Suppressing Fast Dipolar Noise in Solid-State Spin Qubits

TL;DR

This work tackles fast dipolar noise in solid-state spin qubits by introducing Hybrid-LG, a bath-decoupling protocol that combines resonant and LG-detuned bath driving to suppress intra-bath dipolar interactions. To model dense spin baths around NV centers, the authors develop a mean-field–augmented cluster correlation expansion framework and implement partitioned CCE (pCCE) to manage large spin clusters efficiently. Numerical results for NV ensembles in a dense ^15N-P1 bath show at least a twofold extension of the Hahn-echo coherence time $T_2$ compared with standard resonant driving, with performance comparable to four-tone resonant schemes but without additional power. The methodology provides a scalable, physically grounded route to enhance solid-state qubit coherence, with potential applicability across diverse bath-driven quantum technologies and materials systems. The combination of Hybrid-LG, mean-field adaptations, and pCCE enables accurate simulation of driven baths in dense spin environments, offering practical insights for implementing robust quantum sensors and processors.

Abstract

Spin qubit coherence is a fundamental resource for the realization of quantum technologies. For solid-state platforms, spin decoherence is dominated by the magneto-active environment in the lattice, limiting their applicability. While standard dynamical decoupling techniques, such as the Hahn echo, extend central spin coherence, they fail to suppress the fast noise arising from strong dipolar interactions within the bath. Here, we present a decoupling mechanism, Hybrid-LG, that suppresses intra-bath dipolar interactions -- thus, fast noise acting on spin qubits- and demonstrate its effectiveness in extending spin coherence through efficient in-house CCE simulations. Specifically, we investigate one of the most widely exploited solid-state quantum platforms: an ensemble of nitrogen-vacancy (NV) centers in diamond coupled to a large and dense bath of substitutional nitrogen paramagnetic impurities (P1 centers). Our results reveal at least a twofold enhancement in NV coherence time relative to standard techniques including P1 center driving, without requiring additional control power.

Figures (12)

• Figure 1: Schematic of the system. A central spin (in black) is surrounded by a magnetic environment composed of clusters of strongly interacting spins (in blue). A Hahn echo sequence is applied to the central spin while a driving field of strength $\Omega$, which can be detuned by an amount $\Delta$ from the bath resonant (target) frequency $\omega_t$, decouples the environment.
• Figure 2: Simulated resonance structure of ^15N-P1 center bath in diamond. A hyperfine interaction produces different energy configurations depending on both the orientation of the P1 center in the lattice and the nitrogen spin state. The labels D (A, B, C) indicate orientations aligned (misaligned) with the external field $B_0$, here taken to be $B_0 = 0.4$ T. The target frequencies of the two-tone resonant (Hybrid-LG) bath drivings are indicated by blue (orange) arrows. Note that, in the Hybrid-LG protocol, one of these is detuned from the resonant frequency by an amount $\Delta = \Omega / \sqrt{2}$.
• Figure 3: Hahn echo coherence time $T_2$ of an ensemble of NV centers as a function of the P1 impurity concentration $\rho_{P1}$ for different spin bath driving protocols, simulated with pCCE(2,4). All points are extracted from the coherence function, $\mathcal{L}(\tau)$, simulated as the average over 50 NV centers, each coupled to a unique bath of 180 randomly distributed P1 impurities. The sampled pulse spacing ($\tau$) of the Hahn echo was chosen to avoid resonance with the Rabi frequency ($\Omega$). In every protocol, each driving tone has $\Omega = 7 \,\mathrm{MHz}$. For no bath driving (black), the characteristic $T_2 \propto 1/\rho_{P1}$ scaling is observed. Under bath driving, a systematic two-fold increase in the coherence time is achieved using Hybrid-LG (orange) with respect to the standard resonant approach (blue). Furthermore, decoupling of Hybrid-LG is comparable to the four-tone resonant protocol (red). The inset shows the values of the stretched-exponential parameter $p$ for the same impurity concentrations.
• Figure S1: The P1 center in an external magnetic field. Carbon (^12C) atoms are depicted in brown, the nitrogen (^14N/^15N) atom in blue and the electron in light blue. The labels A, B, C and D refer to the possible orientations of the center. The case shown corresponds to an on-axis P1 center (labeled D).
• Figure S2: Simulated DEER Spectrum of a P1 bath formed with (a) ^14N and (b) ^15N. Dashed lines indicate the theoretical prediction of Eq. (\ref{['SMEq: 14NHf']}) and (\ref{['SMEq: 15NHf']}). The labeling of each resonance peak (top) indicates the corresponding orientation of the center, while the labels in the bottom indicate the nitrogen dressed state.