Steady-state quantum coherence in driven open quantum system: An optimal transformation analysis

Understanding quantum coherence and proposing protection mechanisms has become one of the fundamental challenges in quantum physics research. We investigate a generic driven open quantum system, i.e., the driven spin-boson model, beyond the rotating-wave approximation. Although steady-state coherence vanishes in Floquet-Markov and Bloch-Redfield approaches, it becomes finite within a time-non-local master equation with a memory kernel. We analytically reveal that the steady-state coherence is associated with the overlap between the spectral densities associated with neighboring Floquet quasifrequencies. Motivated by this, we show that increasing temperature and introducing mixed transverse and longitudinal baths broadens the spectral density, thereby enhancing steady-state coherence. This is described by resonance fluorescence spectra, which exhibit clear spectral broadening and enhanced steady-state values. For a transverse dissipative coupling to the bath, three transition frequencies emerge in the Floquet basis, corresponding to the Mollow triplet. For weak resonant driving, these quasienergies become nearly degenerate, leading to closely spaced peaks in the resonance fluorescence spectrum, and the steady-state quantum coherence asymptotically approaches its maximum. For a longitudinal coupling to the bath, the quantum system exhibits a single transition frequency, thereby resulting in a complete suppression of the steady-state quantum coherence. We systematically investigate the influences of driving strength, frequency, temperature, and various dissipative baths on steady-state quantum coherence. These findings provide a foundational framework for efficiently engineering steady-state quantum coherence in nanoscale open quantum devices under optical field excitation.