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

This paper investigates how periodic longitudinal driving affects the geometric phase (GP) of a dissipative qubit. While previous research has explored how environments deform the GP, this study specifically asks how a time-dependent drive field can be used to control these deformations by restructuring the system's interaction with its dissipative environment.

The author employs the numerically exact PT-TEMPO (process-tensor time-evolving matrix product operator) method to simulate the dynamics of a symmetric spin-boson model. To isolate the cooperative effects of the drive and the bath, the paper introduces a non-additive measure, delta-gamma, which quantifies the deviation of the driven dissipative GP from the sum of its driven-unitary and undriven-dissipative components. The results are interpreted through Floquet theory, which describes how the drive creates quasienergy sidebands that sample different regions of the bath's spectral density.

The study demonstrates that periodic driving is a powerful tool for controlling the dissipative GP. Rather than simply changing the system's coherent evolution, the drive performs 'Floquet spectral steering.' By redistributing the system's dynamical weight across multiple Floquet sidebands, the drive changes the effective transition frequencies that couple to the environment. Consequently, the dissipative deformation of the GP is determined by the joint action of Floquet matrix-element weights and the bath's spectral density at those specific sideband frequencies. The author finds that the drive can effectively protect the GP from environmental distortion in certain parameter regimes, though this protection is highly sensitive to the bath cutoff frequency and the drive amplitude.

These findings establish a direct link between Floquet engineering and the geometric phase in open quantum systems. By showing that external fields can be used to steer open-system dynamics spectrally, the paper provides a framework for designing control protocols that mitigate environmental decoherence. This approach moves beyond simple Hamiltonian renormalization, suggesting that one can manipulate the dissipative pathways of a quantum system to preserve its geometric properties.