Nuclear Spin Bath Research Articles

Realization of robust quantum noise characterization in the presence of coherent errors

Complex quantum systems and their various applications are susceptible to noise of coherent and incoherent nature. Characterization of noise and its sources is an open, key challenge in quantum technology applications, especially in terms of distinguishing between inherent incoherent noise and systematic coherent errors. In this paper, we study a scheme of repeated sequential measurements that enables the characterization of incoherent errors by reducing the effects of coherent errors. We demonstrate this approach using a coherently controlled nitrogen vacancy in diamond, coupled to both a natural nuclear spin bath (non-Markovian) and to experimentally controlled relaxation through an optical pumping process (nearly Markovian). Our results show mitigation of coherent errors both for Markovian and non-Markovian incoherent noise profiles. We apply this scheme to the estimation of the dephasing time (T2*) due to incoherent noise. We observe an improved robustness against coherent errors in the estimation of dephasing time (T2*) compared to the standard (Ramsey) measurement.

Sensing Coherent Nuclear Spin Dynamics with an Ensemble of Paramagnetic Nitrogen Spins

The unpolarized spin environment surrounding a central spin qubit is typically considered as an incoherent source of dephasing, however, precise characterization and control of the spin bath can yield a resource for storing and sensing with quantum states. In this work, we use nitrogen-vacancy (NV) centers in diamond to measure the coherence of optically dark paramagnetic nitrogen defects (P1 centers) and detect coherent interactions between the P1 centers and a local bath of 13C nuclear spins. The dipolar coupling between the P1 centers and 13C nuclear spins is identified by signature periodic collapses and revivals in the P1 spin coherence signal. We then demonstrate, using a range of dynamical decoupling protocols, that the probing NV centers and the P1 spins are coupled to independent ensembles of 13C nuclear spins. Our work illustrates how the optically dark P1 spins can be used to extract information from their local environment and offers new insight into the interactions within a many-body system. Published by the American Physical Society 2024

High-Fidelity Optical Readout of a Nuclear-Spin Qubit in Silicon Carbide.

Quantum state readout is a key requirement for a successful qubit platform. In this work, we demonstrate a high-fidelity quantum state readout of a V2 center nuclear spin based on a repetitive readout technique. We demonstrate up to 99.5% readout fidelity and 99% for state preparation. Using this efficient readout, we initialize the nuclear spin by measurement and demonstrate its Rabi and Ramsey nutation. Finally, we use the nuclear spin as a long-lived memory for quantum sensing application of a weakly coupled diatomic nuclear-spin bath.

Digital noise spectroscopy with a quantum sensor

We introduce and experimentally demonstrate a quantum sensing protocol to sample and reconstruct the autocorrelation of a noise process using a single-qubit sensor under digital control modulation. This Walsh noise spectroscopy method exploits simple sequences of spin-flip pulses to generate a complete basis of digital filters that directly sample the power spectrum of the target noise in the sequency domain, from which the autocorrelation function in the time domain, as well as the power spectrum in the frequency domain, can be reconstructed using linear transformations. Our method, which can also be seen as an implementation of frame-based noise spectroscopy, solves the fundamental difficulty in sampling continuous functions with digital filters by introducing a transformation that relates the arithmetic and logical time domains. In comparison to standard, frequency-based dynamical-decoupling noise spectroscopy protocols, the accuracy of our method is only limited by sampling and discretization in the time domain and can be easily improved, even under limited evolution time due to decoherence and hardware limitations. Finally, we experimentally reconstruct the autocorrelation function of the effective magnetic field produced by the nuclear-spin bath on the electronic spin of a single nitrogen-vacancy center in diamond, discuss practical limitations of the method, and avenues to further improve the reconstruction accuracy.

Nuclear Spin-Depleted, Isotopically Enriched 70 Ge/28 Si70 Ge Quantum Wells.

The p-symmetry of the hole wavefunction is associated with a weaker hyperfine interaction, which makes hole spin qubits attractive candidates to implement quantum processors. However, recent studies demonstrate that hole qubits are still very sensitive to nuclear spin bath, thus highlighting the need for nuclear spin-free germanium (Ge) qubits to suppress this decoherence channel. Herein, this work demonstrates the epitaxial growth of 73 Ge- and 29 Si-depleted, isotopically enriched 70 Ge/silicon-germanium (SiGe) quantum wells. The growth is achieved by reduced pressure chemical vapor deposition using isotopically purified monogermane 70 GeH4 and monosilane 28 SiH4 with an isotopic purity higher than 99.9% and 99.99%, respectively. The quantum wells consist of a series of 70 Ge/SiGe heterostructures grown on Si wafers. The isotopic purity is investigated using atom probe tomography (APT) following an analytical procedure addressing the discrepancies caused by the overlap of isotope peaks in mass spectra. The nuclear spin background is found to be sensitive to the growth conditions with the lowest concentration of 73 Ge and 29 Si is below 0.01% in the Ge well and SiGe barriers. The measured average distance between nuclear spins reaches 3-4 nm in 70 Ge/28 Si70 Ge, which is an order of magnitude larger than in natural Ge/SiGe heterostructures.The spread of the hole wavefunction and the residual nuclear spin background in APT voluminals comparable to the size of realistic quantum dots are also discussed.

Extending Spin Dephasing Time of Perfectly Aligned Nitrogen‐Vacancy Centers by Mitigating Stress Distribution on Highly Misoriented Chemical‐Vapor‐Deposition Diamond

AbstractExtending the spin‐dephasing time (T2*) of perfectly aligned nitrogen‐vacancy (NV) centers in large‐volume chemical vapor deposition (CVD) diamonds leads to enhanced DC magnetic sensitivity. However, T2* of the NV centers is significantly reduced by the stress distribution in the diamond film as its thickness increases. To overcome this issue, they developed a method to mitigate the stress distribution in the CVD diamond films, leading to a T2* extension of the ensemble NV centers. CVD diamond films of ≈60 µm thickness with perfectly aligned NV centers are formed on (111) diamond substrates with misorientation angles of 2.0°, 3.7°, 5.0°, and 10.0°. The study found that T2* of the ensemble of NV centers increased to approach its value limited only by the electron and nuclear spin bath with increasing the misorientation angle. Microscopic stress imaging revealed that the stress distribution is highly inhomogeneous along the depth direction in the CVD diamond film at low misorientation angles, whereas the inhomogeneity is largely suppressed on highly misoriented substrates. The reduced stress distribution possibly originates from the reduction of the dislocation density in the CVD diamond. This study provides an important method for synthesizing high‐quality diamond materials for use in highly sensitive quantum sensors.

Active hyperpolarization of the nuclear spin lattice: Application to hexagonal boron nitride color centers

The hyperpolarization of nuclear spin ensembles through their interaction with optically active color centers has emerged as a promising technique with applications ranging from sensing and imaging to quantum computation. Here, we investigate the efficiency of this approach for the hyperpolarization of the nuclear-spin bath in a monolayer of hexagonal boron nitride via the optically active boron vacancy centers (${\mathrm{V}}_{\mathrm{B}}$). To that end we design a polarization sequence based on the suitable combination of optical polarization and microwave driving of the ${\mathrm{V}}_{\mathrm{B}}$, which we optimize numerically. To extend our study to realistic systems with a large number of interacting spins, we employ an approximate method based on the Holstein-Primakoff transformation, whose validity we benchmark against exact numerics for small system sizes. Our results suggest that a high-degree of polarization in the boron and nitrogen nuclear-spin lattices is achievable also at room temperature. Our work provides the first step toward the realization of a two-dimensional quantum simulator based on natural nuclear spins and it can prove useful for extending the coherence time of the ${\mathrm{V}}_{\mathrm{B}}$ centers.

Truncated Wigner approximation for the bosonic model of large spin baths

The central spin model has a wide applicability. It is ideally suited to describe a small quantum system, for instance a quantum bit, in contact to a bath of spins, e.g., nuclear spins or other small quantum systems in general. According to previous work [R. R\"ohrig et al., Phys. Rev. B 97, 165431 (2018)], a large bath of quantum spins can be described as a bath of quantum harmonic oscillators. But the resulting quantum model is still far from being straightforwardly solvable. Hence we consider a chain representation for the bosonic degrees of freedom to study how well a semi-classical truncated Wigner approximation of the effective model of harmonic oscillators (bTWA) works in comparison with other approximate and exact methods. We find that the bTWA works well for short times, but deviates from the results of other methods for long times. The general message is that the applicability of semi-classical approaches strongly depends on the variables in terms of which the model is formulated. Numerically, we examine the effect of the number of bath spins and of the truncation level, i.e., the chain length.

Nuclear pair electron spin echo envelope modulation

The interaction of electron spins with homonuclear spin pairs in their vicinity is one of the dominating mechanisms of electron spin echo decay at low temperature and low concentration. Here, we study this mechanism using established concepts of electron spin echo envelope modulation (ESEEM). We obtain analytical expressions for the Hahn echo, the refocused echo, the stimulated echo, and Carr–Purcell pulse trains with small numbers of π pulses. Hahn echo decay is well approximated by the product of nuclear pair ESEEM functions. The same approximation can explain dependence of stimulated echo decay on the first interpulse delay and provides reasonable time scale estimates for decay of Carr–Purcell echos after an odd number of π pulses. Carr–Purcell echoes after an even number of π pulses are rather sensitive to correlations within larger nuclear spin clusters. Approximations improve for both odd and even numbers of π pulses by factorising the nuclear spin bath into disjoint clusters, provided that modulation due to pairs of spins belonging to different clusters is considered in addition to cluster modulation. The analytical ESEEM expressions for the Hahn echo and the Carr–Purcell echo after two π pulses have the same mathematical form as the filter functions of these sequences of spin noise spectroscopy. This coincidence provides a computationally very efficient way of predicting Hahn echo decay induced by homonuclear spin pairs. The analytical pair product approximation predicts the previously observed (Bahrenberg et al., 2021) increase of the refocused echo amplitude when one refocusing time is incremented and other one is fixed but longer. In contrast, the spin-noise concept fails to predict this effect.

Probing details of spin-orbit coupling through Pauli spin blockade

Spin-orbit interaction (SOI) plays a fundamental role in many low-dimensional semiconductor and hybrid quantum devices. In the rapidly evolving field of semiconductor spin qubits, SOI is an essential ingredient that can allow for ultrafast qubit control. The exact manifestation of SOI in a given device is, however, often both hard to predict theoretically and probe experimentally. Here, we develop a detailed theoretical connection between the leakage current through a double quantum dot in Pauli spin blockade and the underlying SOI in the system. We present a general analytic expression for the leakage current, which allows to connect experimentally observable features to both the magnitude and orientation of an effective spin-orbit field acting on the moving carriers. Motivated by the large recent interest in hole-based quantum devices, we further zoom in on the case of Pauli blockade of hole spins, assuming a strong transverse confinement potential. In this limit we also find an analytic expression for the current at low external magnetic field, that includes the effect of hyperfine coupling of the hole spins to randomly fluctuating nuclear spin baths. This result can be used to extract information about both hyperfine and spin-orbit coupling parameters for hole spins in devices with a significant fraction of nonzero nuclear spins.

Anti-Zeno purification of spin baths by quantum probe measurements

The quantum Zeno and anti-Zeno paradigms have thus far addressed the evolution control of a quantum system coupled to an immutable bath via non-selective measurements performed at appropriate intervals. We fundamentally modify these paradigms by introducing, theoretically and experimentally, the concept of controlling the bath state via selective measurements of the system (a qubit). We show that at intervals corresponding to the anti-Zeno regime of the system-bath exchange, a sequence of measurements has strongly correlated outcomes. These correlations can dramatically enhance the bath-state purity and yield a low-entropy steady state of the bath. The purified bath state persists long after the measurements are completed. Such purification enables the exploitation of spin baths as long-lived quantum memories or as quantum-enhanced sensors. The experiment involved a repeatedly probed defect center dephased by a nuclear spin bath in a diamond at low-temperature.

Robust Dynamical Decoupling for the Manipulation of a Spin Network Via a Single Spin

High-fidelity control of quantum systems is crucial for quantum information processing, but is often limited by perturbations from the environment and imperfections in the applied control fields. Here, we investigate the combination of dynamical decoupling (DD) and robust optimal control (ROC) to address this problem. In this combination, ROC is employed to find robust shaped pulses, wherein the directional derivatives of the controlled dynamics with respect to control errors are reduced to a desired order. Then, we incorporate ROC pulses into DD sequences, achieving a remarkable improvement of robustness against multiple error channels. We demonstrate this method in the example of manipulating nuclear spin bath via an electron spin in the nitrogen-vacancy center system. Simulation results indicate that ROC-based DD sequences outperform the state-of-the-art robust DD sequences. Our work has implications for robust quantum control on near-term noisy quantum devices.

Decoherence of a spin-valley qubit in a MoS2 quantum dot

Transition metal dichalcogenide (TMD)-based quantum dots (QDs) have proven to be a successful and promising device for physically implementing electron spin-valley based qubits. Although the electron spin in a TMDs monolayer semiconductor QD can be isolated and controlled with high precision, decoherence occurs due to unavoidable coupling with the surrounding environment, such as nuclear spin environments. In this paper, using an exact master equation (ME) of spin qubit dynamics coupled to a nuclear spin bath in terms of hyperfine interaction (HI), we have investigated the controllability of dynamics processes with varying degrees of non-Markovianity. In large magnetic fields, we show that pure spin or valley qubits can be created. We calculate the loss of fidelity due to the Overhauser field of HI in a wide range of nuclear spin. In this context, we prove that this field restricts the decoherence process of the central electron spin, which can regain its coherence. Finally, we discuss how the coherence of the spin qubit remains robust for large .

Precession-induced nonclassicality of the free induction decay of NV centers by a dynamical polarized nuclear spin bath

The ongoing exploration of the ambiguous boundary between the quantum and the classical worlds has spurred substantial developments in quantum science and technology. Recently, the nonclassicality of dynamical processes has been proposed from a quantum-information-theoretic perspective, in terms of witnessing nonclassical correlations with Hamiltonian ensemble simulations. To acquire insights into the quantum-dynamical mechanism of the process nonclassicality, here we propose to investigate the nonclassicality of the electron spin free-induction-decay process associated with an NV− center. By controlling the nuclear spin precession dynamics via an external magnetic field and nuclear spin polarization, it is possible to manipulate the dynamical behavior of the electron spin, showing a transition between classicality and nonclassicality. We propose an explanation of the classicality–nonclassicality transition in terms of the nuclear spin precession axis orientation and dynamics. We have also performed a series of numerical simulations supporting our findings. Consequently, we can attribute the nonclassical trait of the electron spin dynamics to the behavior of nuclear spin precession dynamics.

(Invited) Spin and Optical Properties of the Silicon Vacancy in 4H-SiC for Quantum Science and Technology

Silicon vacancies in SiC are of significant interest for quantum information and sensing due to their unusual combination of long spin coherence time, optical addressability, and room-temperature operation in an industrially-relevant semiconductor. We characterize the spin and optical properties of the V2 silicon vacancy in 4H-SiC for both single defects and ensembles. We also show that they can be deterministically placed with sub-micron precision using focused Li ion implantation. Low-temperature photoluminescence excitation spectroscopy of the spin-dependent optical transitions of single silicon vacancies reveals two sharp lines with linewidths near the radiative lifetime limit. These lines correspond to the ms=±1/2 and ms=±3/2 states of an S=3/2 spin system that can be optically initialized, coherently manipulated with RF pulses, and read out via spin-dependent photoluminescence. We measure the different properties of spins in the two bases, and compare them to theoretical models. To suppress the limiting effects of the nuclear spin bath, we grow isotopically purified SiC with a very low abundance of 29Si and 13C. Our room temperature spin coherence measurements show orders-of-magnitude improvement of the coherence times in these materials. In particular, the inhomogeneous dephasing time T2 * in the ms=±1/2 basis shows a ~100x improvement, reaching 20 μs. We consider the prospects of this system for quantum sensing and as an efficient spin-photon interface for use in quantum networks.This work was supported by the U.S. Office of Naval Research, the OSD Quantum Sciences and Engineering Program, the Defense Threat Reduction Agency, and the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.

First-principles theory of extending the spin qubit coherence time in hexagonal boron nitride

Negatively charged boron vacancies (VB−) in hexagonal boron nitride (h-BN) are a rapidly developing qubit platform in two-dimensional materials for solid-state quantum applications. However, their spin coherence time (T2) is very short, limited to a few microseconds owing to the inherently dense nuclear spin bath of the h-BN host. As the coherence time is one of the most fundamental properties of spin qubits, the short T2 time of VB− could significantly limit its potential as a promising spin qubit candidate. In this study, we theoretically proposed two materials engineering methods, which can substantially extend the T2 time of the VB− spin by four times more than its intrinsic T2. We performed quantum many-body computations by combining density functional theory and cluster correlation expansion and showed that replacing all the boron atoms in h-BN with the 10B isotope leads to the coherence enhancement of the VB− spin by a factor of three. In addition, the T2 time of the VB− can be enhanced by a factor of 1.3 by inducing a curvature around VB−. Herein, we elucidate that the curvature-induced inhomogeneous strain creates spatially varying quadrupole nuclear interactions, which effectively suppress the nuclear spin flip-flop dynamics in the bath. Importantly, we find that the combination of isotopic enrichment and strain engineering can maximize the T2 time of VB−, yielding 207.2 μs and 161.9 μs for single- and multi-layer h-10BN, respectively. Furthermore, our results can be applied to any spin qubit in h-BN, strengthening their potential as material platforms to realize high-precision quantum sensors, quantum spin registers, and atomically thin quantum magnets.

Theoretical Design of Optimal Molecular Qudits for Quantum Error Correction.

We pinpoint the key ingredients ruling decoherence in multispin clusters, and we engineer the system Hamiltonian to design optimal molecules embedding quantum error correction. These are antiferromagnetically coupled systems with competing exchange interactions, characterized by many low-energy states in which decoherence is dramatically suppressed and does not increase with the system size. This feature allows us to derive optimized code words, enhancing the power of the quantum error correction code by orders of magnitude. We demonstrate this by a complete simulation of the system dynamics, including the effect of decoherence driven by a nuclear spin bath and the full sequence of pulses to implement error correction and logical gates between protected states.

Computational Study of the Silicon Vacancy in 3C-SiC and Perspectives for Quantum Technologies

We theoretically study point defects in 3C-SiC for applications in Quantum Technologies, focusing on the neutral silicon vacancy, with an electron spin of 1, magnetically interacting with the SiC nuclear spin bath containing Si-29 and C-13 nuclei. Initially, the system's energetics are explored with ab-initio methods based on the Density Functional Theory. Thereon, we apply a Hahn-echo sequence on the electron spin and study the effects of the bath dynamics on the electron spin's coherence. The Electron Spin Echo Envelope Modulation (ESEEM) phenomenon, due to single nuclear spin flipping processes, and the overall decay, or decoherence, due to the electron spin's entanglement with the bath, are examined. We exploit the Cluster Correlation Expansion (CCE) theory for calculating an approximate version of the coherence function, at various orders of approximation, in order to associate the different coherence function behaviors to given n-body correlations within the bath.

Formula omitted]Silicon-on-insulator for optically interfaced quantum emitters

The coherence of optical emitters in silicon waveguides is impaired by the coupling to the surrounding bath of 29Si nuclear spins. We eliminate this obstacle by fabricating isotopically enriched silicon-on-insulator (SOI) chips. To this end, we use molecular beam epitaxy to grow a 0.4μm thin 28Si layer with a 29Si concentration <0.006% on a 70nm thin SOI seed chip. the resulting layer reveals a high crystalline quality and has a low defect concentration, determined from secondary ion mass spectroscopy, dark field plane-view and cross-view transmission electron microscope images as well as X-ray diffraction. With its low surface roughness, measured by atomic force microscopy, the grown layer is a promising material for the integration of optically interfaced quantum emitters in low-loss nanophotonic waveguides that are free from nuclear spins.

Nuclear-spin polaron formation: Anisotropy effects and quantum phase transition

We study theoretically the formation of the nuclear-spin polaron state in semiconductor nanosystems within the Lindblad equation approach. To this end, we derive a general Lindblad equation for the density operator that complies with the symmetry of the system Hamiltonian and address the nuclear-spin polaron formation for localized charge carriers subject to an arbitrarily anisotropic hyperfine interaction when optically cooling the nuclei. The steady-state solution of the density matrix for an anisotropic central spin model is presented as a function of the electron and nuclear spin bath temperature. Results for the electron-nuclear spin correlator as well as data for the nuclear spin distribution function serve as a measure of spin-entanglement. The features in both of them clearly indicate the formation of the nuclear polaron state at low temperatures where the crossover regime coincides with an enhancement of quantum fluctuations and agrees with the mean-field prediction of the critical temperature line. We can identify two distinct polaron states dependent upon the hyperfine anisotropy which are separated by a quantum phase transition at the isotropic point. These states are reflected in the temporal spin auto-correlation functions accessible in experiment via spin-noise measurements.