Transition to sub-Planck structures through the superposition of q-oscillator stationary states

Abstract

We investigate the superposition of four different quantum states based on the $q$-oscillator. These quantum states are expressed by means of Rogers-Szegö polynomials. We show that such a superposition has the properties of the quantum harmonic oscillator when $q\to 1$, and those of a compass state with the appearance of chessboard-type interference patterns when $q\to 0$.

5 pages, 6 eps files

References in corpus (8)

• Sub-Planck spots of Schroedinger cats and quantum decoherence
• Sub-Planck phase-space structures and Heisenberg-limited measurements
• Decay of the Loschmidt Echo for quantum states with sub-Planck scale structures
• Sub-Planck scale structures in a vibrating molecule in the presence of decoherence
• Entanglement induced Sub-Planck structures
• Teleportation fidelity as a probe of sub-Planck phase-space structure
• The Wigner function of a q-deformed harmonic oscillator model
• Measuring sub-Planck structural analogues in chronocyclic phase space

Cited by in corpus (5)

• The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass
• Coherent control of mesoscopic superpositions in a diatomic molecule
• Sub-Planck structure in a mixed state
• Cat state, sub-Planck structure and weak measurement
• Impact of the non-canonical approach to the exact solution of the ideal one-dimensional electron gas confined with an anisotropic quantum wire of oscillator-shaped profile