Dynamical Lamb effect in a superconducting circuit

The dynamical Lamb effect is predicted to arise in superconducting circuits when the coupling of a superconducting qubit with a resonator is periodically switched “on” and “off” nonadiabatically. We show that by using a superconducting circuit which allows one to switch between longitudinal and transverse coupling of a qubit to a resonator, it is possible to observe the dynamical Lamb effect. The switching between longitudinal and transverse coupling can be achieved by modulating the magnetic flux through the circuit loops. By solving the Schrödinger equation for a qubit coupled to a resonator, we calculate the time evolution of the number of excitations in the qubit and the resonator due to the dynamical Lamb effect. The number of excitations created in the system is maximum when the coupling is periodically switched between longitudinal and transverse using a square-wave or sinusoidal modulation of the magnetic flux with frequency equal to the sum of the average qubit and photon transition frequencies.