Quantum-Optical States in Finite-Dimensional Hilbert Space. I. General Formalism

Quantum-Optical States in Finite-Dimensional Hilbert Space. II. State Generation

“…Clearly, this result resembles that for a two-level atom in an external field [34] and the dynamics of the system exhibits well-known oscillatory behavior. This result is identical to that derived for the simplest case (i.e., for N = s + 1 = 2) of the FD generalized coherent states discussed by us in the first part of this work [1]. Of course, one should keep in mind that the set of Eqs.…”

“…We shall concentrate on the states proposed by Bužek et al [2] and further discussed by Miranowicz et al [3,23], where both the Glauber displacement operator and the states are defined in the FD Hilbert space [1]. The method of generation discussed here is based on the quantum systems containing a Kerr medium represented by nonlinear oscillator.…”

“…As it was mentioned in the first part of this study [1], the finite-dimensional (FD) quantum-optical states have been a subject of numerous papers. For instance, various kinds of FD coherent states [2]- [6], FD Schrödinger cats [5,6,7], FD displaced number states [5], FD phase states [8], FD squeezed states [9,10] were studied by many authors.…”

Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

“…We have already noted that once a tomogram is obtained for a finite dimensional system, it is possible to transform it to obtain the Wigner function for the system, and vice verse, but in an experiment we obtain tomograms. A lot of work has been devoted to the study of Wigner functions for finite dimensional systems [7,[72][73][74]. Some efforts have also been made to study tomograms for finite dimensional coherent states [7,8,74].…”

Kerr nonlinear coupler and entanglement

“…As a consequence, we can expect that in the evolution of the system many of the states corresponding to great number of photons will be involved. However, we can overcome this difficulty by applying the nonlinear quantum scissors method discussed in [24] (for the discussion concerning quantum states defined in finite-dimensional Hilbert spaces and the methods of their generation see the review papers [25,26] and the references cited therein). Namely, it is seen from the form ofĤ N L that this Hamiltonian produces degenerate levels of the energy equal to zero, corresponding to the following four states:…”