Floquet Dressing and Bath Spectral Effects on the Geometric Phase of a Driven Dissipative Qubit

Abstract

Building on recent work by Wang et al. on the dissipative geometric phase (GP) in the spin-boson model (SBM), the GP dynamics of a periodically driven symmetric SBM are investigated using the numerically exact process-tensor time-evolving matrix product operator (PT-TEMPO) method. A symmetric two-level system subjected to a longitudinal monochromatic drive along the same system coordinate that couples to an Ohmic bosonic environment exhibits rich GP dynamics arising from the interplay between driving and dissipation. To isolate cooperative drive-bath effects, a non-additive GP contribution is introduced that separates the driven dissipative response from its driven-unitary and undriven-dissipative components. Periodic driving is found to either suppress or enhance bath-induced GP deformation depending on the interplay between drive and bath timescales. These trends are interpreted through Floquet spectral steering, whereby the drive redistributes the coherent dynamics among quasienergy sidebands whose transition frequencies and Fourier-resolved system-bath matrix elements determine their coupling to the environmental spectrum. Floquet analysis shows that the dominant dissipative pathways are governed jointly by Floquet matrix-element weights and bath spectral overlap, rather than by either alone. These results connect Floquet engineering, quantum dissipation, and GP dynamics and establish periodic driving as a means of controlling the GP of open quantum systems (OQSs).