Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator

Abstract

Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.

Graphene coherent states

“…(18), where Ψ n are the eigenfunctions of the Dirac-Weyl Hamiltonian (see Eq. (2)), for the graphene coherent states we have that…”

“…As we shall see below, under particular physical conditions, a problem similar to that considered in [18] arises naturally. Due to this, it seems obvious the need to build up the coherent states for the graphene, and then to analyze their properties.…”

Multiphoton supercoherent states

“…These states have been studied in some previous works [20,[23][24][25], and they can be used also in generalized Jaynes-Cummings models [26], for the construction of superalgebras [27] and Q-balls [28,29], among other applications. Taking into account the previous ideas, our goal in this article is to extend the construction of the multiphoton coherent states for the supersymmetric harmonic oscillator, i.e., to build the multiphoton supercoherent states for the special SAO arising from (6) by taking k 1 = k 4 = 1, k 3 = 0 and to analyze then some of their physical properties.…”

“…k i ∈ C being arbitrary parameters. Despite its generality, this form is not unique (as discussed in [20,[23][24][25]). The previous two proposals are recovered either by taking k 1 = k 4 = 1 and k 2 = k 3 = 0, which leads to the most obvious diagonal SAO, or through the choice k 1 = k 2 = k 4 = 1 and k 3 = 0, that produces the simplest non-diagonal SAO [20,23].…”

“…These states have been studied in some previous works [20,[23][24][25], and they can be used also in generalized Jaynes-Cummings models [26], for the construction of superalgebras [27] and Q-balls [28,29], among other applications.…”