Solid-state Spin Ensemble Research Articles

Extending radiowave frequency detection range with dressed states of solid-state spin ensembles

Quantum sensors using solid-state spin defects excel in the detection of radiofrequency (RF) fields, serving various applications in communication, ranging, and sensing. For this purpose, pulsed dynamical decoupling (PDD) protocols are typically applied, which enhance sensitivity to RF signals. However, these methods are limited to frequencies of a few megahertz, which poses a challenge for sensing higher frequencies. We introduce an alternative approach based on a continuous dynamical decoupling (CDD) scheme involving dressed states of nitrogen vacancy (NV) ensemble spins driven within a microwave resonator. We compare the CDD methods to established PDD protocols and demonstrate the detection of RF signals up to ~85 MHz, about ten times the current limit imposed by the PDD approach under identical conditions. Implementing the CDD method in a heterodyne/synchronized protocol combines the high-frequency detection with high spectral resolution. This advancement extends to various domains requiring detection in the high frequency (HF) and very high frequency (VHF) ranges of the RF spectrum, including spin sensor-based magnetic resonance spectroscopy at high magnetic fields.

Quantum Logic Enhanced Sensing in Solid-State Spin Ensembles.

We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble of solid-state, hybrid two-qubit sensors. We achieve over a factor of 30 improvement in the single-shot signal-to-noise ratio, translating to an ac magnetic field sensitivity enhancement exceeding an order of magnitude for time-averaged measurements. Using the electronic spins of nitrogen vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen nuclear spins of the NV centers as memory qubits, in combination with homogeneous and stable bias and control fields, ensuring that all of the ∼10^{9} two-qubit sensors are sufficiently identical to permit global control of the NV ensemble spin states. We find quantum logic sensitivity enhancement for multiple measurement protocols with varying optimal sensing intervals, including XY8 and DROID-60 dynamical decoupling, as well as correlation spectroscopy, using an applied ac magnetic field signal. The results are independent of the nature of the target signal and broadly applicable to measurements using NV centers and other solid-state spin ensembles. This work provides a benchmark for macroscopic ensembles of quantum sensors that employ quantum logic or quantum error correction algorithms for enhanced sensitivity.

Broadband microwave antenna for uniform manipulation of millimeter-scale volumes of diamond quantum sensors

Quantum sensors based on nitrogen-vacancy (NV) centers in diamond are expected to demonstrate a wide variety of applications. For high-sensitivity quantum sensors with NV center ensembles, uniform manipulation of the electron spins of the NV centers in large volumes is required. In addition, a broad microwave frequency bandwidth for manipulating the NV centers' electron spin is necessary for vector magnetometry and measurement under a finite static magnetic field. Here, we demonstrate a broadband microwave antenna for uniform manipulation of millimeter-scale volumes of diamond quantum sensors. The simulation shows that the current is distributed at both edges of the loop coil of a single copper plate due to the skin effect. The loop coil acts like a Helmholtz coil, which realizes uniformity in the z-direction of the microwave magnetic field (B1). The plate structure has a higher mechanical stability, durability, and a larger heat capacity than the Helmholtz coil, due to its large volume. The antenna achieves a higher performance than previously reported antennae, with a maximal B1 of 4.5 G, a broad bandwidth of 287 ± 6 MHz, and a peak-to-peak variation of 9.2% over a 3.1 mm3 cylinder volume. These performances show that the presented antenna is suitable for manipulating solid-state spin ensembles for high-sensitivity quantum sensors.

Enhanced quantum sensing with room-temperature solid-state masers.

Quantum sensing with solid-state electron spin systems finds broad applications in diverse areas ranging from material and biomedical sciences to fundamental physics. Exploiting collective behavior of noninteracting spins holds the promise of pushing the detection limit to even lower levels, while to date, those levels are scarcely reached because of the broadened linewidth and inefficient readout of solid-state spin ensembles. Here, we experimentally demonstrate that such drawbacks can be overcome by a reborn maser technology at room temperature in the solid state. Owing to maser action, we observe a fourfold reduction in the electron paramagnetic resonance linewidth of an inhomogeneously broadened molecular spin ensemble, which is narrower than the same measured from single spins at cryogenic temperatures. The maser-based readout applied to near zero-field magnetometry showcases the measurement signal-to-noise ratio of 133 for single shots. This technique would be an important addition to the toolbox for boosting the sensitivity of solid-state ensemble spin sensors.

Realistic simulations of spin squeezing and cooperative coupling effects in large ensembles of interacting two-level systems

We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which combines the mean-field dynamics of a spin ensemble with a Monte Carlo sampling of discrete initial spin values to account for quantum correlations. Here we show how this approach can be generalized for dissipative spin systems by replacing the deterministic mean-field evolution by a stochastic process, which describes the decay of coherences and populations while preserving the length of each spin. We demonstrate the application of this technique for simulating nonclassical spin-squeezing effects or the dynamics and steady states of cavity QED models with hundred thousand interacting two-level systems and without relying on any symmetries. This opens up the possibility to perform accurate real-scale simulations of a diverse range of experiments in quantum optics or with solid-state spin ensembles under realistic laboratory conditions.

Robust and Accurate Electric Field Sensing with Solid State Spin Ensembles.

Electron spins in solids constitute remarkable quantum sensors. Individual defect centers in diamond were used to detect individual nuclear spins with a nanometer scale resolution, and ensemble magnetometers rival SQUID and vapor cell magnetometers when taking into account room-temperature operation and size. NV center spins can also detect electric field vectors, despite their weak coupling to electric fields. Here, we employ ensembles of NV center spins to measure macroscopic AC electric fields with high precision. We utilize low strain, 12C enriched diamond to achieve the maximum sensitivity and tailor the spin Hamiltonian via the proper magnetic field adjustment to map out the AC electric field strength and polarization and arrive at refined electric field coupling constants. For high-precision measurements, we combine classical lock-in detection with aspects from quantum phase estimation for the effective suppression of technical noise. Eventually, this enables t-1/2 uncertainty scaling of the electric field strength over extended averaging periods, enabling us to reach a precision down to 10-7 V/μm for an AC electric field with a frequency of 2 kHz and an amplitude of 0.012 V/ μm.

Hamiltonian engineering with constrained optimization for quantum sensing and control

While quantum devices rely on interactions between constituent subsystems and with their environment to operate, native interactions alone often fail to deliver targeted performance. Coherent pulsed control provides the ability to tailor effective interactions, known as Hamiltonian engineering. We propose a Hamiltonian engineering method that maximizes desired interactions while mitigating deleterious ones by conducting a pulse sequence search using constrained optimization. The optimization formulation incorporates pulse sequence length and cardinality penalties consistent with linear or integer programming. We apply the general technique to magnetometry with solid state spin ensembles in which inhomogeneous interactions between sensing spins limit coherence. Defining figures of merit for broadband Ramsey magnetometry, we present novel pulse sequences which outperform known techniques for homonuclear spin decoupling in both spin-1/2 and spin-1 systems. When applied to nitrogen vacancy (NV) centers in diamond, this scheme partially preserves the Zeeman interaction while zeroing dipolar coupling between negatively charged NV− centers. Such a scheme is of interest for NV− magnetometers which have reached the NV−–NV− coupling limit. We discuss experimental implementation in NV ensembles, as well as applicability of the current approach to more general spin bath decoupling and superconducting qubit control.

Microwave Field Uniformity Impact on DC Magnetic Sensing With NV Ensembles in Diamond

Magnetic sensing based on nitrogen-vacancy (NV) center ensembles provides unique signal-to-noise ratio and sensitivity for physical and biological measurements at room temperature. However, inhomogeneous microwave (MW) coupling with NV ensembles and different field projections onto the NV axes lead to nonsynchronous spin dephasing and pose severe challenges to magnetic sensing. In this paper, we experimentally investigated the impact of the MW field uniformity on the DC magnetic sensing based on NV ensembles. We obtained different MW field uniformity between 42% and 93% in the same direction using a square split ring resonator. The uniformity and direction of the MW field was mapped using a wide-field magnetic imaging system. The magnetic sensing with the MW frequency modulation technology confirmed the consistence between the theoretical analysis and experimental results. The sensitivity was enhanced by nearly seven times with the best MW field uniformity. Our study can promote the further application and development of magnetic sensing devices based on solid-state spin ensembles.

Transfer of Phase Information between Microwave and Optical Fields via an Electron Spin.

We demonstrate the coherent coupling and the resulting transfer of phase information between microwave and optical fields in a single nitrogen vacancy center in diamond. The relative phase of two microwave fields is encoded in a coherent superposition spin state. This phase information is then retrieved with a pair of optical fields. A related process is also used for the transfer of phase information from optical to microwave fields. These studies show the essential role of dark states, including optical pumping into the dark states, in the coherent microwave-optical coupling and open the door to the full quantum state transfer between microwave and optical fields in a solid-state spin ensemble.

Depolarization Dynamics in a Strongly Interacting Solid-State Spin Ensemble.

We study the depolarization dynamics of a dense ensemble of dipolar interacting spins, associated with nitrogen-vacancy centers in diamond. We observe anomalously fast, density-dependent, and nonexponential spin relaxation. To explain these observations, we propose a microscopic model where an interplay of long-range interactions, disorder, and dissipation leads to predictions that are in quantitative agreement with both current and prior experimental results. Our results pave the way for controlled many-body experiments with long-lived and strongly interacting ensembles of solid-state spins.

Spin Ensembles Coupled to Superconducting Resonators: A Scalable Architecture for Solid-State Quantum Computing

A design is proposed for scalable solid-state quantum computing, which is based on collectively enhanced magnetic coupling between nitrogen-vacancy center ensembles and superconducting transmission line resonators interconnected by current-biased Josephson junction superconducting phase qubit. In this hybrid system, we realize distant multi-qubit controlled phase gate operations and generate distant multi-qubit entangled W-like states, being indispensable resource to quantum computation. Our proposed architecture consists of solid-state spin ensembles and circuit QED, and could achieve quantum computing in a solid-state environment with high-fidelity and scalable way. The experimental feasibility is discussed, and the implementation efficiency is demonstrated numerically.

Dissipation-assisted generation of steady-state single-mode squeezing of collective excitations in a solid-state spin ensemble

A hybrid device consisting of a nitrogen-vacancy-center ensemble $($NVE$)$ in diamond magnetically coupled to a superconducting flux qubit is investigated. The flux qubit is suitably driven by a bichromatic microwave field to induce sidebands, which leads to the desired qubit-NVE coupling. The distinct feature of the present scheme is that the qubit decay as a resource is utilized to steer the stationary state of the NVE into a single-mode squeezed vacuum state via a dissipative repumping process.

Proposal for a coherent quantum memory for propagating microwave photons

We describe a multi-mode quantum memory for propagating microwave photons that combines a solid-state spin ensemble resonantly coupled to a frequency tunable single-mode microwave cavity. We first show that high efficiency mapping of the quantum state transported by a free photon to the spin ensemble is possible both for strong and weak coupling between the cavity mode and the spin ensemble. We also show that even in the weak coupling limit unit efficiency and faithful retrieval can be obtained through time reversal inhomogeneous dephasing based on spin echo techniques. This is possible provided that the cavity containing the spin ensemble and the transmission line are impedance matched. We finally discuss the prospects for an experimental implementation using a rare-earth doped crystal coupled to a superconducting resonator.

Solid-state electronic spin coherence time approaching one second

Solid-state spin systems such as nitrogen-vacancy colour centres in diamond are promising for applications of quantum information, sensing and metrology. However, a key challenge for such solid-state systems is to realize a spin coherence time that is much longer than the time for quantum spin manipulation protocols. Here we demonstrate an improvement of more than two orders of magnitude in the spin coherence time (T₂) of nitrogen-vacancy centres compared with previous measurements: T₂≈0.6 s at 77 K. We employed dynamical decoupling pulse sequences to suppress nitrogen-vacancy spin decoherence, and found that T₂ is limited to approximately half of the longitudinal spin relaxation time over a wide range of temperatures, which we attribute to phonon-induced decoherence. Our results apply to ensembles of nitrogen-vacancy spins, and thus could advance quantum sensing, enable squeezing and many-body entanglement, and open a path to simulating driven, interaction-dominated quantum many-body Hamiltonians.

Entanglement detection and quantum metrology by Raman photon-diffraction imaging

We show that far-field diffraction images of spontaneously scattered Raman photons can be used for detection of spin entanglement and for metrology of field gradients in cold atomic ensembles. For many-body states with small or maximum uncertainty in the spin-excitation number, entanglement is simply witnessed by the presence of a sharp diffraction peak or dip. The gradient vector of external fields is measured by the displacement of a diffraction peak due to inhomogeneous spin precession, which suggests a possibility for precision measurements beyond the standard quantum limit without entanglement. Monitoring of the temporal decay of the diffraction peak can also realize a nondemolition probe of the temperature and collisional interactions in trapped cold atomic gases. The approach can be readily generalized to cold molecules, trapped ions, and solid-state spin ensembles.