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Pure dephasing originates from the non-dissipative 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.

We present a theory of the nonlinear optical response of cavity embedded interacting electron systems which does not rely on semiclassical factorization. The theory provides a unified basis for understanding nonlinear quantum dynamics in cavity embedded quantum wells. Nonclassical behavior of transmitted light is found.

We show that a spontaneous release of virtual photon pairs can occur in a quantum optical system in the ultrastrong coupling regime. In this regime, which is attracting interest both in semiconductor and superconducting systems, the light-matter coupling rate {\Omega}R becomes comparable to the bare resonance frequency of photons {\omega}0. In contrast to the dynamical Casimir effect and other pair creation mechanisms, this phenomenon does not require external forces or time dependent parameters in the Hamiltonian., Comment: To appear on Phys. Rev. Lett

We study the all-optical time-control of the strong coupling between a single cascade three-level quantum emitter and a microcavity. We find that only specific arrival-times of the control pulses succeed in switching-off the Rabi oscillations. Depending on the arrival times of control pulses, a variety of exotic non-adiabatic cavity quantum electrodynamics effects can be observed. We show that only control pulses with specific arrival times are able to suddenly switch-off and -on first-order coherence of cavity photons, without affecting their strong coupling population dynamics. Such behavior may be understood as a manifestation of quantum complementarity.

In a recent letter Chicanne {\em et al.} [1] reported the experimental observation of the electromagnetic local density of states LDOS established by gold nanostructures. The obtained images have been compared with combinations of partial LDOSs defined in terms of the imaginary part of the Green-tensor ${\bf G}^I = [{\bf G}-{\bf G}^\dag]/(2i)$ calculated at the tip position. Moreover just this comparison was the criterion for the choice of the optimum tip design. These results support the point of view that ${\cal G}_{\bf u} =-({2 \omega}/{\pi c^2}) {\bf u} \cdot {\bf G}^I({\bf r}, {\bf r}, \omega) \cdot {\bf u}$ (${\bf u}$ is the unit vector used to define the effective dipole associated to the illuminating tip) is the key quantity to interpret SNOM images in analogy with the electronic LDOS measured by the scanning tunneling microscope (STM). Rigorous Green-tensor analysis shows that ${\cal G}_{\bf u}$ (that is also the key quantity determining spontaneous decay rates of molecular transitions) is not the correct key quantity, and that measurements in Ref. [1] should have been compared with a different quantity. Moreover the identification of ${\cal G}_{\bf u}$ with the detected SNOM signal can lead to unphysical results.