Pure Dephasing of Light-Matter Systems in the Ultrastrong and Deep-Strong Coupling Regimes

Pure dephasing originates from the nondissipative information exchange between quantum systems and environments, and plays a key role in both spectroscopy and quantum information technology. Often pure dephasing constitutes the main mechanism of decay of quantum correlations. Here we investigate how pure dephasing of one of the components of a hybrid quantum system affects the dephasing rate of the system transitions. We find that, in turn, the interaction, in the case of a light-matter system, can significantly affect the form of the stochastic perturbation describing the dephasing of a subsystem, depending on the adopted gauge. Neglecting this issue can lead to wrong and unphysical results when the interaction becomes comparable to the bare resonance frequencies of subsystems, which correspond to the ultrastrong and deep-strong coupling regimes. We present results for two prototypical models of cavity quantun electrodynamics: the quantum Rabi and the Hopfield model.

Figure 1

Pictorial representation of a two-level system interacting with a single-mode cavity field, when both subsystems are affected by pure dephasing.

Figure 2

Quantum Rabi model. Normalized pure dephasing rate for the two lowest energy transitions, for a small qubit-cavity detuning $\delta =3\times {10}^{-3}$ and considering only the qubit pure dephasing. (a) Correct gauge-invariant versus (b) wrong Coulomb gauge results.

Figure 3

Hopfield model. Normalized pure dephasing rate of the lower and upper polaritons, originating from exciton dephasing, versus the normalized coupling strength, obtained for different exciton-cavity detunings, and considering only the matter pure dephasing.

Figure 4

Hopfield model. Wrong (see text) normalized pure dephasing rates of the lower and upper polaritons, originating from exciton dephasing, versus the normalized coupling strength, obtained for two different exciton-cavity detunings, and considering only the matter pure dephasing (a),(b). (c) Frequencies of the two polariton modes for a qubit-cavity detuning $\delta /{\omega }_c=3\times {10}^{-3}$.