Theory of biphoton generation in a single-resonant optical parametric oscillator far below threshold

TL;DR

This paper provides a quantum-theoretical analysis of biphoton generation in a single-resonant optical parametric oscillator operating far below threshold, deriving explicit expressions for generation rate, wave function, and spectral properties.

Contribution

It introduces a detailed quantum model for biphoton production in a specific cavity setup, including explicit formulas and spectral analysis, which advances understanding of entangled photon generation.

Findings

Derived explicit biphoton generation rate and wave function.

Showed the asymmetry of the second-order cross-correlation function.

Revealed the idler spectrum reflects the cavity's longitudinal mode structure.

Abstract

We present a quantum-theoretical treatment of biphoton generation in single-resonant type-II parametric down-conversion. The nonlinear medium is continuously pumped and is placed inside a cavity which is resonant for the signal field, but nonresonant for the idler deflected by an intra-cavity polarizing beam splitter. The intensity of the classical pump is assumed to be sufficiently low in order to yield a biphoton production rate that is small compared to the cavity loss rate. Explicit expressions are derived for the rate of biphoton generation and for the biphoton wave function. The output spectra of the signal and idler field are determined, as well as the second-order signal-idler cross-correlation function which is shown to be asymmetric with respect to the time delay. Due to frequency entanglement in the signal-idler photon pair, the idler spectrum is found to reveal the longitudinal mode structure of the cavity, even though the idler field is not resonant.