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The Squeezing Operator and the Squeezing States of Superspace

Ma Ai-Qun, Yan Changzhi, Shi Weichun, Lu Qiquang

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

In this paper ,the unitary squeezing operator of 'superspace' is introduced and by making this operator act on the supercoherent state, the squeezing supercoherent states are obtained, then come out the four orthonormalization eigenstates of the square of annihilation operator A of the supersymmetry harmonic oscillator, and their squeezing character is also studied.

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In this paper ,the unitary squeezing operator of 'superspace' is introduced and by making this operator act on the supercoherent state, the squeezing supercoherent states are obtained, then come out the four orthonormalization eigenstates of the square of annihilation operator A of the supersymmetry harmonic oscillator, and their squeezing character is also studied.
We discuss the superoscillators in thc supersymmetric quantum systems, and give the solution to the system. By making use of the annihilation and creation operators and their q -deformed operators, we also give the q -deformed quantum harmonic oscillator model in the supersymmetric quantum systems. The q -supercoherent states associated with the q -deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated. The uncertainty relations for q -supercoherent states are discussed as well.
The authors present the supercoherent states. They are introduced as the eigenstates of the supersymmetric annihilation operator of the quantum mechanical supersymmetric harmonic oscillator. They have a compact expression in terms of the standard (bosonic) coherent states. For each value of the complex parameter z there are two linearly independent orthogonal supercoherent states. One of them has pure fermionic character and is the more classical, while the other is fully supersymmetric (i.e. the mean value of the Klein operator when the system is set in this state vanishes). There are no purely bosonic supercoherent states. The supercoherent fermionic states saturate both the Heisenberg uncertainty relation and the new entropic uncertainty recently introduced by Deutsch (1983), while the supersymmetric ones almost (but not exactly) make it. They give a classical (or almost classical) mean value for the energy of the system and do not spread along their time evolution.
A general approach is presented for constructing coherent states for supersymmetric systems. It uses Rogers's supermanifold formulation of supergroups to extend the group-theoretic method. Supercoherent states are explicitly obtained for the supersymmetric harmonic oscillator. They are shown to be eigenstates of the supersymmetric annihilation operator and to be minimum-uncertainty states. Two more-complex situations with extended physical supersymmetries are also considered: an electron moving in a constant magnetic field, and the electron-monopole system. The supercoherent states for these systems are found using super Baker-Campbell-Hausdorff relations and their interpretation is elucidated.
A displacement operator for a subset of the supercoherent states is found. It is also shown that a diagonal version of the squeezing operator reduces the fluctuations of one of the quadratures, but the reduction is not enough to go below the standard quantum noise level. New states are found, which are minimum uncertainty for the new operators X and P, and lead to coherence and squeezing, in the sense of equal fluctuations in the two quadrature and reduction in one of them, respectively. Moreover, these states are associated with the model of Jaynes and Cummings (1963) in the strong-coupling limit.