Strictly localized three-dimensional states close to single photons

TL;DR

This paper constructs strictly localized quantum states that closely approximate single photons, providing bounds on their fidelity and extending the concept to multi-photon states, thereby advancing understanding of photon localization limits.

Contribution

It introduces a class of strictly localized states near single photons and generalizes the concept to multi-photon states, defining the limits of photon localization.

Findings

States can be made arbitrarily close to single photons at small scales

Bounds for fidelity between localized states and single photons are provided

Results extend to states near n-photons

Abstract

A class of strictly localized states which can be made arbitrarily close to single photons is constructed, and expressions for central properties are provided. It is demonstrated that single photon states can be well approximated by these states down to localization scales on the order of a few pulse cycles. The results readily generalize to states close to $n$-photons. We also provide upper and lower bounds for the fidelity between a given single photon and any state strictly localized to a given volume. These results constitute the limit of photon localization, complementary to the weak-localization limit (I. Bialynicki-Birula, Phys. Rev. Lett. 80, 5247 (1998)).