Differences and similarities between lasing and multiple-photon subtracted states

TL;DR

This paper investigates how multiple-photon subtraction affects the statistical properties of light, revealing that thermal states do not become lasing states despite autocorrelation functions converging to one, and establishes criteria for initial states to resemble lasing.

Contribution

It provides a detailed analysis of photon subtraction effects on light states and derives a criterion for initial states to attain pseudo-lasing properties.

Findings

Thermal states do not transform into lasing states after photon subtraction.

Autocorrelation functions at zero delay time converge to one for various states.

A general criterion for initial states to reach pseudo-lasing behavior is established.

Abstract

We examine the effect that the subtraction of multiple photons has on the statistical characteristics of a light field. In particular, we are interested in the question whether an initial state transforms into a lasing state, i.e.,~a (phase diffused) coherent state, after infinitely many photon subtractions. This question is discussed in terms of the Glauber P-representation $P(\alpha)$, the photon number distribution $P[n]$, and the experimentally relevant autocorrelation functions $g^{(m)}$. We show that a thermal state does not converge to a lasing state, although all of its autocorrelation functions at zero delay time converge to one. This contradiction is resolved by the analysis of the involved limits, and a general criterion for an initial state to reach at least such a pseudo-lasing state ($g^{(m)}\to 1$) is derived, revealing that they can be generated from a large class of initial states.