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Journal of Physics A Mathematical and Theoretical

Fourier transform in multimode systems in the Bargmann representation

Chao Lei, Apostol Vourdas

Published May 22, 2007• 0 citations
Publisher

Abstract

A Fourier transform in a multimode system is studied, using the Bargmann representation. The growth of a Bargmann function is shown to be related to the second-order correlation of the corresponding state. Both the total growth and the total second-order correlation remain unchanged under the Fourier transform. Examples with coherent states, squeezed states and Mittag?Leffler states are discussed.

DOI
10.1088/1751-8113/40/23/013

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A Fourier transform in a multimode system is studied, using the Bargmann representation. The growth of a Bargmann function is shown to be related to the second-order correlation of the corresponding state. Both the total growth and the total second-order correlation remain unchanged under the Fourier transform. Examples with coherent states, squeezed states and Mittag?Leffler states are discussed.
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By using the localized character of canonical coherent states, we give a straightforward derivation of the Bargmann integral representation of the Wigner function ( W ). A non-integral representation is presented in terms of a quadratic form W ∝ V † F V , where F is a self-adjoint matrix whose entries are tabulated functions and V is a vector depending, in a simple recursive way, on the derivatives of the Bargmann function. Such a representation may be of use in numerical computations. We discuss a relation involving the geometry of the Wigner function and the spatial uncertainty of the coherent state basis we use to represent it.