Theory of photon-pair correlations in parametric downconversion in a microcavity

Area of Science:

• Quantum optics
• Nonlinear optics
• Cavity quantum electrodynamics

Background:

• Spontaneous parametric downconversion (SPDC) is a key process for generating entangled photon pairs.
• Integrating nonlinear crystals within microcavities offers enhanced light-matter interaction.
• Previous studies often treated atom and field variables classically or semi-classically.

Purpose of the Study:

• To develop a fully quantized theoretical model for SPDC in a microcavity.
• To investigate the impact of the microcavity on the temporal properties of entangled photon pairs.
• To analyze the resonant behavior of photon-pair generation rates as a function of cavity parameters.

Main Methods:

• Fully quantizing both atom and field variables.
• Calculating the photon-correlation function for entangled photon pairs.
• Modeling the photon-pair count rate, considering resonant suppression and enhancement effects.

Main Results:

• The theoretical model predicts significantly longer photon-pair correlation times (~0.4 ns) when SPDC occurs within a microcavity, compared to free-space generation (subpicoseconds).
• The photon-correlation function can be directly measured using fast photodetectors.
• Calculations show resonant suppression and enhancement in photon-pair count rates dependent on cavity length.

Conclusions:

• The microcavity significantly enhances the temporal coherence of entangled photon pairs produced via SPDC.
• The developed theory provides a framework for understanding and optimizing entangled photon generation in integrated photonic devices.
• The theoretical predictions show qualitative agreement with recent experimental findings in microcavity-based SPDC.