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arXiv:quant-ph/0504140 · Europhysics Letters (EPL)

Coherent population trapping in quantized light field

A. V Taĭchenachev, A. M Tumaĭkin, V. I Yudin

Published Oct 13, 2005• 8 citations
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Abstract

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.

DOI
10.1209/epl/i2005-10277-9

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Journal of Experimental and Theoretical Physics Letters•Jan 1, 2004•1 citation
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.
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 FgtoFeF_g\\to F_eFg​toFe​, including bright transitions FtoF+1F\\to F+1FtoF+1 and F′′toF′′F''\\to F''F′′toF′′ with F′′F''F′′ a half-integer, for which the CPT effect is absent in a classical field.
There presented basic information on coherent population trapping (CPT) and related phenomenon of electromagnetically induced transparence, ‘dark’ and ‘bright’ (anomalous absorption) states is presented. Spectrum transformation is considered in probe field spectroscopy for Λ-scheme in various settings. The close relation is revealed between the effect of CPT in the manifold of magnetic sublevels and the phenomenon of optical pumping (optical orientation and optical alignment). CPT is shown to be generalized to the case of several transitions with a common upper level and with the corresponding number of light fields each being in quasiresonance with its ‘own’ transition.
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.
For jg equals j yields je equals j - 1 and jg equals j yields je equals j optical transitions (where jg, je are the total angular momenta of ground (g) and excited (e) states) previously unknown exact solution of quantum self-consistent problem on resonant atom-electromagnetic field interaction is found. This solution describes arbitrary set of field modes having same uniform elliptical polarization and atoms being in noninteracting with field coherent population trapping (CPT)-state. Some peculiarities of this spontaneous CPT-effect are investigated. We define the geometrical conditions (the relative orientation of light and static fields) for the existence of spontaneous CPT-effect in atoms + quantized field system in the presence of external static magnetic and electric fields.
Coherent population trapping (CPT), under the resonant interaction of elliptically polarized light with atoms having degenerated energy levels, is analytically treated without the use of a specific coordinate frame. Tensors describing dark states are presented in an explicit and invariant form for all atomic transitions, where CPT takes place. A 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.