# Deterministic quantum nonlinear optics with single atoms and virtual photons

## TL;DR

This paper demonstrates how various nonlinear optics phenomena can be simulated using single atoms and virtual photons in resonator systems, leveraging higher-order virtual processes to create effective couplings.

## Contribution

It introduces a method to realize nonlinear optics analogues with one or more two-level atoms and resonator modes via virtual photon processes, expanding quantum optics capabilities.

## Key findings

- Analogues of nonlinear optics phenomena can be realized with virtual photons.
- Effective couplings decrease with more intermediate steps.
- Many phenomena are feasible with current ultrastrong coupling technology.

## Abstract

We show how analogues of a large number of well-known nonlinear-optics phenomena can be realized with one or more two-level atoms coupled to one or more resonator modes. Through higher-order processes, where virtual photons are created and annihilated, an effective deterministic coupling between two states of such a system can be created. In this way, analogues of three-wave mixing, four-wave mixing, higher-harmonic and -subharmonic generation (i.e., up- and downconversion), multiphoton absorption, parametric amplification, Raman and hyper-Raman scattering, the Kerr effect, and other nonlinear processes can be realized. The effective coupling becomes weaker the more intermediate transition steps are needed. However, given the recent experimental progress in ultrastrong light-matter coupling, especially in the field of circuit quantum electrodynamics, we estimate that many of these nonlinear-optics analogues can be realized with currently available technology.