Dominant spin-spin relaxation mechanism at clock transition of the $Ho_{x}Y_{1-x}W_{10}$ complex at different concentrations

TL;DR

The paper addresses decoherence of clock-transition qubits in Ho_xY_{1-x}W_{10}, focusing on the electron-spin bath because the nuclear spin bath is suppressed at the clock transition and thus less detrimental to coherence ($T_2$).A theoretical framework combining an S=1 multi-spin Hamiltonian, projection to a qubit basis, spin-echo dynamics, and realistic HoW10 structures is used, with both exact diagonalization and cluster correlation expansion (CCE) to quantify bath effects as a function of bath density and inhomogeneity.Key findings show that increasing bath density accelerates decoherence and reduces $T_2$, while inhomogeneity in qubit gaps can mitigate this effect and spatially uniform spin distributions can significantly extend coherence; CCE results corroborate ED trends for small systems.These results have practical implications for designing qubit densities and bath configurations to protect coherence in molecular magnets and related quantum devices, guiding future experiments and simulations.

Abstract

Spin decoherence poses a significant challenge in molecular magnets, with the nuclear spin bath serving as a prominent source. Intriguingly, spin qubits at the clock transition exhibit remarkable insensitivity to the surrounding nuclear spins. Recent experimental studies have unveiled a correlation between the decoherence time and the density of spin qubits, prompting our investigation into the contribution of the qubit bath to spin decoherence. In this paper, we present a comprehensive theoretical analysis of a few S=1 spin qubits, focusing on their interaction at the clock transition. Employing the exact diagonalization and the cluster correlation expansion (CCE) method, we simulate the dynamics of spin decoherence while varying the density of the qubit bath. To ensure the realism of our simulations, we incorporate structural and energetic parameters derived from previous studies on the HoW10 crystal. Our findings indicate that when the energy mismatch between the energy splittings of two qubits exceeds their interaction strength, they can become effectively insensitive to each other, offering an explanation for the absence of observed changes in the T2 time during experiments with lower qubit densities. Understanding the role of qubit bath density in spin decoherence at the clock transition not only advances our knowledge of decoherence mechanisms but also provides insights for the development of strategies to protect coherence in molecular magnets and other quantum systems. By optimizing the density of spin qubits, we can enhance the coherence properties and pave the way for improved performance of quantum devices. Overall, this study offers valuable insights into the relationship between qubit bath density and spin decoherence at the clock transition, contributing to the broader understanding and control of quantum systems in molecular magnets.

Figures (13)

• Figure 1: Zeeman diagram of the model Hamiltonian. Red and Blue curves indicate the qubit $\ket{\uparrow}$ and $\ket{\downarrow}$ states respectively. The clock transition is at $B_0=B_{min}=23.6mT$ and the qubit energy gap $\Delta=2E$. The dots represet the zeeman diagram of the projected Hamiltonian, which overlaps with the original Hamiltonian.
• Figure 2: (a) the unit-cell of crystal HoW10 structure with all the atoms.(b) the same unit-cell with only the Ho sites. This cell will be repeated to build supercells. The two two host positions are filled with Ho atoms.
• Figure 3: Schematics of the spherical box with radius of $R$. $R$ is determined by the number of spins we want to generate with respect to the density $x$.
• Figure 4: (a)Schematics of the dissected square when separated. (b) Dissected square when assembled. (c) Actual square cell that is color-coded to match the schematics.
• Figure 5: (a) coherence signals between one electron spin and one proton spin in different magnetic fields $B-B_{min}$ in units of mT. As the field approaches to CT, the signal amplitude decreases and disappears at CT, which makes the proton bath invisible to the electron spin. (b) coherence signals between two electron spins near CT magnetic fields. In this case, the signal amplitude decreases as the field moves away from CT. Interaction between the two electron spins is set to 1 MHz which matches the frequency of the signal cosine function.