Hybrid Atomistic-Parametric Decoherence Model for Molecular Spin Qubits

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 $δB\sim 10\,μ{\rm T}- 1\,{\rm mT}$ 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.

Figures (4)

• Figure 1: Atomistic $g$-tensor fluctuations. (a) Evolution of the diagonal tensor elements $g_{ii}(t)$ of copper qubits ($S=1/2, I=3/2$) in metal-organic frameworks (Cu-PCN-224) at 10 K, sampled from equilibrium molecular dynamics simulation. Time-averaged values are shown in dashed horizontal lines. (b) Off-diagonal elements $g_{ij}$ around their zero-valued time averages at 10 K. (c) Zeeman spectrum of the copper qubit obtained from atomistic time-averaged $g$-tensor elements at 10K, compared with experimental data from Ref. yu2019concentrated.
• Figure 2: Spectrum of $g$-tensor fluctuations. (a) $G_{zz}$ fluctuation spectrum at different temperatures. The inset shows a sample autocorrelation function (ACF) for $zz$ fluctuations at 10 K. (b) Temperature scaling power $\alpha$ in $G_{ii}\sim T^\alpha$ for $xx$ and $zz$ components, evaluated at different frequencies. The inset shows the histogram of $\alpha$ values for the $zz$ component
• Figure 3: Hybrid spectral density for copper qubits. Total spectral density $J_{zz}$ (solid line) obtained by combining the atomistic spectral density $J_{zz}^{\delta g}$ at $10$ K (dashed line) with a model magnetic noise spectral density $J^{\delta B}_{zz}$ having field-independent noise amplitude (dotted line; $\gamma_{\rm pd} = 0.001$ cm$^{-1}$, $a = 16\times 10^{-10}$ T$^{2}$, $b = 0$).
• Figure 4: Relaxation and dephasing of copper qubits. (a) $T_{1}$ as a function of field strength $B$ for different spectral density models: atomistic spin-lattice at 10 K (green solid) and hybrid-atomistic with field-independent (blue dashed) and field-dependent magnetic noise (red solid). Results for a modified Hamiltonian without hyperfine interactions ($A_{ij}=0)$ are also given. Experimental results from Ref. yu2019concentrated at 5 K are shown for comparison. (b) $T_2$ as a function of field strength for the models in panel (a). The pure relaxation limit $T_2=2T_1$ is shown for comparison (black dashed line). $\gamma_{\rm pd} = 0.001$ cm$^{-1}$ for all magnetic noise models.