Input-output theory of cavities in the ultra-strong coupling regime: the case of a time-independent vacuum Rabi frequency

TL;DR

This paper develops a comprehensive quantum model for the dissipative dynamics of optical cavities in the ultra-strong coupling regime, accounting for anti-resonant terms and applicable to semiconductor quantum wells.

Contribution

It introduces a full quantum theoretical framework for cavities in the ultra-strong coupling regime, including dissipation and anti-resonant effects, with analytical spectra calculations.

Findings

Analytical expressions for observable spectra in the ultra-strong coupling regime.

Inclusion of anti-resonant terms significantly affects cavity dynamics.

Model applicable to intersubband transitions in doped semiconductor quantum wells.

Abstract

We present a full quantum theory for the dissipative dynamics of an optical cavity in the ultra-strong light-matter coupling regime, in which the vacuum Rabi frequency is comparable to the electronic transition frequency and the anti-resonant terms of the light-matter coupling play an important role. In particular, our model can be applied to the case of intersubband transitions in doped semiconductor quantum wells embedded in a microcavity. The coupling of the intracavity photonic mode and of the electronic polarization to the external, frequency-dependent, dissipation baths is taken into account by means of quantum Langevin equations in the input-output formalism. Observable spectra (reflection, absorption, transmission and electroluminescence) are calculated analytically in the case of a time-independent vacuum Rabi frequency.