Fractional squeezing: spectra and dynamics from generalized squeezing Hamiltonian with fractional orders

TL;DR

This paper extends the concept of squeezing in quantum systems to fractional orders, enabling precise identification of critical points where spectral and oscillatory behaviors change, with implications for quantum control and analysis.

Contribution

It introduces a generalized squeezing Hamiltonian with fractional orders, providing new methods to locate critical points and analyze spectral and dynamical transitions.

Findings

Identified the transition point from continuous to discrete spectrum.

Determined the change from infinite to finite oscillation amplitudes.

Analyzed behavior in the large fractional order regime.

Abstract

We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately predict the behaviour at these critical points, which are challenging for conventional computational methods. Based on our numerical calculations, we identify with a high degree of confidence the point at which the spectrum turns from continuous to discrete and the point at which oscillations turn from having asymptotically infinite amplitudes to finite amplitudes. Furthermore, we numerically investigate the behaviour in the large $n$ regime and provide an intuitive explanation that coincides with the numerical results.