Control of memory effects in a spin-boson system by periodic driving

TL;DR

This work investigates memory effects (non-Markovianity) in a finite-temperature spin-boson system subjected to a time-periodic drive, revealing a pronounced peak structure in the non-Markovianity measure as a function of driving amplitude, quantified by $\mathcal{N}$. Using numerically exact HEOM simulations and Floquet theory, the authors connect the observed peaks to degeneracies of the quasienergy spectrum, which modify the Floquet-Lindblad jump operators. At quasienergy crossings the master equation exhibits a nearly decoherence-free subspace with longer relaxation times and enhanced information backflow, yielding top-level peaks in $\mathcal{N}$. The results propose periodic driving as a general, robust strategy to control relaxation rates and non-Markovian memory effects in open quantum systems, with implications for coherence protection in solid-state qubits.

Abstract

We study the emergence of quantum memory effects in a spin-boson system at finite temperature driven by an external time-periodic force. Quantifying memory effects by the trace-distance based measure for non-Markovianity and performing numerical simulations employing the hierarchical equations of motion approach, we find a pronounced peak structure when plotting the non-Markovianity measure as a function of the driving amplitude. This distinctive feature is interpreted using Floquet theory and the Floquet-Lindblad master equation, associating the peaks with the degeneracies of the quasienergy spectrum which lead to a strong enhancement of the relaxation times of the system. These results suggest strategies for the efficient control of non-Markovianity in open quantum systems by periodic driving.

Figures (3)

• Figure 1: Non-Markovianity (top) and relaxation time (bottom) of the driven spin-boson model as a function of the driving amplitude $\Omega$ for resonant driving. Parameters in units of the system frequency $\omega_0$ are $k_BT = 1.0$, $\alpha = 0.1$ and $\omega_c = 1.0$.
• Figure 2: Quasienergies of the driven spin system as a function of the driving amplitude $\Omega$, for the same parameters considered in Fig. \ref{['Fig:non_markovyrela_times']}.
• Figure 3: Pure states defining optimal pairs which maximize the non-Markovianity measure $\mathcal{N}$ for each value of the driving amplitude $\Omega$. To simplify the visualization, all states are displayed in the positive octant of the Bloch sphere, with the corresponding non-Markovianity measure represented as a heatmap. The highest value of non-Markovianity corresponding to the red points are indeed obtained for pure states in the $x$ direction.