Phase Space Structure of Generalized Gaussian Cat States

TL;DR

This paper investigates the phase space structure of generalized Gaussian cat states, revealing a unique interference pattern characterized by a quadratic form, and demonstrates its robustness under thermal noise.

Contribution

It introduces a detailed analysis of the interference structure of superpositions of arbitrary Gaussian states, extending understanding beyond standard coherent state superpositions.

Findings

Interference term characterized by a quadratic form in phase space

Phase structure remains stable under thermal reservoir interactions

Analysis includes superpositions of mixed Gaussian states and nonlinear dynamics

Abstract

We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states, e.g., a coherent state and a squeezed state. The Wigner functions of such states exhibit the typical pair of Gaussian hills plus an interference term which presents a novel structure, as compared with the standard superposition of coherent states (degenerate case). We prove that, in any dimensions, the structure of the interference term is characterized by a particular quadratic form; in one degree of freedom the phase is hyperbolic. This phase-space structure survives the action of a thermal reservoir. We also discuss certain superpositions of {\em mixed} Gaussian states generated by conditional Gaussian operations or Kerr-type dynamics on thermal states.