Coherent quantum squeezing due to the phase space noncommutativity

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.

12 pages, 2 figures, as an Invited Comment for Physica Scripta

References in corpus (7)

• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Berry Phase in the Gravitational Quantum Well and the Seiberg-Witten map
• Entropic Gravity, Phase-Space Noncommutativity and the Equivalence Principle
• Phase-space noncommutative formulation of Ozawa's uncertainty principle
• Non-Canonical Phase-Space Noncommutativity and the Kantowski-Sachs singularity for Black Holes
• Exact master equation for a noncommutative Brownian particle
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Cited by in corpus (7)

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• Emergent entropy of exotic oscillators and squeezing in three-wave mixing process
• Quantum cloning and teleportation fidelity in the noncommutative phase-space
• Phase-space elementary information content of confined Dirac spinors
• Relativistic dispersion relation and putative metric structure in noncommutative phase-space
• Quantum information aspects of noncommutative quantum mechanics
• Additive monotones for resource theories of parallel-combinable processes with discarding