Hybrid Atomistic-Parametric Decoherence Model for Molecular Spin Qubits

TL;DR

This paper develops a hybrid atomistic-parametric model to predict quantum coherence times in molecular spin qubits, incorporating lattice dynamics and magnetic noise to match experimental data.

Contribution

It introduces a novel random Hamiltonian approach combining molecular dynamics and magnetic noise modeling for accurate decoherence predictions.

Findings

Atomistic $T_1$ overestimates experimental data without magnetic noise correction.

Magnetic field noise amplitude ranges from 10 μT to 1 mT for copper porphyrin qubits.

T_1 scales as 1/B and T_2 as 1/B^2 due to combined effects of spin-lattice and magnetic noise.

Abstract

Solid-state molecular qubits with open-shell ground states have great potential for addressability, scalability, and tunability, but understanding the fundamental limits of quantum coherence in these systems is challenging due to the complexity of the qubit environment. To address this, we develop a random Hamiltonian approach where the molecular $g$-tensor fluctuates due to classical lattice motion obtained from molecular dynamics simulations at constant temperature. Atomistic $g$-tensor fluctuations are used to construct Redfield quantum master equations that predict the relaxation $T_1$ and dephasing $T_2$ times of copper porphyrin qubits in a crystalline framework. Assuming one-phonon spin-lattice interaction processes, $1/T$ temperature scaling and $1/B^3$ magnetic field scaling of $T_1$ are established using atomistic bath correlation functions. Atomistic $T_1$ predictions overestimate the available experimental data by orders of magnitude. Quantitative agreement with measurements at all magnetic fields is restored by introducing a magnetic field noise model to describe lattice nuclear spins, with field-dependent noise amplitude in the range $\delta B\sim 10\,\mu{\rm T}- 1\,{\rm mT}$ for the copper porphyrin system. We show that while $T_1$ scales as $1/B$ experimentally due to a combination of spin-lattice and magnetic noise contributions, $T_2$ scales strictly as $ 1/B^2$ due to low-frequency dephasing processes associated with magnetic field noise. Our work demonstrates the potential of dynamical methods for modeling the open quantum system dynamics of molecular spin qubits.