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arXiv:2607.07642

Acoustic-phonon-driven spin-lattice relaxation of the hBN boron vacancy in the sub-THz regime

Priyo Adhikary, Pramey Upadhyaya

cond-mat.mtrl-sciquant-phSubmitted Jul 8, 2026• Announced Jul 9, 2026
arXivHTMLPDF

Abstract

The negatively charged boron vacancy center in hexagonal boron nitride is a premier candidate for quantum sensing, yet its performance is critically limited by longitudinal spin-lattice relaxation time ($T_1$). A microscopic understanding of spin relaxation in the high magnetic field regime remains elusive, as the relevant Zeeman transitions lie far below the optical phonon energies typically invoked to describe the relaxation process. Here, we apply an \textit{ab initio} acoustic mode spin-phonon relaxation theory to this problem and quantitatively reproduce the experimental magnetic field and temperature dependence of $T_1$ without empirical fitting parameters. We demonstrate that the relaxation dynamics are driven by a direct one-phonon emission and absorption process resonant with the Zeeman splitting. Furthermore, we identify the out-of-plane flexural phonon branch which is unique to two-dimensional hosts, as the primary source of decoherence, creating a distinct low-energy spectral function that facilitates spin relaxation. Our results provide a microscopic interpretation of the experimentally observed non-monotonic field and temperature dependence in two-dimensional quantum defect centers.

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Juan M. Florez, Eric Suárez Morell

The negatively charged boron vacancy ($\VB$) in hexagonal boron nitride (\hBN{}) was the first optically addressable spin qubit identified inside a van der Waals crystal, allowing atomically defined placement relative to a target. Its coherence in bulk \hBN{} is limited by the boron nuclei of the layers flanking the defect plane, which a thin flake removes. Here, we use a generalized cluster-correlation expansion with an extended central-spin block to calculate the Hahn-echo coherence time of $\VB$ in h$^{11}$B$^{15}$N as a function of layer number. Our results show that $T_2$ rises from $199\ns$ in the bulk limit to $653\ns$ in a monolayer, a factor of $3.3$ that is already saturated at three layers and that a sublattice decomposition attributes entirely to boron. The enhancement is confined to low field, is insensitive to stacking registry and twist angle, and requires alignment to within about two degrees, an onset we reproduce with no free parameters. Under dynamical decoupling, a $1/e$ threshold returns $206\ns$ for every thickness, but this is a zero of the first-shell modulation rather than a decay: measured without a threshold, the layer contrast survives and reaches a factor of $170$. Layer number thus emerges as a design parameter for $\VB$-based sensing.

cond-mat.mes-hallCross-listedarXiv:2609.01812•Sep 3, 2026
The negatively charged boron vacancy center in hexagonal boron nitride is a premier candidate for quantum sensing, yet its performance is critically limited by longitudinal spin-lattice relaxation time (T1T_1T1​). A microscopic understanding of spin relaxation in the high magnetic field regime remains elusive, as the relevant Zeeman transitions lie far below the optical phonon energies typically invoked to describe the relaxation process. Here, we apply an \textit{ab initio} acoustic mode spin-phonon relaxation theory to this problem and quantitatively reproduce the experimental magnetic field and temperature dependence of T1T_1T1​ without empirical fitting parameters. We demonstrate that the relaxation dynamics are driven by a direct one-phonon emission and absorption process resonant with the Zeeman splitting. Furthermore, we identify the out-of-plane flexural phonon branch which is unique to two-dimensional hosts, as the primary source of decoherence, creating a distinct low-energy spectral function that facilitates spin relaxation. Our results provide a microscopic interpretation of the experimentally observed non-monotonic field and temperature dependence in two-dimensional quantum defect centers.
Negatively charged boron vacancies (VB−_{\text{B}}^{-}B−​) in hexagonal boron nitride (hBN) comprise a promising quantum sensing platform, optically addressable at room temperature and transferrable onto samples. However, broad hyperfine-split spin transitions of the ensemble pose challenges for quantum sensing with conventional resonant excitation due to limited spectral coverage. While isotopically enriched hBN using 10^{10}10B and 15^{15}15N isotopes (h10^{10}10B15^{15}15N) exhibits sharper spectral features, significant inhomogeneous broadening persists. We demonstrate that, implemented via frequency modulation on an FPGA, a frequency-ramped microwave pulse achieves around 4-fold greater ∣0⟩→∣−1⟩|0\rangle\rightarrow|-1\rangle∣0⟩→∣−1⟩ spin-state population transfer and thus contrast than resonant microwave excitation and thus 16-fold shorter measurement time for spin relaxation based quantum sensing. Quantum dynamics simulations reveal that an effective two-state Landau-Zener model captures the complex relationship between population inversion and pulse length with relaxations incorporated. Our approach is robust and valuable for quantum relaxometry with spin defects in hBN in noisy environments.
Transferable hexagonal boron nitride (hBN) hosting negatively charged boron-vacancy (VB−^{-}−) spin defects offers a versatile platform for integrated quantum magnetometry, yet quantitative imaging of magnetic microstructures remains challenging. Here, we integrate a transferred hBN flake with a 4 μμμm-diameter permalloy (Py = Ni81{81}81Fe19{19}19) microdisk and perform spatially resolved optically detected magnetic resonance measurements at room temperature. An applied in-plane magnetic field distorts the vortex-state magnetization, generating edge-localized magnetic surface charges and pronounced stray-field signatures at opposite disk edges. By referencing each pixel to its local zero-field splitting and correcting for a residual out-of-plane bias field, we quantitatively reconstruct the out-of-plane stray-field distribution, revealing peak fields of approximately 11.2 mT. An edge-charge model reproduces the spatial distribution and amplitude of the reconstructed field, linking the ODMR response to the field-driven evolution of the vortex state. These results establish transferred hBN VB−^{-}− sensors for quantitative magnetometry of magnetic microstructures.
Mechanically isolated defect centers in hexagonal boron nitride are promising coherent quantum emitters, yet spectral instabilities persist, and their spin-related nature remains unclear. Here we investigate a single mechanically isolated quantum emitter in hBN integrated onto a coplanar waveguide. The emitter exhibits exceptionally bright resonant fluorescence with saturation count rates exceeding 10 Mc/s10\,\mathrm{Mc/s}10Mc/s. High-resolution spectroscopy reveals two closely spaced zero-phonon-line transitions originating from the same defect complex. Time-resolved spectroscopy shows that these transitions exhibit markedly different spectral diffusion dynamics, consistent with distinct donor-acceptor-pair-like recombination pathways with different sensitivities to local electrostatic fluctuations. Off-resonant blue illumination redistributes emission between the two transitions and increases the emission duty cycle without significantly modifying the dominant spectral diffusion rates at low temperature, indicating repumping from long-lived shelving states. Magnetic-field-dependent photoluminescence, optically detected magnetic resonance, and pump-probe measurements reveal millisecond-scale relaxation dynamics and magnetic-field-dependent fluorescence contrast, demonstrating spin-dependent population dynamics in the metastable shelving state. These results clarify how charge-driven spectral fluctuations and spin-dependent shelving jointly shape the optical cycling dynamics.
The design of polarization-encoded quantum interfaces relies on the assumption that solid-state emitters possess static transition dipoles defined by the host lattice symmetry. Here, we demonstrate that the transition dipole moment of single hexagonal boron nitride quantum emitters is not a static property but rotates as a function of photon energy. Through high-resolution energy-resolved spectroscopy, we reveal a continuous rotation of the emission dipole orientation reaching up to 40∘40^{\circ}40∘ across the vibronic manifold at room temperature, driven by coupling to the phonon bath. This spectral rotation is effectively suppressed at cryogenic temperatures (6 K), where the acoustic phonon population is negligible, identifying thermally activated lattice vibrations as the primary driver of the reorientation. First-principles calculations on two representative defects spanning weak and strong electron-phonon coupling regimes confirm that phonon-displaced geometries produce a systematic deviation of the transition dipole orientation from the zero-phonon line, with the magnitude scaling with vibronic coupling strength. The experimental observations and calculations demonstrate that single quantum emitters can operate beyond the Condon approximation, with the transition dipole acquiring a dependence on the instantaneous nuclear configuration. Our results identify a fundamental limit for polarization fidelity in solid-state quantum networks and connect solid-state single-emitter physics to a class of effects previously accessible only in ensemble measurements in molecular and biological spectroscopy.
Understanding the effect of vibrations on the relaxation process of individual spins is crucial for implementing nanosystems for quantum information and quantum metrology applications. In this work, we present a theoretical microscopic model to describe the spin-lattice relaxation of individual electronic spins associated to negatively charged nitrogen-vacancy centers in diamond, although our results can be extended to other spin-boson systems. Starting from a general spin-lattice interaction Hamiltonian, we provide a detailed description and solution of the quantum master equation of an electronic spin-one system coupled to a phononic bath in thermal equilibrium. Special attention is given to the dynamics of one-phonon processes below 1 K where our results agree with recent experimental findings and analytically describe the temperature and magnetic-field scaling. At higher temperatures, linear and second-order terms in the interaction Hamiltonian are considered and the temperature scaling is discussed for acoustic and quasilocalized phonons when appropriate. Our results, in addition to confirming a T5{T}^{5}T5 temperature dependence of the longitudinal relaxation rate at higher temperatures, in agreement with experimental observations, provide a theoretical background for modeling the spin-lattice relaxation at a wide range of temperatures where different temperature scalings might be expected.
The negatively charged boron vacancy ($\VB$) in hexagonal boron nitride (\hBN{}) was the first optically addressable spin qubit identified inside a van der Waals crystal, allowing atomically defined placement relative to a target. Its coherence in bulk \hBN{} is limited by the boron nuclei of the layers flanking the defect plane, which a thin flake removes. Here, we use a generalized cluster-correlation expansion with an extended central-spin block to calculate the Hahn-echo coherence time of $\VB$ in h11^{11}11B15^{15}15N as a function of layer number. Our results show that T2T_2T2​ rises from $199\ns$ in the bulk limit to $653\ns$ in a monolayer, a factor of 3.33.33.3 that is already saturated at three layers and that a sublattice decomposition attributes entirely to boron. The enhancement is confined to low field, is insensitive to stacking registry and twist angle, and requires alignment to within about two degrees, an onset we reproduce with no free parameters. Under dynamical decoupling, a 1/e1/e1/e threshold returns $206\ns$ for every thickness, but this is a zero of the first-shell modulation rather than a decay: measured without a threshold, the layer contrast survives and reaches a factor of 170170170. Layer number thus emerges as a design parameter for $\VB$-based sensing.