Dynamical Lamb Effect in a Tunable Superconducting Qubit-Cavity System

We suggest that a transmission line cavity coupled with a superconducting qubit can be used for the experimental investigation of the dynamical Lamb effect, which can be viewed as an 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.