Limits for realizing single photons

TL;DR

This paper investigates the fundamental limits of generating single photons on demand, showing that practical realizations inevitably contain multiphoton components, especially for short target pulses, and provides bounds on achievable fidelity.

Contribution

It introduces two incompatible ways to specify target single photon states and derives bounds on the maximum fidelity of realizable states relative to these targets.

Findings

Short target pulses lead to states with multiphoton components

Upper and lower bounds on fidelity depend on the tail size of the target state

Bounds are generalized to arbitrary photon-number states

Abstract

Exact single photons cannot be generated on demand due to their infinite tails. To quantify how close realizable optical states can be to some target single photon in one dimension, we argue that there are two natural but incompatible ways to specify the target state. Either it can be expressed as a photon with a chosen positive-frequency spectrum, or it can be described as an (unphysical) photon in a chosen positive-time pulse. The results show that for sufficiently short target pulses, the closest realizable states contain substantial multiphoton components. Upper and lower bounds for the maximum fidelity are derived and are expressed as functions of the size of the target state's tail, for negative time or negative frequency, respectively. We also generalize the bounds to arbitrary photon-number states.