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.
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.
The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.
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.
Cavity quantum-electrodynamics (QED) is a rich area of optical physics, where extreme light–matter coupling can give rise to ultrastrong coupling. The ultrastrong coupling regime presents some fascinating uniquely quantum mechanical effects, such as ground state virtual photons and vacuum squeezing. Focusing on the widely adopted Hopfield model with cavity dissipation, we show how the linear spectrum of an ultrastrong coupled cavity and a dipole can be described either classically or quantum mechanically, but only when the quantum model includes (i) corrections to maintain gauge invariance, and (ii) a specific type of cavity bath coupling, which has so far not been identified. We also show the impact of this bath model on the quantum Rabi model, which has no classical analog in ultrastrong coupling. These results can be used to guide emerging experiments and significantly impact current models and interpretations of ultrastrong coupling between light and matter.
The ultrastrong and deep strong coupling regimes exhibit a variety of intriguing physical phenomena. In this work, we utilize the Hopfield model of a two-mode bosonic system, with each mode interacting with a heat reservoir, to research the behavior of quantum coherence. Our results indicate that a coupled oscillator system can exhibit significant quantum coherence in the ultrastrong and deep strong coupling regimes. In the ground state, the photon mode and the matter mode coherences are equal. The larger coherences that encompass the photon mode, the matter mode, and the overall system are achieved at lower optical frequencies and with increased coupling strengths. Notably, the beam splitter and phase rotation terms alone do not generate coherences for either total coherence or subsystem coherences; instead, the generation of quantum coherences originates from the one-mode and two-mode squeezing terms. When hot environments are present, the total coherence can be enhanced by the beam splitter and phase rotation terms, while it has no effect on subsystem coherences. Moreover, when the one-mode and two-mode squeezing terms and the beam splitter and phase rotation terms are considered together, the total coherence increases with stronger coupling. We also observe that lower frequencies maximize total coherence in the deep strong coupling regime. These results demonstrate that the ultrastrong coupling and deep strong coupling regimes give rise to characteristics of quantum coherences. This work provides valuable insights into the quantum coherence properties, particularly in the ultrastrong and deep strong coupling regimes between light and matter, and may have potential applications in quantum information processing.
Cavity and circuit QED study light-matter interaction at its most fundamental level. Yet, this interaction is most often neglected when considering the coupling of this system with an environment. In this paper, we show how this simplification, which leads to the standard quantum optics master equation, is at the root of unphysical effects. Including qubit relaxation and dephasing, and cavity relaxation, we derive a master equation that takes into account the qubit-resonator coupling. Special attention is given to the ultrastrong coupling regime, where the failure of the quantum optical master equation is manifest. In this situation, our model predicts an asymmetry in the vacuum Rabi splitting that could be used to probe dephasing noise at unexplored frequencies. We also show how fluctuations in the qubit frequency can cause sideband transitions, squeezing, and Casimir-like photon generation.
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.