Floquet approach to the study of the dynamical Lamb effect

The dynamics of N qubits coupled to a harmonic oscillator with time-periodic coupling is investigated in the framework of Floquet theory. This system can be used to model nonadiabatic phenomena that require a periodic modulation of the parameters of the system. An example is the dynamical Lamb effect, the simultaneous excitation of the qubits and the harmonic oscillator out of the ground state due to the nonadiabatic change in boundary condition of the system. The time-dependent Schroedinger equation describing the system’s dynamics is solved within the Floquet formalism and two other equivalent methods that rely on a perturbative approach in the time- and Laplace-domain. Because of the periodicity of the problem analyzed, the Floquet formalism provides a framework where analytical and numerical results are closest to each other. Nonetheless, the time- or Laplace-domain perturbative approaches can be used in the presence of simple or complicated, respectively, aperiodic time-dependent terms in the Hamiltonian.