Polynomial deformations of the Lie algebrasl(2) in problems of quantum optics

Karasev, V. P.

doi:10.1007/bf01015889

Cited by 15 publications

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“…Squeezed or nonclassical states in this case can be defined by the inequality (21) for any of the components α = x, y. The mean values of the variances of the operators are expressed in terms of steady state atom-field means by the following simple relation:…”

Section: Squeezed States Of a Collective System On The Basis Of The Cmentioning

confidence: 99%

“…The descrip tion of such systems by polynomial algebras obtained by a deformation of the original angular momentum algebra su(2) is given in [20], where the authors inves tigated the interaction between an atomic ensemble localized in a microcavity and an optically forbidden atomic transition under the conditions of combination resonance between external electromagnetic fields and the quanta of the cavity mode. The concept of a poly nomial algebra in quantum optics was introduced in [21] and, combined with the concept of quasispin [22], was used to introduced the concept of a polariza tion scalar light [23] and for the description of polar ization quantum tomography [24] and polarization transformations of multimode light fields [25]. Poly nomial algebras are also applied to the description of collective cluster states [26].…”

Section: Introductionmentioning

confidence: 99%

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Dual squeezed states in an atom-photon cluster and their manifestations

Trubilko

2012

J. Exp. Theor. Phys.

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The general kinetic equation for an isolated two level atom and a high Q cavity mode in a heat bath exhibiting quantum correlations (entangled bath) is applied to the analysis of the squeezed states of the collective system. Two types of collective operators are introduced for the analysis: one is based on bosonic commutation relations, and the other, on the commutation relations of the algebra obtained by a polynomial deformation of the angular momentum algebra. On the basis of these relations, formulas for observables are constructed that identify squeezed states in the system. It is shown that, under certain conditions, the collec tive system exhibits dual squeezing within the relations for boson operators, as well as for the operators con structed from the angular momentum algebra. Such squeezing is demonstrated under a projective measure ment of an atom and for an entanglement swapping protocol. In the latter case, when measuring two initially independent atomic systems, depending on the type of measurement, two cavity modes collapse into a non separable state, which is described either by a nonseparability relation based on boson operators or by a rela tion based on the operators of the algebra of the quasimomentum of the collective system consisting of these two modes.

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Section: Squeezed States Of a Collective System On The Basis Of The Cmentioning

confidence: 99%