Time-dependent periodic perturbation of a two-level quantum system

Xian-Geng Zhao

We study the dynamics of two-level systems under the influence of time-dependent external fields. An oscillation period describing the transition between two states is obtained analytically by the use of perturbation theory, from which the results for any special case can be derived. We illustrate two examples to show the advantage of our theory, in which the phenomenon of localization/delocalization can be addressed uniformly by oscillation period.

Rainer Dick

Yingying Han, Xiao‐Qing Luo, Tiefu Li +1 more

Floquet theory combined with the generalized Van Vleck nearly degenerate perturbation theory has been widely employed for studying various two-level systems that are driven by external fields via time-dependent longitudinal (i.e., diagonal) couplings. However, three-level systems strongly driven by time-dependent transverse (i.e., off-diagonal) couplings have rarely been investigated, due to the breakdown of the traditional rotating wave approximation. Meanwhile, the conventional perturbation theory is not directly applicable, since a small parameter for the perturbed part is no longer apparent. Here we develop a double-unitary-transformation approach to deal with periodically modulated and strongly driven systems, where the time-dependent Hamiltonian has large off-diagonal elements. The first unitary transformation converts strong off-diagonal elements to diagonal ones, and the second enables us to harness the generalized Van Vleck perturbation theory to deal with the transformed Floquet matrix and also allows us to reduce the infinite-dimensional Floquet Hamiltonian to a finite effective one. For a strongly modulated three-level system, with the combination of the Floquet theory and the transformed generalized Van Vleck perturbation theory, we obtain analytical results of the system, which agree well with exact numerical solutions. This method offers a useful tool to analytically study multilevel systems with strong transverse couplings.

Rainer Dick

A. M. Korostił, Ju. Korostil

We present exact analytic solutions for non-linear quantum dynamics of \n twolevel \nsystem (TLS) subject to \n periodic-in-time external field. >n constructing the \nexactly solvable models, we use \n approach where the form of external perturbation \nis chosen to preserve \nn integrability constraint, which yields \n single non-linear \ndifferential equation for the ac-field. solution to this equation is expressed in terms \nof Jacobi elliptic functions with three independent parameters that allows n to \nchoose the frequency, average value, and amplitude of the time-dependent field at \nwill. This form of the ac-drive is especially relevant to the problem of dynamics of \nTLS charge defects that cause dielectric losses ?n superconducting qubits.

Rainer Dick