# Photon-Photon Interactions in Dynamically Coupled Cavities

## TL;DR

This paper proposes a method for controlling photon interactions in dynamically coupled nonlinear cavities, enabling high-fidelity quantum operations and overcoming limitations of passive cavity systems.

## Contribution

It introduces a tunable coupling scheme for loading photons into cavities and demonstrates its advantages for quantum information processing with various nonlinearities.

## Key findings

- High fidelity photon loading achieved with dynamic coupling
- Elimination of wave packet distortions in cavity transmission
- Potential for high-fidelity two-qubit entangling gates

## Abstract

We study theoretically the interaction between two photons in a nonlinear cavity. The photons are loaded into the cavity via a method we propose here, in which the input/output coupling of the cavity is effectively controlled via a tunable coupling to a second cavity mode that is itself strongly output-coupled. Incoming photon wave packets can be loaded into the cavity with high fidelity when the timescale of the control is smaller than the duration of the wave packets. Dynamically coupled cavities can be used to avoid limitations in the photon-photon interaction time set by the delay-bandwidth product of passive cavities. Additionally, they enable the elimination of wave packet distortions caused by dispersive cavity transmission and reflection. We consider three kinds of nonlinearities, those arising from $\chi^{\scriptscriptstyle(2)}$ and $\chi^{\scriptscriptstyle(3)}$ materials and that due to an interaction with a two-level emitter. To analyze the input and output of few-photon wave packets we use a Schr\"odinger-picture formalism in which travelling-wave fields are discretized into infinitesimal time-bins. We suggest that dynamically coupled cavities provide a very useful tool for improving the performance of quantum devices relying on cavity-enhanced light-matter interactions such as single-photon sources and atom-like quantum memories with photon interfaces. As an example, we present simulation results showing that high fidelity two-qubit entangling gates may be constructed using any of the considered nonlinear interactions.