Two-mode Floquet Redfield quantum master approach for quantum transport

TL;DR

This work addresses quantum transport in open quantum systems subjected to two simultaneous periodic drives with frequencies $\omega_1$ and $\omega_2$. It develops a two-mode Floquet LvN formalism and connects it to a two-mode Shirley-inspired evolution, enabling explicit, time-local dissipators within a Wangsness-Bloch-Redfield master equation under weak coupling and wide-band assumptions. The framework is demonstrated on spinless and spinful two-level dots, revealing that dual-frequency driving increases the number of quantized current steps and induces quasi-steady oscillatory observables. By avoiding the rotating-wave approximation, the method preserves information while providing a practical route to engineer transport features via two-mode Floquet control, with broad potential applications in Floquet engineering and open quantum systems.

Abstract

Simultaneous driving by two periodic oscillations yields a practical technique for further engineering quantum systems. For quantum transport through mesoscopic systems driven by two strong periodic terms, a non-perturbative Floquet-based quantum master equation (QME) approach is developed using a set of dissipative time-dependent terms and the reduced density matrix of the system. This work extends our previous Floquet approach for transport through quantum dots (at finite temperature and arbitrary bias) driven periodically by a single frequency. In a pedagogical way, we derive explicit time-dependent dissipative terms. Our theory begins with the derivation of the two-mode Floquet Liouville-von Neumann equation. We then explain the second-order Wangsness-Bloch-Redfield QME with a slightly modified definition of the interaction picture. Subsequently, the two-mode Shirley time evolution formula is applied, allowing for the integration of reservoir dynamics. Consequently, the established formalism has a wide range of applications in open quantum systems driven by two modes in the weak coupling regime. The formalism's potential applications are demonstrated through various examples.

Figures (4)

• Figure 1: Schematic setup for quantum transport through a multi-level mesoscopic system driven simultaneously by two periodic oscillations.
• Figure 2: (color online). Quasi-steady and dynamics of an open two-level dot driven by two additive drivings. (a) Quasi-steady charge number. (b) Quasi-steady left-current. (c)-(f) The corresponding time-dependent charge number and left-current.
• Figure 3: (color online). Quasi-steady state and dynamics of an open two-level quantum dot driven by multiplying the main resonant driving by an envelope function $\sin^2(\omega_2 t)$. (a) Quasi-steady charge number for primary drivings $g\!=\!A_1\sin(\omega_1 t)$ and $g\!=\!A_1\exp(i\omega_1 t)$. (b) Quasi-steady left current for the two $g$. (c) Time-dependent charge number for the real-valued driving at few plateaus in (a) and (b). (d) Same as (c) for time-dependent left current. (e,f) Analogous to (c,d) for the complex-valued driving. Curves of identical color in (c) [(e)] and (d)[(f)] correspond pairwise.
• Figure 4: (color online). (a) Quasi-steady spin-resolved left-current for the additive term two-mode driving scenario with $\omega_2=0.750~\mathrm{eV}$. (b) Same as (a) for $\omega_2=0.875~\mathrm{eV}$. Here, the solid gray line corresponds to the absence of the e-e interaction. (c) Quasi-steady left-current for the multiplicative scenario when $g\!=\!A_1\sin(\omega_1t)$. (d) Same as (c) when $g\!=\!A_1\exp(i\omega_1t)$.