Symmetry analysis of the quantum oscillator

A.A. Abdullaev

Biswabibek Bandyopadhyay, Tanmoy Banerjee

We study the effect of Kerr anharmonicity on the symmetry-breaking phenomena of coupled quantum oscillators. Two types of symmetry-breaking processes are studied, namely, the inhomogeneous steady state (or quantum oscillation death state) and quantum chimera state. Remarkably, it is found that Kerr nonlinearity hinders the process of symmetry breaking in both the cases. We establish our results using direct simulation of the quantum master equation and analysis of the stochastic semiclassical model. Interestingly, in the case of quantum oscillation death, an increase in the strength of Kerr nonlinearity tends to favor the symmetry and at the same time decreases the degree of quantum mechanical entanglement. This paper presents a useful mean to control and engineer symmetry-breaking states for quantum technology.

S. Krivonos, Armen Nersessian

Performing the Hamiltonian analysis we explicitly established the canonical equivalence of the deformed oscillator, constructed in arXiv:1607.03756[hep-th], with the ordinary one. As an immediate consequence, we proved that the SU(1,2) symmetry is the dynamical symmetry of the ordinary two-dimensional oscillator. The characteristic feature of this SU(1,2) symmetry is a non-polynomial structure of its generators written it terms of the oscillator variables.

Paul Bracken

Carlo Jacoboni

Owen L. de Lange, R. E. Raab

Abstract In both classical and quantum physics the harmonic oscillator is one of the most important physical systems [1–4]. Furthermore, because of the simplicity and symmetry of the Hamiltonian operator, the quantum mechanical oscillator is particularly suited to analysis by abstract operator methods. For this reason the study of the one dimensional oscillator is a useful introduction to the application of operator methods in quantum mechanics. In Sections 2.1–2.4 we use these methods to determine energy eigenvalues and eigenkets, and matrix elements; the analysis is extended to isotropic multidimensional oscillators in Section 2.10. Quasiclassical states of the oscillator are discussed in Section 2.5. In Section 2.6 shift operators are used to calculate wave functions. In Sections 2.7–2.11 we discuss some applications of the theory of the oscillator.