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arXiv:0908.3045 · Journal of Optics B Quantum and Semiclassical Optics

Squeezing evolution with non-dissipativeSU(1,1) systems

Faisal A A El-Orany, S S Hassan, M Sebawe Abdalla

Published Sep 15, 2003• 10 citations
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Abstract

We investigate the squeezed regions in the phase plane for non-dissipative dynamical systems controlled by SU (1,1) Lie algebra. We analyse such a study for the two SU (1,1) generalized coherent states, namely the Perelomov coherent state and the Barut–Girardello coherent state.
DOI
10.1088/1464-4266/5/5/004

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We examine the time-dependent squeezing of fluctuations associated with the atomic coherent state of the SU (2) Lie algebra. Based on the exact solutions for a non-dissipative SU (2) system, regions of squeezing and its symmetric/asymmetric patterns are investigated in the cases of weak and strong coupling and for the resonance condition. For a spontaneously damped two-level atom, transient squeezing occurs in the atomic polarization components with initial atomic coherent state |θ,ϕ⟩, with asymmetric structure with respect to the state-of-zero atomic inversion. The rapidly vanishing squeezed regions for <θ<π are accompanied by entropy reduction.
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Abstract A new type of pair quantum states is introduced. Which can be considered as pair Barut-Girardello coherent states. It is an eigenstate of the operators K − ab = K − a K − b and K 3 a − K 3 b . We construct these eigenstates and generation scheme is proposed in terms of two mode state described in terms of su(1, 1) Lie algebra , We employ the second-order correlation function to discuss some non-classical properties,and violations of Cauchy-Schwarz inequalities. The phenomenon of squeezing is examined , squeezing is clear and Q-functions support that. Finally the phase distribution in the framework of an appropriate Pegg and Barnett formalism is considered and discussed.
The Robertson–Schrödinger uncertainty relation for two observables A and B is shown to be minimized in the eigenstates of the operator λA+iB, λ being a complex number. Such states, called generalized intelligent states (GIS), can exhibit arbitrarily strong squeezing of A or B. The time evolution of GIS is stable for Hamiltonians which admit linear in A and B invariants. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the spin CS are a subset of SU(2) GIS. CS for an arbitrary semisimple Lie group can be considered as a GIS for the quadratures of the Weyl generators.