Decoherence of a single spin coupled to an interacting spin bath

TL;DR

This paper investigates how a single spin loses coherence when coupled to an interacting spin bath, using two computational methods, revealing complex dynamics influenced by bath initial conditions and coupling strengths.

Contribution

It introduces and compares exact equations of motion and Chebyshev expansion techniques to analyze central spin decoherence in an interacting bath with specific topology and initial states.

Findings

Decoherence exhibits collapse-revival behavior in certain conditions.

Plateau values of decoherence depend non-monotonically on intrabath coupling.

Oscillatory behavior of decoherence plateau related to bath size parity.

Abstract

Decoherence of a central spin coupled to an interacting spin bath via inhomogeneous Heisenberg coupling is studied by two different approaches, namely an exact equations of motion (EOMs) method and a Chebyshev expansion technique (CET). By assuming a wheel topology of the bath spins with uniform nearest-neighbor $XX$-type intrabath coupling, we examine the central spin dynamics with the bath prepared in two different types of bath initial conditions. For fully polarized baths in strong magnetic fields, the polarization dynamics of the central spin exhibits a collapse-revival behavior in the intermediate-time regime. Under an antiferromagnetic bath initial condition, the two methods give excellently consistent central spin decoherence dynamics for finite-size baths of $N\leq14$ bath spins. The decoherence factor is found to drop off abruptly on a short time scale and approach a finite plateau value which depends on the intrabath coupling strength non-monotonically. In the ultrastrong intrabath coupling regime, the plateau values show an oscillatory behavior depending on whether $N/2$ is even or odd. The observed results are interpreted qualitatively within the framework of the EOM and perturbation analysis. The effects of anisotropic spin-bath coupling and inhomogeneous intrabath bath couplings are briefly discussed. Possible experimental realization of the model in a modified quantum corral setup is suggested.