arXiv:2511.16529

Analytical Fock Representation of Two-Mode Squeezing for Quantum Interference

Xuemei Gu, Carlos Ruiz-Gonzalez, Mario Krenn

quant-phSubmitted Nov 20, 2025• Announced Nov 21, 2025• 0 citations• Revised Feb 10, 2026 (v2)

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.

Comments: 8 pages, 4 figures; 6 pages appendix

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