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Journal of Modern Optics

Two-modeSU(2) andSU(2) schrödinger cat states

Christopher C. Gerry, R. Grobe

Published Jan 1, 1997• 41 citations
Publisher

Abstract

We study the non-classical properties of Schrödinger cat states given as superpositions of two-mode SU(1, 1) and SU(2) coherent states. The SU(1, 1) and SU(2) coherent states themselves have strong non-classical properties and we find that these properties are enhanced at least for some superpositions. We propose a method of generating such states in the context of cavity quantum electrodynamics.

DOI
10.1080/09500349708232898

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We study the non-classical properties of Schrödinger cat states given as superpositions of two-mode SU(1, 1) and SU(2) coherent states. The SU(1, 1) and SU(2) coherent states themselves have strong non-classical properties and we find that these properties are enhanced at least for some superpositions. We propose a method of generating such states in the context of cavity quantum electrodynamics.
We describe the properties of a quantum system prepared in superpositions of classically distinguishable states. These states, often called Schrödinger cat states, are of great interest at present. We discuss how they may be realized in quantum optics using nonlinear interactions and cavity quantum electrodynamics. We first describe the quantum properties of field states in a cavity, and demonstrate the interference properties which characterize superposition states and discuss how fragile they are in dissipative environments. Finally, we review current experimental approaches which may realize these states.
Strong laser-atom interactions can produce highly non-classical states of light by using the process of high-harmonic generation in atoms. When the high-harmonic generation is present, the quantum state of the fundamental mode following the interaction is known as the Schrödinger cat state, which is a superposition of the laser’s initial coherent state and the coherent state with a smaller amplitude that results from its interaction with atoms. Here, we demonstrate that new light states with significantly different Wigner function distributions can be produced by combining two separate Schrödinger cat states. Through the engineering of Schrödinger cat states’ parameters, we are able to produce Wigner functions that exhibit high sensitivity in relation to the system parameter. Our research paves the way for the creation of non-classical light by superposing Schrödinger cat states with application in such as quantum sensing.
In this paper, we first suggest a scheme for the generation of a particular class of Gilmore–Perelomov-type SU(1,1) coherent states, which may be established as nonlinear coherent states. The proposal employs a two-level atom that interacts with a single-mode quantized cavity field (by using an intensity-dependent Jaynes–Cummings model) and at the same time a strong external classical field. The time evolution of the system first leads to the generation of a superposition of SU(1,1) coherent states. Depending on the initial states of the atom and the field which may be appropriately prepared, and also under the conditions in which the atom is detected (in the excited or ground state) after the occurrence of the interaction, the field will be collapsed to arbitrary combinations or a single class of Gilmore–Perelomov-type SU(1,1) coherent states. Then, it is shown that, following a similar procedure, our proposed scheme can successfully generate various superpositions and, in particular, a single class of SU(2) coherent states, too.