Photon-added BarutGirardello like coherent states of time-dependent Landau problem

TL;DR

This paper extends the analysis of a time-dependent Landau problem by constructing Barut-Girardello coherent states, analyzing their properties, and demonstrating their sub-Poissonian statistics and the effects of photon addition.

Contribution

It introduces photon-added Barut-Girardello coherent states for the time-dependent Landau problem and analyzes their statistical and mathematical properties.

Findings

States are sub-Poissonian in nature.

Photon addition enhances statistical properties.

States satisfy Klauder's criteria for coherent states.

Abstract

Recently, we have determined the spectrum and the wave functions of the Hamiltonian of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field[J. Math. Phys. 56, 072104 (2018)]. In the present paper we extend the study of this model that we name the time-dependent Landau problem into the context of coherent states. By means of the traditional factorization method of the eigenfunctions of this system expressed in terms of the generalized Laguerre polynomials, we derive the generators of the su(1,1) Lie algebra and we construct the coherent states a la Barut-Girardello. These states are shown to satisfy the Klauder's mathematical requirement to build coherent states and some of their statistical properties are calculated and analyzed. We find that these states are sub-Poissonian in nature. We show that, addition of photons from these coherent states, increases the statistical properties and changes the mathematical properties of these states.