Extremal states for photon number and quadratures as gauges for nonclassicality

TL;DR

This paper explores the relationship between photon number and quadrature measurements, establishing uncertainty relations, characterizing special states, and developing measures to identify nonclassical states like photon-added and cat states.

Contribution

It introduces exact and weaker uncertainty relations for photon number and quadratures, characterizes intelligent states, and creates new measures for nonclassicality detection.

Findings

Derived an exact uncertainty relation for photon number and quadratures

Characterized intelligent states saturating the relation

Developed measures to diagnose nonclassical states

Abstract

Rotated quadratures carry the phase-dependent information of the electromagnetic field, so they are somehow conjugate to the photon number. We analyze this noncanonical pair, finding an exact uncertatinty relation, as well as a couple of weaker inequalities obtained by relaxing some restrictions of the problem. We also find the intelligent states saturating that relation and complete their characterization by considering extra constraints on the second-order moments of the variables involved. Using these moments, we construct performance measures tailored to diagnose photon-added and Schr\"odinger catlike states, among others.