1088/1464-4266/6/12/006

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The interaction between an ensemble of two-level identical atoms and three-mode light when one of the modes is classical and its Rabi frequency far exceeds the effective Rabi frequencies of the remaining quantized modes is considered. An effective Hamiltonian that describes a process like non-degenerate down conversion is found and the statistics of the quantized modes is discussed with the use of an exact solution of the Schrodinger equation for a field in the Fock–Bargmann representation. It is found that the occupation number of each quantized mode can depend exponentially on the number of atoms and the light state may be squeezed. The squeezing obtained is nearly perfect and results in a continuous analogue of the maximally entangled Einstein–Podolski–Rosen state of the light with a macroscopically large number of photons.
The simultaneous interaction of N two-level atoms with a quasi-resonant classical field and two quantized modes is considered under the assumption that the Rabi parameter of the classical mode substantially exceeds the effective Rabi parameters of the quantized modes. It is shown that, in a certain domain of the parameters, the population of the quantized modes exponentially depends on time and the number N . At certain instants of time, the states of the quantized modes prove to be close to the totally entangled state.
The light squeezing effects in the system of two identical two-level atoms in the Bell state interacting with the two-mode entangled coherent states field are investigated by means of Schrdinger equation solution and numerical calculations.The results show that light squeezing effects not only depends on the mean photon numbers and atomic initial state but also the degree of entanglement of the two-mode entangled coherent state optics field,whereas the coupling between two atoms does not affect the light squeezing effects.The light squeezing effects does not appear for a special kind of Bell state |β11〉,however there can appear the light squeezing effects under some conditions for the other three Bell states.
Abstract The dynamics of an atom of three levels in Λ configuration interacting with a quantized field of two modes in a cavity is studied within the rotating wave approximation by considering experimental values of accessible hyperfine levels of alkali atoms. The Hamiltonian model is constructed on the basis of the direct product of the atomic states with Fock states of light. This simplified basis allows us to generalize the state of light to any quantum field. The interaction term of the Hamiltonian restricts the system to a 3D Hilbert space. The system’s time evolution results show some similarities with the effective two-level system, such as the presence of collapses and revivals and the atom-field entanglement. By an analysis of the statistics of the photons, we show that when the three-level atom is interacting with a coherent field of two modes, it is possible to control experimentally the statistics of the field to be super-Poissonian or sub-Poissonian by the choice of the initial atomic state.
In this paper, we study the interaction between a two-level atom and a three types of nonlinear interaction of two modes, two as a degenerate two photon and the third of the converter form. The solution to the Schrodinger equation is obtained exactly under a certain specific condition. By using this solution we discuss numerically the atomic inversion, the degree of entanglement through the atomic Wehrl entropy, the geometric phase entropy for chosen values of the detuning and coupling parameters. Statistical properties of the investigated system is discussed by the evolution of the Mandel parameter.