Method of pseudo-coherent states in nonlinear quantum systems

Ioan Zaharie, Dušan Popov

The aim of this work is to construct nonlinear coherent states of the pseudo-harmonic oscillator and to analyze some of its properties. The pseudo-harmonic potential can be viewed as an intermediate case between the harmonic and inharmonic potentials. The fact allows the implementation (with notable results), for inharmonic potentials, of some methods well known for harmonic potentials. An example is represented by the construction of nonlinear coherent states, which in the case of harmonic oscillator has found a lot of applications.

J. Récamier, M. Gorayeb, Wolf Luis Mochán +1 more

R. Román-Ancheyta, J. Récamier

Jaewan Kim, Juhui Lee, Se-Wan Ji +3 more

Optical coherent states can be interpreted as d-dimensional quantum systems, or qudits of even superposition of pseudo-number states. Cross-Kerr nonlinear interaction can generate the maximal entanglements of pseudo- phase and pseudo-number states from two opticl coherent states. Extended network of these entangled coherent states is a qudit cluster state and can be used as qudit communication network for d-dimensional teleportation or multi-user quantum cryptographic network.

Marek Czachor

D. A. Trifonov

Nonlinear pseudo-fermions of degree n ( n -pseudo-fermions) are introduced as (pseudo) particles with creation and annihilation operators b and a , b ≠ a †, obeying the simple nonlinear anticommutation relation ab + b n a n = 1. The ( n + 1)-order nilpotency of these operators follows from the existence of unique (up to a bi-normalization factor) a -vacuum. Supposing appropriate ( n + 1)-order nilpotent para-Grassmann variables and integration rules the sets of n -pseudo-fermion number states, 'right' and 'left' ladder operator bi-overcomplete sets of coherent states are constructed. Explicit examples of n -pseudo-fermion ladder operators are provided, and the relation of pseudo-fermions to finite level pseudo-Hermitian systems is briefly considered. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Quantum physics with non-Hermitian operators'.