Cavity nonlinear optics with few photons and ultracold quantum particles

TL;DR

This paper explores how few-photon interactions in a high-Q cavity with ultracold particles induce nonlinear optical effects, including phase shifts and squeezing, with potential for quantum control and entanglement.

Contribution

It derives an effective Hamiltonian capturing nonlinear photon-particle interactions at the few-photon level, supported by wave-function simulations showing entanglement.

Findings

Nonlinear phase shifts occur at the few-photon level.

Significant particle-field entanglement is demonstrated.

The effective Hamiltonian predicts squeezing effects.

Abstract

The light force on particles trapped in the field of a high-Q cavity mode depends on the quantum state of field and particle. Different photon numbers generate different optical potentials anddifferent motional states induce different field evolution. Even for weak saturation and linear polarizability the induced particle motion leads to nonlinear field dynamics. We derive a corresponding effective field Hamiltonian containing all the powers of the photon number operator, which predicts nonlinear phase shifts and squeezing even at the few-photon level. Wave-function simulations of the full particle-field dynamics confirm this and show significant particle-field entanglement in addition.