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

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 à 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.