A perturbative non-Markovian treatment to low-temperature spin decoherence

TL;DR

The paper addresses low-temperature electron-spin dephasing in molecular spin qubits caused by coupling to a nuclear-spin bath, where non-Markovian effects are essential. They derive a non-Markovian time-convolutionless master equation to second order in the system–bath interaction (TCL2) with an embedded Hahn-echo pulse, linking ab initio electronic-structure parameters such as hyperfine tensors $A_k$ and nuclear dipolar terms to the coherence through the decoherence function $W(t)$. A factorized multi-spin extension yields $\rho_e^{01}(t)=\rho_e^{01}(0)\exp(-\sum_{kl}W_{kl}(t))$, with pair-specific amplitude $\alpha_{kl}^2=(\frac{2b_{kl}\Delta_{kl}}{b_{kl}^2+\Delta_{kl}^2})^2$ and frequency $f_{kl}=\frac{1}{4}\sqrt{\Delta_{kl}^2+b_{kl}^2}$ where $\Delta_{kl}=A_k-A_l$, enabling predictions of decoherence across vanadium-oxo molecular qubits (V1-V4) embedded in a hydrogen spin bath. The method demonstrates good agreement with numerically exact simulations for frequency and reasonable accuracy for modulation depth, while remaining computationally efficient since it requires only a single electronic-structure calculation per species. These results provide a practical, parameter-connected framework to screen and interpret low-temperature decoherence trends in molecular spin systems.

Abstract

Molecular spins are promising candidates for quantum information science, leveraging coherent electronic spin states for quantum sensing and computation. However, the practical application of these systems is hindered by electronic spin decoherence, driven by interactions with nuclear spins in the molecule and the surrounding environment at low temperatures. Predicting dephasing dynamics remains a formidable challenge due to the complexity of the spin bath. In this work, we develop a non-Markovian time-convolutionless master equation to treat an electronic spin coupled to a nuclear-spin bath. By relating ab initio electronic structure parameters directly to the decoherence dynamics, we provide a framework that accounts for pure dephasing in the low-temperature limit. We apply this method to a series of molecular qubit candidates and demonstrate good agreement with experimental relaxation trends. This approach offers a computationally efficient path for the prediction of low-temperature decoherence trends in molecular spin systems.

Figures (3)

• Figure 1: Fidelity between the TCL2 and numerically exact density matrices as a function of $\alpha_{12}^2$. The left side of the figure represents when $|b_{12}|<|\Delta_{12}|$ and the right side when $|b_{12}|>|\Delta_{12}|$.
• Figure 2: Echo decay for four different vanadium-oxo molecules using the factorized TCL2 approach.
• Figure 3: Echo decay of the vanadium-oxo molecules interacting with a bath of hydrogen spins.