Photon number projective measurement in Schr\"odinger cat quantum state preparation procedure after parametric down-conversion interaction

TL;DR

This paper develops a theoretical framework and numerical methods for photon number projective measurement in Schrödinger cat state preparation using parametric down-conversion with pump depletion.

Contribution

It introduces a general theory of SPDC with pump depletion, along with an efficient numerical approach and a practical protocol for Schrödinger cat state generation.

Findings

Formulated a comprehensive theoretical model of SPDC with pump depletion.

Developed an efficient numerical method for simulating SPDC dynamics.

Proposed a practical protocol for Schrödinger cat state preparation.

Abstract

Schr\"odinger-cat (SC) states are an important resource for continuous-variable quantum computing and quantum metrology. In our previous work [JOSA B, 42, 2 (2025)], we proposed a probabilistic protocol for generating bright squeezed SC states via degenerate spontaneous parametric down-conversion (SPDC) with pump depletion, followed by projective measurement of the pump mode. In the present work, we formulate a general theoretical description of SPDC with pump depletion, introduce an efficient numerical method for computing its dynamics, and develop a practical version of the protocol proposed in [JOSA B, 42, 2 (2025)].