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

Abstract

The geometric phase (GP) of a periodically driven symmetricspin-boson model (SBM) is investigated using the process-tensor time-evolving matrix product operator (PT-TEMPO) method. A longitudinal monochromatic field drives the qubit along the \emph{same} coordinate that couples to an Ohmic bosonic environment. The gauge-invariant kinematic GP is evaluated from the reduced-statetrajectory, and a circular non-additivity measure quantifies the combined effects of driving and dissipation relative to driven-unitary and undriven-dissipative references. Amplitude, frequency, coupling-strength, and bath-cutoff sweeps reveal regimes in which periodic driving reduces or enhances environmental phase deformation relative to the unitary counterpart. The one-cycle GP exhibits pronounced nonmonotonic drive frequency dependence, while its bath-induced shift depends sensitively on both coupling strength and cutoff. These trends are interpreted qualitatively in terms of Floquet dressing and bath spectral structure. A two-cycle echo provides a complementary reversibility diagnostic, whose persistence signal does not generally measure the Tong GP. The results characterize the non-additive influence of driving and dissipation on geometric-phase dynamics and identify parameter regimes of reduced bath-induced deformation.