Squeezed states from a quantum deformed oscillator Hamiltonian

• Published in: Physics letters. A Vol. 380; no. 11-12; pp. 1117 - 1124
• Main Authors: Ramírez, R., Reboiro, M.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 11-03-2016
• Subjects: Constants; Coupling; Deformation; Evolution; Hamiltonian functions; Mathematical models; Non-standard realizations; Oscillators; Pseudo-hermitian Hamiltonians; Quantum deformations; Solid state physics; Squeezed states; Swanson Hamiltonian; Pseudo-hermitian Hamiltonians; Quantum deformations; Squeezed states; Swanson Hamiltonian; Non-standard realizations
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2016.01.027

The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions.
•A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra.•It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian.•It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state.•The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.