Coherent quantum squeezing due to the phase space noncommutativity

TL;DR

This paper explores how phase space noncommutativity induces squeezing in coherent states of a two-dimensional quantum system, revealing new dynamics and properties through a noncommutative deformation approach.

Contribution

It demonstrates that phase space noncommutativity can produce squeezing effects in coherent states via a noncommutative deformation of harmonic oscillators without direct interactions.

Findings

Noncommutativity induces squeezing in initial coherent states.

Effective interactions lead to logarithmic spiral patterns in phase space.

Wigner functions reveal the impact of noncommutativity on quantum states.

Abstract

The effect of phase space general noncommutativity on producing deformed coherent squeezed states is examined. A two-dimensional noncommutative quantum system supported by a deformed mathematical structure similar to that of Hadamard billiards is obtained and their components behavior are monitored in time. It is assumed that the independent degrees of freedom are two \emph{free} 1D harmonic oscillators (HO's), so the system Hamiltonian does not contain interaction terms. Through the noncommutative deformation parameterized by a Seiberg-Witten transform on the original canonical variables, one gets the standard commutation relations for the new ones, such that the obtained Hamiltonian represents then two \emph{interacting} 1D HO's. By assuming that one HO is inverted relatively to the other, we show that their effective interaction induces a squeezing dynamics for initial coherent states imaged in the phase space. A suitable pattern of logarithmic spirals is obtained and some relevant properties are discussed in terms of Wigner functions, which are essential to put in evidence the effects of the noncommutativity.