concentrate on the crossover from few-qubit systems to the system of many qubits and analyze how collective behavior of coupled qubits-cavity system emerges despite of the broadening. We show that quantum interference effects survive in the mesoscopic regime — dynamics of an entangled Bell state encoded into the qubit subsystem remains highly sensitive to the symmetry of the total wave function. Moreover, relaxation of these states is slowed down due to the formation of collective dark states weakly coupled to light. Dark states also significantly influence dynamics of excitations of photon subsystem by absorbing them into the qubit subsystem and releasing quasiperiodically in time. We argue that predicted phenomena can be useful in quantum technologies based on superconducting qubits. For instance, they provide tools to deeply probe both collective and quantum properties of such artificial macroscopic systems.

of an atom due to the nonadiabatic modulation of its Lamb shift. This effect has been initially introduced for a natural atom in a varying cavity, while we suggested its realization in a superconducting qubit-cavity system with dynamically tunable coupling. In the present paper, we study the interplay between the dynamical Lamb effect and the energy dissipation, which is unavoidable in realistic systems. We find that despite of naive expectations this interplay can lead to unexpected dynamical regimes. One of the most striking results is that photon generation from vacuum can be strongly enhanced due to the qubit relaxation, which opens a new channel for such a process. We also show that dissipation in the cavity can increase the qubit excited state population. Our results can be used for the experimental observation and investigation of the dynamical Lamb effect and accompanying quantum effects.

atom excitation due to the nonadiabatic modulation of atomic level Lamb shift. The qubit (artificial macroscopic atom) and resonator can be integrated in a tunable way. By varying nonadiabatically the coupling strength, it is possible to parametrically excite the qubit. This approach allows one to get rid of Casimir photons and thus to isolate the mechanism of the qubit excitation due to the dynamical Lamb effect from another mechanism due to the Casimir photons absorbtion. We evaluate a qubit excitation probability within the Jaynes-Cummings model using the perturbation theory and also numerically. We argue that the most efficient method to increase an excitation probability is a periodic driving of a qubit-resonator coupling constant. We also study a statistics of photon states and show that a significant squeezing can be obtained by using a suggested approach.