Nonlinear coherent state of an exciton in a wide quantum dot

Abstract

In this paper, we derive the dynamical algebra of a particle confined in an infinite spherical well by using the f -deformed oscillator approach. We consider an exciton with definite angular momentum in a wide quantum dot interacting with two laser beams. We show that under the weak confinement condition, and quantization of the center-of-mass motion of exciton, the stationary state of it can be considered as a special kind of nonlinear coherent states which exhibits the quadrature squeezing.

A single trapped ion in a finite range trap

“…Such kind of the Paul traps have considered recently [18]. It is shown that [21], each quantum system which has an unequal spaced energy spectrum can be considered as an f-deformed oscillator. Therefore, according to the energy spectrum of the MPT potential, this system can be considered as an f-deformed oscillator [24].…”

“…x n is the frequency of the ion transition between energy levels of the finite range trap. Because energy spectrum of the trap depends on the energy level numbers and we consider a transition between specific side-band levels, hence, we show the transition frequency with definite dependence to n. In the above Hamiltonian,Ĥ int ðtÞ;x is the operator of the center-of-mass position and may be defined as [21] x ¼ g k l ð þ y Þ; ð14Þ…”

“…It is worth to note that the confining model potential which is considered here is used for other confined physical systems, such as the Bose-Einstein condensate [19], and carriers in a quantum well [20]. The f-deformed oscillator approach where we have considered here, has been used before for some other confined systems [21]. This paper presents a method to describe dynamics of an ion confined in a finite range trap.…”

Preparation of a nonlinear coherent state of the mechanical resonator in an optomechanical microcavity

“…The generation schemes of the NCS are explored in some other literatures, e.g. a single-atom laser [17], a micromaser under the intensity-dependent Jaynes-Cummings model [24], an exciton in a wide quantum dot [25], and a trapped ion [21,26]. The stationary state of a single-atom laser is shown to be a phase-averaged NCS and the interaction-induced transition probabilities of the single-atom laser effectively depend on the field intensity [17].…”

Nonclassical properties of a particle in a finite range trap: The f-deformed quantum oscillator approach

“…This approach has been accomplished, for instance, in the study of the stationary states of the center-of-mass motion of an ion in the harmonic trap [9] and under effects associated with the curvature of physical space [14], the influence of the spatial confinement on the center-of-mass motion of an exciton in a quantum dot [15], the influence of atomic collisions and the finite number of atoms in a Bose-Einstein condensate on controlled manipulation of the nonclassical properties of radiation field [10], some nonlinear processes in high intensity photon beam [6], intensity-dependent atom-field interaction in absence and in presence of nonlinear quantum dissipation in a micromaser [16] and finally, incorporating the effects of interactions among the particles in the framework of the q-deformed algebra [17].…”