Multiparticle quantum interference in Bogoliubov bosonic transformations

TL;DR

This paper develops a simple recurrence-based framework to analyze multiparticle quantum interference in Gaussian unitaries, revealing new suppression effects and extending the Hong-Ou-Mandel phenomenon to more complex optical systems.

Contribution

It introduces a recurrence relation approach for transition probabilities in Gaussian unitaries, uncovering interference effects beyond traditional two-photon systems.

Findings

Recurrence equations characterize multiparticle transition probabilities.

Discovery of a generalized interference suppression effect in optical amplifiers.

Validation of the framework through examples like beam splitters and parametric amplifiers.

Abstract

We explore the multiparticle transition probabilities in Gaussian unitaries effected by a two-mode Bogoliubov bosonic transformation on the mode annihilation and creation operators. We show that the transition probabilities can be characterized by remarkably simple, yet unsuspected recurrence equations involving a linear combination of probabilities. The recurrence exhibits an interferometric suppression term - a negative probability - which generalizes the seminal Hong-Ou-Mandel effect to more than two indistinguishable photons impinging on a beam splitter of rational transmittance. Unexpectedly, interferences thus originate in this description from the cancellation of probabilities instead of amplitudes. Our framework, which builds on the generating function of the non-Gaussian matrix elements of Gaussian unitaries in Fock basis, is illustrated here for the most common passive and active linear coupling between two optical modes driven by a beam splitter or a parametric amplifier. Hence, it also allows us to predict unsuspected multiphoton interference effects in an optical amplifier of rational gain. In particular, we confirm the newly found two-photon interferometric suppression effect in an amplifier of gain 2 originating from timelike indistinguishability (arXiv:2012.15165 [quant-ph]). Overall, going beyond standard two-mode optical components, we expect our method will prove valuable for describing general quantum circuits involving Bogoliubov bosonic transformations.