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Journal of Experimental and Theoretical Physics Letters

Generalized dark states in the system “Bose atoms and quantized field”

А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin

Published Jan 1, 2004• 1 citation
Publisher

Abstract

Three new classes of dark states describing the coherent population trapping effect in a quantum system of resonantly interacting Bose atoms and electromagnetic field are presented.
DOI
10.1134/1.1690353

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A full quantum treatment of coherent population trapping (CPT) is given for a system of resonantly coupled atoms and electromagnetic field. We develop a regular analytical method of the construction of generalized dark states (GDS). It turns out that GDS do exist for all optical transitions F g → F e , including bright transitions F → F + 1 and F '' → F '' with F '' a half-integer, for which the CPT effect is absent in a classical field. We propose an idea to use an optically thick medium with a transition F '' → F '' with F '' ⩾ 3/2 a half-integer as a "quantum filter", which transmits only a quantum light with limited number of photons. Such a quantum filter can be used as a deterministic source of Fock's state of light.
The coherent population trapping (CPT) under resonance interaction of elliptically polarized light, with atoms having degenerated energy levels, is analytically treated in an invariant way, without using a specific coordinate frame. Tensors describing dark states are found in an explicit and invariant form for all atomic transitions, where CPT takes place. The correspondence between elliptical polarization vectors and pairs of unit spinors is established. It is shown that all dark states in the problem under consideration, can be constructed from these spinors, by taking multiple tensor products. In the case of an integer angular momentum, this general construction is reduced to a multiple tensor product of vectors. A general significance and some applications of these results are indicted.