Trapped bosons in mean field QED, nonlinear resonance cascades and dynamical BEC formation

Abstract

In this paper, we study a system of bosons trapped in a confining potential, interacting with a quantized field of coherent photons in the mean field description of non-relativistic Quantum Electrodynamics (QED) obtained by N. Leopold and P. Pickl in [1]. We derive the effective nonlinear cascade equations governing the emission and absorption of coherent photons by the boson subsystem in a combined weak coupling and macroscopic time scaling limit. We demonstrate that solutions to this nonlinear cascade describe a monotone decreasing energy flow in the boson subsystem. Thereby, we prove that a Bose-Einstein condensate (BEC) forms dynamically, under conservation of the total boson \(L^2\) mass. We note that this process is crucially different from thermal relaxation to the ground state, and fundamentally depends on the nonlinear nature of the cascade dynamics.

Click here to read or download the full paper

References

[1] Leopold, N., and Pickl, P. (2017). Mean-field limits of particles in interaction with quantized radiation fields. In Workshop on Macroscopic Limits of Quantum Systems (pp. 185–214). Springer.