# Limits on manipulating conditional photon statistics via interference of weak lasers

## TL;DR

This paper theoretically investigates the limits of manipulating photon statistics through interference of weak lasers, showing that while super-Poissonian statistics are achievable, sub-Poissonian anti-bunching cannot be obtained with this method.

## Contribution

It clarifies the fundamental limits of using interference of weak lasers for controlling photon statistics, correcting misconceptions about achieving anti-bunching.

## Key findings

- Conditional photon statistics can be super-Poissonian.
- Photon anti-bunching cannot be achieved with interference of weak lasers.
- Proper accounting of higher-order photon terms is crucial.

## Abstract

Photon anti-bunching, measured via the Hanbury-Brown-Twiss experiment, is one of the key signatures of quantum light and is tied to sub-Poissonian photon number statistics. Recently, it has been reported that photon anti-bunching or conditional sub-Poissonian photon number statistics can be obtained via second-order interference of mutually incoherent weak lasers and heralding based on photon counting. Here, we report theoretical analysis on the limits of manipulating conditional photon statistics via interference of weak lasers. It is shown that conditional photon number statistics can become super-Poissonian in such a scheme. We, however, demonstrate explicitly that it cannot become sub-Poissonian, i.e., photon anti-bunching cannot be obtained in such a scheme. We point out that incorrect results can be obtained if one does not properly account for seemingly negligible higher-order photon number expansions of the coherent state.