Squeezed quantum multiplets: properties and phase space representation

TL;DR

This paper introduces and analyzes squeezed quantum multiplets, exploring their properties, phase space representations, and potential for high-sensitivity applications in quantum metrology.

Contribution

It defines squeezed quantum multiplets, compares ordinary and higher-order states, and provides analytical phase-space distributions highlighting their sensitivity to perturbations.

Findings

Ordinary and higher-order squeezed multiplets share key properties.

Squeezed multiplets exhibit high sensitivity to phase-space perturbations.

Analytical phase-space functions for squeezed multiplets are derived.

Abstract

We define and study the properties of ``squeezed quantum multiplets''. Ordinary multiplets are sets of $D$-orthonormal quantum states formed by superpositions of states squeezed along $D$ equally spaced directions in quadrature space. More generally, we also discuss superpositions of ``higher-order squeezed states'', including tri-squeezed and quad-squeezed states. All these states involve superpositions of multiples of $p$ photons. We compare states in ordinary ($p=2$) multiplets and higher-order ones ($p>2$) in the most relevant cases, showing that ordinary squeezed multiplets and higher-order ones share some important similarities, as well as some differences. Finally, we present analytical expressions for phase-space distributions (Wigner and characteristic functions) representing ordinary squeezed multiplets. We use this to show that some squeezed multiplets are highly sensitive to perturbations in all phase-space directions, making them interesting for metrological applications.