Robust Nuclear Spin Polarization via Ground-State Level Anti-Crossing of Boron Vacancy Defects in Hexagonal Boron Nitride (2024)

Shihao RuS. R., Z. J., H. L. and J. K. contributed equally to this work.Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore  Zhengzhi JiangS. R., Z. J., H. L. and J. K. contributed equally to this work.Department of Chemistry, National University of Singapore, Singapore 117543, SingaporeJoint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, P. R. China  Haidong LiangS. R., Z. J., H. L. and J. K. contributed equally to this work.Centre for Ion Beam Applications, Department of Physics, National University of Singapore, Singapore 117542, Singapore  Jonathan KennyS. R., Z. J., H. L. and J. K. contributed equally to this work.Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore  Hongbing CaiDivision of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, SingaporeThe Photonics Institute and Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore  Xiaodan LyuDivision of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, SingaporeThe Photonics Institute and Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore  Robert CernanskyInstitute for Quantum Optics and Centre for Integrated Quantum Science and technology (IQST), Ulm University, Albert-Einstein-Allee 11, 89081 Ulm, Germany  Feifei ZhouDivision of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore  Yuzhe YangDivision of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore  Kenji WatanabeInternational Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba 305-0044, Japan  Takashi TaniguchInternational Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba 305-0044, Japan  Fuli LiSchool of Physics, Xi’an Jiaotong University, Xi’an 710049, China  Teck Seng KohDivision of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore  Xiaogang LiuDepartment of Chemistry, National University of Singapore, Singapore 117543, SingaporeJoint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, P. R. China  Fedor Jelezkofedor.jelezko@uni-ulm.deInstitute for Quantum Optics and Centre for Integrated Quantum Science and technology (IQST), Ulm University, Albert-Einstein-Allee 11, 89081 Ulm, Germany  Andrew A. Bettiola.bettiol@nus.edu.sgCentre for Ion Beam Applications, Department of Physics, National University of Singapore, Singapore 117542, Singapore  Weibo Gaowbgao@ntu.edu.sgDivision of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, SingaporeThe Photonics Institute and Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, SingaporeCentre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore

(June 1, 2024)

Optically addressable solid-state spin defects in wide band-gap materials serve as promising artificial atoms for quantum information sciences. For instance, spin defects in diamond and silicon carbide exhibit long spin coherence times, high-fidelity spin manipulations, and entangled electron-nuclear spin pairs at room temperature Bar-Gilletal. (2013); Christleetal. (2015); Toganetal. (2010); Christleetal. (2017); Fuchsetal. (2011); Bourassaetal. (2020). In addition, layered van der Waals materials offer alternative platforms for solid-state spin defects, with reduced dimensionality facilitating scalable two-dimensional quantum device design. Among them, hexagonal boron nitride (h-BN) has attracted significant interest due to its exceptional properties, such as wide bandgap, high thermal conductivity, and robust mechanical strength Liuetal. (2022a). Recently, negatively charged boron vacancy ($\mathrm{V_{B}^{-}}$) defects in h-BN have been extensively studied for their coherently manipulatable spin states and high optically detected magnetic resonance (ODMR) contrast at room temperature Gottscholletal. (2021a); Gaoetal. (2021), critical for sensitivity in quantum sensing applications Gottscholletal. (2021b); Lyuetal. (2022); Liuetal. (2021); Huangetal. (2022); Healeyetal. (2022); Allertetal. (2022). Polarization and rapid manipulation of adjacent nitrogen nuclear spins in h-BN via excited-state level anticrossing (ESLAC) have been achieved Gaoetal. (2022), offering avenues to store and manipulate quantum information Caietal. (2013); Tabeshetal. (2023).

The ESLAC approach to nuclear spin polarization in h-BN has limitations, such as the need for high excitation laser power and low level of nuclear spin polarization Jacquesetal. (2009); Gottscholletal. (2020); Yuetal. (2022); Muetal. (2022). To address the challenge, we investigate the use of ground-state level anti-crossing (GSLAC) of $\mathrm{V_{B}^{-}}$ for achieving nuclear spin polarization in h-BN. GSLAC provides several advantages over ESLAC, including increased robustness against excitation laser power fluctuations and higher nuclear spin polarization level. In this paper, we present an in-depth study of the GSLAC method and demonstrate its potential for enhancing the performance of nuclear spin polarization in $\mathrm{V_{B}^{-}}$ systems Gaoetal. (2022); Jacquesetal. (2009); Sangtawesinetal. (2016). We initiate our study by evaluating the levels of nuclear polarization at ESLAC and GSLAC regions. Our findings suggest that, even under comparatively low excitation power, GSLAC can induce high levels of nuclear polarization. Then we measure the nuclear polarization level as a function of magnetic field, aiming to find the optimal nuclear polarization level. Lastly, we have demonstrated the direct optical readout of nuclear spins through optically detected nuclear magnetic resonance (ODNMR). These comprehensive experimental endeavors pave the way for advancing quantum information processing, enhancing nuclear magnetic resonance spectroscopy sensitivity, and enabling the development of high-performance nuclear spin-based sensors.

Boron vacancy and its energy levels. The $\mathrm{V_{B}^{-}}$ defect in h-BN is a point defect that occurs when a boron atom is missing from the crystal lattice, as shown in Fig. 1(a) Gottscholletal. (2021a). A $\mathrm{V_{B}^{-}}$ defect has a triplet ground state, a triplet excited state, and a non-radiative singlet metastable state. When illuminated with a green laser, $\mathrm{V_{B}^{-}}$ defects are optically excited from the ground state to the excited state. The defects can then undergo spin-dependent intersystem crossing (ISC) to the singlet metastable state, leading to spin polarization. The spin-dependent nature of the ISC processes also results in spin-dependent fluorescence, enabling optical detection and manipulation of the $\mathrm{V_{B}^{-}}$ defect’s spin state. The dynamics is shown in Fig. 1(b) Degenetal. (2017).

Nuclear polarization assisted by GSLAC. As the external magnetic field is tuned, the energy levels of $m_{s}=0$ and $m_{s}=-1$ states become nearly degenerate at certain magnetic field values, leading to LAC Gottscholletal. (2021a); Gaoetal. (2022); Jacquesetal. (2009); Scheueretal. (2016). At these points, the wavefunctions of the electronic and nuclear spin states mix, allowing for a strong interaction between them. Through this interaction, the electronic and nuclear spins can exchange spin angular momentum. This can be facilitated by a process called flip-flop, where the electronic spin flips while the nuclear spin flops simultaneously in the opposite direction. A diagram of dynamics of nuclear polarization assisted by GSLAC is shown in Fig. 1(c). The flip-flop process is indicated by grey arrows. As a result, the spin polarization of the electronic spin is transferred to the nuclear spins, enhancing their polarization.

Sample preparation and setup.h-BN flakes with thickness of several $\mathrm{\mu}$m were proton-bombarded at 250 keV energy and 3e16 $\mathrm{cm}^{-2}$ dose to create dense $\mathrm{V_{B}^{-}}$ defects Liangetal. (2023).A homemade confocal microscope were used in the experiment. A 40x/0.6 visible objective focused the excitation laser onto the sample and collected fluorescence. A 532 nm laser modulated by an Acoustic Optical Modulator provided off-resonance excitation. The photoluminescence signal, filtered through a 700-nm long pass and 1000-nm short pass filter, was coupled to a photodiode. The microwave generated by an RF signal generator and gated by an RF switch, was amplified, and applied to the sample via a coplanar waveguide where the h-BN flake was placed. A permanent magnet on a 3-axis motorized translation stage provided the magnetic field. Magnetic field alignment along the sample’s c-axis was done before the experiment Supp_info .

Extraction of populations of nuclear spin states. For $\mathrm{V_{B}^{-}}$ defects, the hyperfine interactions between the central electron spin and the three nearest nitrogen nuclear spins cause each electronic state to split into 7 sublevels.This results in an ODMR peak that consists of 7 subpeaks, separated by a hyperfine value of approximately 47 MHz Gottscholletal. (2021a); Gaoetal. (2022).To analyze the population of the nuclear spin states, the ODMR results are fitted with 7 peaks corresponding to these sublevels. By fitting the ODMR results with 7 subpeaks, we can extract the area of each subpeak, which is proportional to the population of the corresponding nuclear spin state Gaoetal. (2022); Jacquesetal. (2009). This allows us to determine the nuclear spin polarization in the $\mathrm{V_{B}^{-}}$ system and further analyze the effectiveness of the GSLAC and ESLAC techniques for achieving nuclear spin polarization.

Laser Power Dependence in ESLAC and GSLAC: A Comparative Study. The laser power requirements for the ESLAC and GSLAC methods in achieving nuclear spin polarization can be studied with pulsed ODMR spectra. Pulsed ODMR measurements are conducted at magnetic fields indicated by the shaded areas in Fig. 2(a). The lower and upper shaded fields correspond to the regions near ESLAC and GSLAC, respectively. The implemented measurement sequence is outlined in Fig. 2(b). We define the contrast of pulsed ODMR as $(S_{1}-S_{2})/(S_{1}+S_{2})$.

The robustness of GSLAC-assisted nuclear polarization is attributed to the longer residence time in the ground state prior to excitation due to light absorption.The nuclear polarization process entails two steps: initial electron spin polarization through spin-dependent ISC under laser illumination, followed by transfer of this polarization to the nuclear spins.The transfer occurs due to the precession of superposition states, either at the excited states (ESLAC) or the ground states (GSLAC) Jacquesetal. (2009). A shorter residence time, such as the excited state lifetime of about 1.258 ns at room temperature (refer to Supp_info ), restricts the duration for the flip-flop process to occur. This results in the system rapidly reverting to the ground state, thus curtailing the DNP level achievable at low pump power.

Optimization of nuclear polarization. To identify the magnetic field range that yields the highest nuclear polarization level, we assessed the nuclear polarization levels over a magnetic field range spanning from 25 mT to 200 mT. This span encapsulates both the ESLAC and GSLAC regions. It’s important to note that the data corresponding to the precise GSLAC point, occurring around 133 mT in Fig. 3, could not be obtained from ODMR spectra due to significant spin state mixing. To accelerate the measurements and obtain reliable estimates for nuclear polarization levels, we opted for continuous wave (CW) ODMR, which provides superior signal-to-noise ratio. It should be stressed that, within the ESLAC region, CW ODMR enables greater nuclear polarization levels compared to pulsed ODMR, because of the higher average laser power.

The collected data, pertaining to a laser power of 112 mW, are depicted as green dots in Fig. 3. Upon the gradual increment of the magnetic field to 74.9 mT (ESLAC), we observed a peak in the nuclear polarization level. Subsequently, as the magnetic field continued to increase, the polarization level initially decreased, only to start rising again upon entering the GSLAC region. The polarization level exhibits a gradual decline beyond the GSLAC point and this trend persists with further elevation in the magnetic field. The highest nuclear polarization level observed experimentally, $0.262\pm 0.005$, manifests around 141 mT. This magnetic field is the closest measurable point to the GSLAC in our experimental field range.

To estimate the nuclear polarization within the region near the GSLAC (100 to 140 mT), where experimental data could not be obtained, we performed a theoretical simulation. We model the system with a Hamiltonian, consisting of an electronic spin ($\mathrm{V_{B}^{-}}$) and three adjacent nitrogen nuclear spins Supp_info ; Gaoetal. (2022). The population of each state is extracted after arbitrarily long laser interaction to ensure that a steady state is reached.To get the levels of nuclear polarization at the strong mixing range, we extract the population of each $m_{I}$ state from the simulation results. The nuclear polarization levels calculated as a function of magnetic field are depicted as a green curve in Fig. 3. In our simulation, the nuclear polarization peaks at a level of 0.311, occurring near a magnetic field strength of 127 mT. The nuclear polarization levels predicted by our simulation align well with our experimental results within the measurable ranges, underscoring the reliability of our model Heetal. (1993).

It is important to note that the observed relatively low nuclear polarization level can be attributed to the unequal hyperfine interaction components, $A_{xx}$ and $A_{yy}$. These elements contribute to the non-diagonal hyperfine Hamiltonian, which promotes not only zero-quantum transitions but also two-quantum transitions in the vicinity of the LAC WokaunandErnst (1977); HughesandGeiger (1955). Unlike in NV centers, this leads to unprotected highest quantum states in boron vacancies, $\ket{m_{s}=0,m_{Itotal}=+3}$, affecting nuclear polarization. Our simulations, depicted in FIG. S11, support this, showing higher polarization with equal hyperfine components. Future research could beneficially focus on strain engineering as a method to adjust the $A_{xx}$ and $A_{yy}$ hyperfine components, potentially leading to greater polarization levels Supp_info .

Optically detected nuclear magnetic resonance.The nuclear polarization induced by flip-flop can lead to the direct optical readout of nuclear spins. When only zero-quantum transitions are considered,$\left|m_{s}=0,m_{I_{1},I_{2},I_{3}}=+1,+1,+1\right>$ gives the largest fluorescence signal in general because it didn’t go through the flip-flop transition.(any flip of nuclear spins will lead to $\left|m_{s}=+1\right>$,which has different energy level with $\left|m_{s}=0\right>$, and therefor no mixing is happening).Other states, for instance, $\left|m_{s}=0,m_{I_{1},I_{2},I_{3}}=0,+1,+1\right>$ can mix with $\left|m_{s}=-1,m_{I_{1},I_{2},I_{3}}=+1,+1,+1\right>$, which subsequently transits to a dark state via ISC.Therefore, this reduces the fluorescence from such states since it goes through the dark state. This mechanism will allow us to read the nuclear state directly with sequence as shown in Fig. 4(a) and (b), an approach as ODNMR. The role of two-quantum transitions on ODNMR is discussed in the Ref. Supp_info .

Fig. 4(c) shows an example of ODNMR spectrum for the transitions within spin sublevels for $\left|m_{s}=0\right>$ at magnetic field of 80 mT.The RF applied will address the transition between two states and therefore reduce the fluorescence if there is a discrepancy in the brightness of the two states, as shown in inset.This leads to a negative value in the ODNMR contrast, which is calculated as (Signal $-$ Reference) / (Signal + Reference).Top panel in Fig. 4(c) denotes the transitions as simulated. The simulation result agrees well with the experimental ODNMR spectrum shown in the bottom panel.Similarly, if we apply additional two microwave $\pi$ pulses, this will allow us to measure the transitions between nuclear spin sublevels for $\left|m_{s}=-1\right>$. Fig. 4(d) shows an example for the transitions for spin sublevels of $\left|m_{s}=-1\right>$. The ODNMR signals below 30 MHz in Fig. 4(d) are attributable to the imperfection of the MW $\pi$ pulse, which leaves a residual population in the $\left|m_{s}=0\right>$ state.

The full scan of ODNMR spectrum as a function of magnetic field is shown in Fig. 4(e) and Fig. 4(f). From Fig. 4(e), in the range of 100 to 140 mT, one can see that a larger ODNMR contrast can be achieved when we are approaching the GSLAC point at 128 mT and the linewidth of ODNMR transitions gets broader due to stronger mixing. At exactly 128 mT, we observe a sudden drop in the contrast of the ODNMR spectra.This decrease can be attributed to extensive state mixing between $m_{s}=0$ and $m_{s}=-1$, resulting in reduced electron spin polarization Heetal. (1993). This is corroborated by our simulation results showcased in FIG. S12. Fig. 4(d) showcases the ODNMR results for the $m_{s}=-1$ branch. Similar conclusions to those previously discussed can be drawn from this data: as the magnetic field enters the range of 100 to 113 mT, and 134 mT to 140 mT, the transitions noticeably broaden, signifying a high degree of state mixing.

Conclusion. In summary, we have demonstrated a robust approach for polarizing nuclear spins in h-BN, leveraging the Ground-State Level Anticrossing of $\mathrm{V_{B}^{-}}$. Notably, this method can be executed under low-power excitation. The durability of the GSLAC-assisted nuclear polarization is attributable to the extended residence time of ground states in comparison to excited states. Our simulations suggest that an optimized level of nuclear polarization can be attained near a magnetic field strength of 133 mT, where strong state mixing occurs.We emphasize that this GSLAC-assisted nuclear polarization method is broadly applicable and not confined to the specific color center examined in this study.Combined with dynamic decoupling methods to extend the coherence time Rizzatoetal. (2023) and the measured coherent rotation of coupled nitrogen nuclear spins results at GSLAC Supp_info , the reliable polarization of nuclear spins in van der Waals materials has promising implications for quantum sensing technologies and quantum information science, including potential applications in hyperpolarization of samples Glennetal. (2018) and quantum registers Duttetal. (2007).