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Springer eBooks

Boson Inverse Operators and New Nonclassical States

Anil Roy

Published Jan 1, 1995• 0 citations
Publisher
DOI
10.1007/978-1-4899-1391-3_10

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Using the nonlinear coherent states method , a formalism for the construction of the coherent states associated with ‘ inverse bosonic operators ’ and their dual family has been proposed. Generalizing the approach, the ‘inverse of f -deformed ladder operators’ corresponding to the nonlinear coherent states in the context of quantum optics and the associated coherent states have been introduced. Finally, after applying the proposal to a few known physical systems, particular nonclassical features as sub-Poissonian statistics and the squeezing of the quadratures of the radiation field corresponding to the introduced states have been investigated.
In this paper, we introduce a new family of photon-added as well as photon-depleted q -deformed coherent states related to the inverse q -boson operators. These states are constructed via the generalized inverse q -boson operator actions on a newly introduced family of q -deformed coherent states (Quesne C 2002 J. Phys. A: Math. Gen. 35 9213 ) which are defined by slightly modifying the maths-type q -deformed coherent states. The quantum statistical properties of these photon-added and photon-depleted states, such as quadrature squeezing and photon-counting statistics, are discussed analytically and numerically in the context of both conventional (nondeformed) and deformed quantum optics.
In this paper,we introduce a new nonclassical quantum state,an inverse coordinate operator excited coherent state.By using the IWOP technique,the normally ordering form of inverse coordinate operator and the normalization factor are derived.It is shown that the normally ordering form is related to Hermit polynomial.On the basis of the coherent state representation of the Wigner operator,the Wigner function is also calculated,whose negative property is used to discuss the nonclassical property of the nonclassical quantum state.