Photon correlations of a sub-threshold optical parametric oscillator

Area of Science:

• Quantum optics
• Nonlinear optics
• Cavity quantum electrodynamics

Background:

• Spontaneous parametric downconversion (SPDC) is a key quantum nonlinear optical process.
• Understanding multimode effects in SPDC within optical cavities is crucial for quantum technologies.
• Previous theories often simplified the complex interactions within cavities.

Purpose of the Study:

• To develop a microscopic multimode theory for collinear type-I SPDC in a cavity.
• To derive single-mode and multimode correlation functions from fundamental principles.
• To relate theoretical predictions to experimental parameters like mirror reflectivities and crystal dispersion.

Main Methods:

• Utilized a fully quantized approach for both atom and electromagnetic field variables.
• Derived analytical expressions for single-mode and multimode correlation functions.
• Calculated the full width at half maximum (FWHM) of the single-mode correlation function and the cavity enhancement factor.

Main Results:

• Presented a microscopic multimode theory for collinear type-I SPDC in a cavity.
• Derived single-mode and multimode correlation functions using quantized variables.
• Obtained the FWHM and cavity enhancement factor in terms of physical parameters.

Conclusions:

• The developed theory provides a fundamental understanding of multimode SPDC in cavities.
• Theoretical predictions show excellent agreement with recent experimental results.
• This work offers a robust framework for designing and analyzing quantum optical devices based on SPDC.