Analytical double-unitary-transformation approach for strongly and periodically driven three-level systems

Abstract

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 the time-dependent longitudinal (i.e., diagonal) couplings. However, three-level systems strongly driven by the 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 the periodically modulated and strongly driven systems, where the time-dependent Hamiltonian has large off-diagonal elements. The first unitary transformation converts the strong off-diagonal elements to the 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 the multi-level systems with strong transverse couplings.

All-optical pulse switching with a periodically driven dissipative quantum system

“…The on (off) state is realized when the control field intensity is sufficiently strong (zero) to generate a transparency window (adsorption peak), suppressing (increasing) the absorption of the input field and resulting in a maximum (minimum) of transmission [29]. We obtain the analytical results of periodically driven dissipation quantum systems under high-frequency expansions by using Floquet-Lindblad theory and Van Vleck perturbation theory [30][31][32], which agree well with the numerical results. Further comparing the properties of the AOPSs controlled by a CW field and an SW field, we find that the SW field is a proper control field for the input pulse we assumed here.…”

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

“…Other possible realizations include such systems as a strongly driven Anderson insulator (Agarwal et al, 2017) or pumping in a Cooper pair sluice (Russomanno et al, 2011). As a further development of the theory, this approach can be used to study the low-frequency limit (Rodriguez-Vega et al, 2018), include the dissipation (Henriet et al, 2014;Kohler, 2017;Restrepo et al, 2016) (Floquet-Markov theory), and considering multilevel systems (Denisenko et al, 2010;Ganeshan et al, 2013;Han et al, 2020;Munyaev and Bastrakova, 2021;Satanin et al, 2014;Zhou et al, 2021).…”

Effective dynamics and applications in periodic kicks systems

“…Although the Floquet theory [1, 2] is a powerful tool to calculate the time-independent effective Hamiltonian of periodic systems [70][71][72][73][74][75][76][77][78][79], it does not work very well in this system due to the singularity of δ-function. In addition, the effective Hamiltonian is hardly obtained by employing the Baker-Campbell-Hausdorff formula [80] as well as the rotating wave approximation [81][82][83][84][85], because we cannot treat the period T as a perturbation in this system due to its arbitrariness.…”