Structure of generalized Heisenberg algebras and quantum decoherence analysis

Abstract

We study how catlike superpositions of generalized Heisenberg algebras (GHA) nonlinear coherent states behave under dissipative decoherence. Two cases are presented: the infinite square well potential and systems whose spectra, given by infinite strictly increasing sequences of nonnegative real numbers, can be considered perturbations of the harmonic oscillator. The decoherence effect caused by the interaction of these systems with a thermal bath is analyzed: from their fidelity behavior we see that a region always exists in the parameter space where the quantum coherence is better preserved as compared to the harmonic oscillator. Moreover, we show that the qualitative behavior of GHA systems under the studied mechanism of decoherence can be inferred from the algebraic structure via the analysis of their GHA characteristic functions.