Exponential decay in a spin bath

Abstract

We show that the coherence of an electron spin interacting with a bath of nuclear spins can exhibit a well-defined purely exponential decay for special (`narrowed') bath initial conditions in the presence of a strong applied magnetic field. This is in contrast to the typical case, where spin-bath dynamics have been investigated in the non-Markovian limit, giving super-exponential or power-law decay of correlation functions. We calculate the relevant decoherence time T_2 explicitly for free-induction decay and find a simple expression with dependence on bath polarization, magnetic field, the shape of the electron wave function, dimensionality, total nuclear spin I, and isotopic concentration for experimentally relevant heteronuclear spin systems.

4+ pages, 3 figures; v2: 9 pages, 3 figures (added four appendices with extensive technical details, version to appear in Phys. Rev. B)

References in corpus (8)

• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Theory of electron spin decoherence by interacting nuclear spins in a quantum dot
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
• Electron spin phase relaxation of phosphorus donors in nuclear spin enriched silicon
• Universal phase shift and non-exponential decay of driven single-spin oscillations
• Semiclassical dynamics and long time asymptotics of the central-spin problem in a quantum dot
• Universal Scaling of Hyperfine-Induced Electron Spin Echo Decay

Cited by in corpus (2)

• Nuclear spin dynamics and Zeno effect in quantum dots and defect centers
• Temperature induced spin coherence dissipation in quantum dots