Generalized squeezed states

Skylar Turner, Brian R. La Cour

Roman S. Ingarden

Anil Roy, C. L. Mehta

Amel Mazouz, M. Bentaïba, Ali Mahieddine

A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.

Chon‐Fai Kam, Wei-Min Zhang, D.H. Feng

Sheng-Chuan Tang, Yue Zhang

ABSTRACT Inspired by the superposition of coherent states, we investigate the superposition of squeezed states (pure Gaussian states) and propose a mathematical characterization under the Fock‐Bargmann representation, with the possibility to further generalize to the superposition of non‐Gaussian states. We introduce generalized circular states constructed by superposing squeezed coherent states symmetrically on a circle. We demonstrate their photon distributions as “trimmed and rescaled” versions of those of the initial squeezed states. We find that squeezing disappears while higher‐order squeezing might be strengthened for some specific generalized circular states. We derive analytic expressions of the Wigner functions, with negativity indicating nonclassicality. This work reveals that circular superpositions of squeezed states possess enhanced quantum features, which are relevant to quantum metrology and information processing.