Quantum Kramers-Henneberger Transformation

TL;DR

This paper extends the classical Kramers-Henneberger transformation to include quantum electrodynamic effects by quantizing the trap position, enabling new quantum simulations in ultracold atom and ion systems.

Contribution

It introduces a quantum electrodynamic extension of the Kramers-Henneberger transformation, accounting for quantum fluctuations of the trap position.

Findings

Quantum corrections to the classical transformation are identified.

An optomechanical setup is proposed to observe these quantum effects.

Potential applications in simulating quantum electrodynamics and ultrafast physics.

Abstract

The classical Kramers-Henneberger transformation connects, via a series of unitary transformations, the dynamics of a quantum particle of mass $m$ located in a trap at position $\alpha(t)$, with the dynamics of a charge $e$ moving in an electric field $e{\cal{E}}(t)=-m\ddot{\alpha}(t)$ within the dipole approximation. In this paper, we extend the classical Kramers-Henneberger transformation to the quantum electrodynamic and quantum optical realm, by explicitly treating the trap location quantum mechanically, thus taking into account the quantum fluctuations of the time-dependent displacement force. Compared to the classical case, we show that quantum electrodynamic corrections appear, and we propose an optomechanical realization for the quantized position of the trap to show that such corrections can manifest in state-of-the-art experiments. These results open the path to novel quantum simulation of quantum electrodynamics and quantum optics of attoscience and ultrafast physics by using ultracold trapped atoms and ions.