Resolution of superluminal signalling in non-perturbative cavity quantum electrodynamics

Carlos Sánchez Muñoz,Simone De Liberato,Franco Nori

doi:10.1038/s41467-018-04339-w

Abstract

Recent technological developments have made it increasingly easy to access the non-perturbative regimes of cavity quantum electrodynamics known as ultrastrong or deep strong coupling, where the light–matter coupling becomes comparable to the bare modal frequencies. In this work, we address the adequacy of the broadly used single-mode cavity approximation to describe such regimes. We demonstrate that, in the non-perturbative light–matter coupling regimes, the single-mode models become unphysical, allowing for superluminal signalling. Moreover, considering the specific example of the quantum Rabi model, we show that the multi-mode description of the electromagnetic field, necessary to account for light propagation at finite speed, yields physical observables that differ radically from their single-mode counterparts already for moderate values of the coupling. Our multi-mode analysis also reveals phenomena of fundamental interest on the dynamics of the intracavity electric field, where a free photonic wavefront and a bound state of virtual photons are shown to coexist.

Highlights

Recent technological developments have made it increasingly easy to access the nonperturbative regimes of cavity quantum electrodynamics known as ultrastrong or deep strong coupling, where the light–matter coupling becomes comparable to the bare modal frequencies
In order to see how this Hamiltonian allows for superluminal signalling when g ’ ωx; ωc, let us consider the situation sketched in Fig. 1b, with an observer placed close to one of the mirrors and the system initialized in a factorized state, with the two-level system (TLS) either in its ground jgi or excited jei energy level and the cavity field in its vacuum state
By means of quasi-exact numerical calculations using matrix product states (MPS), we have studied the multi-mode version of the quantum Rabi model confirming that, beyond certain values of the coupling rate, the single-mode model fails to describe the physics of a TLS coupled to the electric field inside a cavity

Summary

Results

In order to see how this Hamiltonian allows for superluminal signalling when g ’ ωx; ωc, let us consider the situation sketched, with an observer placed close to one of the mirrors and the system initialized in a factorized state, with the TLS either in its ground jgi or excited jei energy level and the cavity field in its vacuum state Such a configuration can be prepared performing only local operations on the TLS, i.e. by non-adiabatically switching on its coupling to the cavity[34, 35]. While for the considered values of the coupling the Rabi oscillations are distorted in the single-mode case, for the multi-mode Hamiltonian the TLS relaxes immediately and remains most of the time in a superposition of jgi and jei yielding a population of 1/2, experiencing a sequence of sharply peaked revivals that bring it back to the excited state at times multiple of the cavity roundtrip time, 2π/ωc. HI takes the form of a collection of driven harmonic oscillators: HI; ±

NÀ1Â ðn þ

NÀ1 n f1

Discussion