Morse-like squeezed coherent states and some of their properties

Abstract

Using the f-deformed oscillator formalism, we introduce two types of squeezed coherent states for a Morse potential system (Morse-like squeezed coherent states) through the following definitions: i) as approximate eigenstates of a linear combination of f-deformed ladder operators and ii) as deformed photon-subtracted coherent states. For the states thus constructed we analyze their statistical properties, their uncertainty relations, and their temporal evolution on phase space.

Qubit-nonlinear-oscillator systems: from the moderate-coupling limit to the ultrastrong-coupling regime

“…Notice that the harmonic-oscillator algebra is retrieved in the limit f (n) → 1. Incidentally, this algebraic framework has formerly been applied to cope with the problem of constructing approximate coherent states defined either as eigenstates of the deformed annihilation operator or by application of a displacement-like operator to the ground state of anharmonic systems, such as the Morse [28,29,30] and symmetric Pöschl-Teller potentials [31]. The latter ones are the class of systems that will be of interest to us and, at this point, we briefly digress to introduce them within their corresponding physical space.…”

“…As regards the oscillator system characterized by the confining potentials V ± (x), x and p are, respectively, the position and momentum operators; µ ± is the respective effective mass; and the conventional coordinate-coordinate coupling between the subsystems involved has also been stated [39,40], with g characterizing the strength of it. Making use of the algebraic equivalent of (30) given by ( 14), together with the coordinate representation of the respective oscillator written in terms of the deformed ladder operators (26), and retaining only up to the first order terms in the expansion, allows us to put forward the approximate Hamiltonian model of the whole system…”

Markovian master equation for nonlinear systems

“…It is worth mentioning that the free evolution of such a system has already been analyzed in Refs. [19,20,21,22] in terms of its nonlinear coherent states. It was first found in Ref.…”

“…The wide applicability of this nonlinear algebraic formalism has been demonstrated in a manifold of circumstances. Among the most representative, we can quote the paper of Man'ko et al [6] about the Weyl-Wigner-Moyal representation for foscillators, in which the well-known Kerr-like nonlinearity of media was taken into account; the description of the centerof-mass motion of a laser-driven trapped ion [7][8][9]; generalizations of the Jaynes-Cummings model in which the interaction between a two or three-level atom and the radiation field is nonlinear in the field variables [10][11][12], as well as including Kerr type nonlinearities [13][14][15]; the relation between the deformation function of the f-deformed oscillator and the two-dimensional harmonic oscillator on the flat space and on the sphere [16]; and generalizations of coherent states for confining systems such as the symmetric Pöschl-Teller potentials [17,18] and the Morse potential [20][21][22][23][24][25][26].…”

Phase state and related nonlinear coherent states

“…Second, coherent states have proved useful in describing the quantum electromagnetic field since their introduction to quantum optics by Sudarshan [13] and Glauber [14]; we owe their inception as minimum uncertainty product states in quantum mechanics to Schrödinger [15]. Some sets of nonlinear coherent states of the field have been brought forward in quantum optics recently [16][17][18][19][20] and, here, we want to provide a couple of nonlinear coherent states related to the exponential phase operator a là Perelomov [21] and relate them to operators that are diagonal in those nonlinear coherent bases a là Barut and Girardello [22]. Finally, we bring forward the propagation of classical light in arrays of coupled waveguides as an example of how these nonlinear coherent states provide a simple solution to their classical optics analogues.…”