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 nonperturbative 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. In this work, we extend 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 potential applications of the formalism are demonstrated through various examples.

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• Quantum transport
• Floquet systems
• Quantum dots
• Quantum master equation