Analytical Fock Representation of Two-Mode Squeezing for Quantum Interference

TL;DR

This paper derives a closed-form Fock-basis expression for two-mode squeezing, enabling detailed analysis of quantum interference effects at any gain level, with implications for quantum sensing and state generation.

Contribution

It introduces a novel analytical Fock-basis framework for two-mode squeezing, revealing new multi-photon interference phenomena and providing design tools for quantum applications.

Findings

Identified a new multi-photon interference effect in a four-crystal setup.

Provided a compact analytic toolkit for analyzing nonlinear interferometers.

Enabled analysis of quantum interference at arbitrary squeezing strengths.

Abstract

Two-mode squeezing is central to entangled-photon generation and nonlinear interferometry, yet standard perturbative low-gain treatments and Gaussian formalisms can obscure the interference of photon-number amplitudes, especially in nonlinear interferometers and at high gain. Here we derive a closed-form Fock-basis expression for the action of the two-mode squeezing operator on arbitrary number states, enabling the direct analysis of nonlinear interferometers in the photon-number basis at arbitrary squeezing strength. Within this framework, we provide intuitive physical interpretations of several known quantum-interference effects and identify a new multi-photon interference phenomenon in a four-crystal geometry that could readily be observed in laboratories. Our work provides a compact analytic toolkit and explicit design rules for engineering multi-photon interference, with applications in quantum sensing, precision metrology, and quantum state generation.