Statistics of photon-subtracted and photon-added states

TL;DR

This paper analyzes how photon subtraction and addition alter the photon statistics of initial states, revealing that effects depend on the initial photon distribution and introducing a new moment generating function for analysis.

Contribution

It provides a detailed analysis of photon-added and photon-subtracted states using a novel moment generating function, clarifying how initial statistics influence the resulting quantum states.

Findings

Photon subtraction from coherent states leaves statistics unchanged.

Photon addition to thermal states increases mean photon number.

The introduced moment generating function aids in analyzing state transformations.

Abstract

The subtraction or addition of a prescribed number of photons to a field mode does not, in general, simply shift the probability distribution by the number of subtracted or added photons. Subtraction of a photon from an initial coherent state, for example, leaves the photon statistics unchanged and the same process applied to an initial thermal state increases the mean photon number. We present a detailed analysis of the effects of the initial photon statistics on those of the state from which the photons have been subtracted or to which they have been added. Our approach is based on two closely-related moment generating functions, one well-established and one that we introduce.