Depolarization Dynamics in a Strongly Interacting Solid-State Spin Ensemble

Near-zero-field microwave-free magnetometry with nitrogen-vacancy centers in nanodiamonds

We study the fluorescence of nanodiamond ensembles as a function of static external magnetic field and observe characteristic dip features close to the zero field with potential for magnetometry applications. We analyze the dependence of the feature's width and the contrast of the feature on the size of the diamond (in the range 30 nm-3000 nm) and on the strength of a bias magnetic field applied transversely to the field being scanned. We also perform optically detected magnetic resonance (ODMR) measurements to quantify the strain splitting of the zero-field ODMR resonance across various nanodiamond sizes and compare it with the width and contrast measurements of the zero-field fluorescence features for both nanodiamonds and bulk samples. The observed properties provide compelling evidence of cross-relaxation effects in the NV system occurring close to zero magnetic fields. Finally, the potential of this technique for use in practical magnetometry is discussed.

Signature of Scramblon Effective Field Theory in Random Spin Models

Information scrambling refers to the propagation of information throughout a quantum system. Its study not only contributes to our understanding of thermalization but also has wide implications in quantum information and black hole physics. Recent studies suggest that information scrambling in large-N systems with all-to-all interactions is mediated by collective modes called scramblons. However, a criterion for the validity of scramblon theory in a specific model is still missing. In this work, we address this issue by investigating the signature of the scramblon effective theory in random spin models with all-to-all interactions. We demonstrate that, in scenarios where the scramblon description holds, the late-time operator size distribution can be predicted from its early-time value, requiring no free parameters. As an illustration, we examine whether Brownian circuits exhibit a scramblon description and obtain a positive confirmation both analytically and numerically. Our findings provide a concrete experimental framework for unraveling the scramblon field theory in random spin models using quantum simulators.

Quasi-Floquet Prethermalization in a Disordered Dipolar Spin Ensemble in Diamond

Floquet (periodic) driving has recently emerged as a powerful technique for engineering quantum systems and realizing nonequilibrium phases of matter. A central challenge to stabilizing quantum phenomena in such systems is the need to prevent energy absorption from the driving field. Fortunately, when the frequency of the drive is significantly larger than the local energy scales of the many-body system, energy absorption is suppressed. The existence of this so-called prethermal regime depends sensitively on the range of interactions and the presence of multiple driving frequencies. Here, we report the observation of Floquet prethermalization in a strongly interacting dipolar spin ensemble in diamond, where the angular dependence of the dipolar coupling helps to mitigate the long-ranged nature of the interaction. Moreover, we extend our experimental observation to quasi-Floquet drives with multiple incommensurate frequencies. In contrast to a single-frequency drive, we find that the existence of prethermalization is extremely sensitive to the smoothness of the applied field. Our results open the door to stabilizing and characterizing nonequilibrium phenomena in quasiperiodically driven systems.

Triggered Superradiance and Spin Inversion Storage in a Hybrid Quantum System

We study the superradiant emission of an inverted spin ensemble strongly coupled to a superconducting cavity. After fast inversion, we detune the spins from the cavity and store the inversion for tens of milliseconds, during which the remaining transverse spin components disappear. Switching back on resonance enables us to study the onset of superradiance. A weak trigger pulse of a few hundred photons shifts the superradiant burst to earlier times and imprints its phase onto the emitted radiation. For long hold times, the inversion decreases below the threshold for spontaneous superradiance. There, the energy stored in the ensemble can be used to amplify microwave pulses passing through the cavity.

Coherent dynamics of strongly interacting electronic spin defects in hexagonal boron nitride

Optically active spin defects in van der Waals materials are promising platforms for modern quantum technologies. Here we investigate the coherent dynamics of strongly interacting ensembles of negatively charged boron-vacancy ([Formula: see text]) centers in hexagonal boron nitride (hBN) with varying defect density. By employing advanced dynamical decoupling sequences to selectively isolate different dephasing sources, we observe more than 5-fold improvement in the measured coherence times across all hBN samples. Crucially, we identify that the many-body interaction within the [Formula: see text] ensemble plays a substantial role in the coherent dynamics, which is then used to directly estimate the concentration of [Formula: see text]. We find that at high ion implantation dosage, only a small portion of the created boron vacancy defects are in the desired negatively charged state. Finally, we investigate the spin response of [Formula: see text] to the local charged defects induced electric field signals, and estimate its ground state transverse electric field susceptibility. Our results provide new insights on the spin and charge properties of [Formula: see text], which are important for future use of defects in hBN as quantum sensors and simulators.

Microwave target location method based on the diamond NV color center

We propose a method for microwave target source localization based on the diamond nitrogen vacancy color center. We use coherent population oscillation effect and modulation and demodulation techniques to achieve the detection of microwave intensity of microwave target sources, with a minimum detection intensity of 0.59 µW. Positioning of the microwave source was achieved within 50×100c m 2 distance from the system 1 m away using the cubic spline interpolation algorithm and minimum mean squared error. The maximum positioning error was 3.5 cm. This method provides a new, to the best of our knowledge, idea for the passive localization of microwave targets.

Probing many-body dynamics in a two-dimensional dipolar spin ensemble

The most direct approach for characterizing the quantum dynamics of a strongly interacting system is to measure the time evolution of its full many-body state. Despite the conceptual simplicity of this approach, it quickly becomes intractable as the system size grows. An alternate approach is to think of the many-body dynamics as generating noise, which can be measured by the decoherence of a probe qubit. Here we investigate what the decoherence dynamics of such a probe tells us about the many-body system. In particular, we utilize optically addressable probe spins to experimentally characterize both static and dynamical properties of strongly interacting magnetic dipoles. Our experimental platform consists of two types of spin defects in nitrogen delta-doped diamond: nitrogen-vacancy colour centres, which we use as probe spins, and a many-body ensemble of substitutional nitrogen impurities. We demonstrate that the many-body system's dimensionality, dynamics and disorder are naturally encoded in the probe spins' decoherence profile. Furthermore, we obtain direct control over the spectral properties of the many-body system, with potential applications in quantum sensing and simulation.

Formation of NV centers in diamond by a femtosecond laser single pulse

The NV centers in a diamond were successfully created by the femtosecond laser single pulse. We also investigated the effect on the diamond lattice induced by the different laser pulse widths from both experimental and theoretical perspectives. Interestingly, in spite of the high thermal conductivity of a diamond, we found that there is a suitable pulse repetition rate of several tens kHz for the formation of NV center ensembles by the femtosecond laser pulse irradiation.

Stabilization of spin states of an open system: bichromatic driving of resonance transitions in NV ensembles in diamond

We apply a laser and two nearly degenerate microwave fields upon an ensemble of nitrogen-vacancy centers in diamond and observe magnetic resonance structures with two-component, composite shapes of nested Lorentzians with different widths. One component of them undergoes regular power-broadening, whereas the linewidth of the other one becomes power-independent and undergoes field-induced stabilization. We show that the observed width stabilization is a general phenomenon that results from competition between coherent driving and non-conservation of populations that occur in open systems. The phenomenon is interpreted in terms of specific combinations of state populations that play the role of bright and dark states.

Diamond surface engineering for molecular sensing with nitrogen-vacancy centers

Quantum sensing using optically addressable atomic-scale defects, such as the nitrogen-vacancy (NV) center in diamond, provides new opportunities for sensitive and highly localized characterization of chemical functionality. Notably, near-surface defects facilitate detection of the minute magnetic fields generated by nuclear or electron spins outside of the diamond crystal, such as those in chemisorbed and physisorbed molecules. However, the promise of NV centers is hindered by a severe degradation of critical sensor properties, namely charge stability and spin coherence, near surfaces (< ca. 10 nm deep). Moreover, applications in the chemical sciences require methods for covalent bonding of target molecules to diamond with robust control over density, orientation, and binding configuration. This forward-looking Review provides a survey of the rapidly converging fields of diamond surface science and NV-center physics, highlighting their combined potential for quantum sensing of molecules. We outline the diamond surface properties that are advantageous for NV-sensing applications, and discuss strategies to mitigate deleterious effects while simultaneously providing avenues for chemical attachment. Finally, we present an outlook on emerging applications in which the unprecedented sensitivity and spatial resolution of NV-based sensing could provide unique insight into chemically functionalized surfaces at the single-molecule level.

Coherent Interactions between Silicon-Vacancy Centers in Diamond

We report tunable excitation-induced dipole-dipole interactions between silicon-vacancy color centers in diamond at cryogenic temperatures. These interactions couple centers into collective states, and excitation-induced shifts tag the excitation level of these collective states against the background of excited single centers. By characterizing the phase and amplitude of the spectrally resolved interaction-induced signal, we observe oscillations in the interaction strength and population state of the collective states as a function of excitation pulse area. Our results demonstrate that excitation-induced dipole-dipole interactions between color centers provide a route to manipulating collective intercenter states in the context of a congested, inhomogeneous ensemble.

Angle Locking of a Levitating Diamond Using Spin Diamagnetism

Nanodiamonds with embedded nitrogen-vacancy (NV) centers have emerged as promising magnetic field sensors, as hyperpolarizing agents in biological environments, as well as efficient tools for spin mechanics with levitating particles. These applications currently suffer from random environmental interactions with the diamond which implies poor control of the N-V direction. Here, we predict and report on a strong diamagnetism of a pure spin origin mediated by a population inversion close to a level crossing in the NV center electronic ground state. We show control of the sign of the magnetic susceptibility as well as angle locking of the crystalline axis of a microdiamond along an external magnetic field, with bright perspectives for these applications.

Imaging dark charge emitters in diamond via carrier-to-photon conversion

The application of color centers in wide-bandgap semiconductors to nanoscale sensing and quantum information processing largely rests on our knowledge of the surrounding crystalline lattice, often obscured by the countless classes of point defects the material can host. Here, we monitor the fluorescence from a negatively charged nitrogen-vacancy (NV⁻) center in diamond as we illuminate its vicinity. Cyclic charge state conversion of neighboring point defects sensitive to the excitation beam leads to a position-dependent stream of photo-generated carriers whose capture by the probe NV⁻ leads to a fluorescence change. This “charge-to-photon” conversion scheme allows us to image other individual point defects surrounding the probe NV, including nonfluorescent “single-charge emitters” that would otherwise remain unnoticed. Given the ubiquity of color center photochromism, this strategy may likely find extensions to material systems other than diamond.

Time-Dependent Variational Principle for Open Quantum Systems with Artificial Neural Networks

We develop a variational approach to simulating the dynamics of open quantum many-body systems using deep autoregressive neural networks. The parameters of a compressed representation of a mixed quantum state are adapted dynamically according to the Lindblad master equation by employing a time-dependent variational principle. We illustrate our approach by solving the dissipative quantum Heisenberg model in one dimension for up to 40 spins and in two dimensions for a 4×4 system and by applying it to the simulation of confinement dynamics in the presence of dissipation.

Long-Lived Ensembles of Shallow NV- Centers in Flat and Nanostructured Diamonds by Photoconversion

Shallow, negatively charged nitrogen-vacancy centers (NV^-) in diamond have been proposed for high-sensitivity magnetometry and spin-polarization transfer applications. However, surface effects tend to favor and stabilize the less useful neutral form, the NV⁰ centers. Here, we report the effects of green laser irradiation on ensembles of nanometer-shallow NV centers in flat and nanostructured diamond surfaces as a function of laser power in a range not previously explored (up to 150 mW/μm²). Fluorescence spectroscopy, optically detected magnetic resonance (ODMR), and charge-photoconversion detection are applied to characterize the properties and dynamics of NV^- and NV⁰ centers. We demonstrate that high laser power strongly promotes photoconversion of NV⁰ to NV^- centers. Surprisingly, the excess NV^- population is stable over a timescale of 100 ms after switching off the laser, resulting in long-lived enrichment of shallow NV^-. The beneficial effect of photoconversion is less marked in nanostructured samples. Our results are important to inform the design of samples and experimental procedures for applications relying on ensembles of shallow NV^- centers in diamond.

Relaxation of a dense ensemble of spins in diamond under a continuous microwave driving field

Decoherence of Rabi oscillation in a two-level quantum system consists of two components, a simple exponential decay and a damped oscillation. In dense-ensemble spin systems like negatively charged nitrogen-vacancy (NV⁻) centers in diamond, fast quantum state decoherence often obscures clear observation of the Rabi nutation. On the other hand, the simple exponential decay (or baseline decay) of the oscillation in such spin systems can be readily detected but has not been thoroughly explored in the past. This study investigates in depth the baseline decay of dense spin ensembles in diamond under continuously driving microwave (MW). It is found that the baseline decay times of NV⁻ spins decrease with the increasing MW field strength and the MW detuning dependence of the decay times shows a Lorentzian-like spectrum. The experimental findings are in good agreement with simulations based on the Bloch formalism for a simple two-level system in the low MW power region after taking into account the effect of inhomogeneous broadening. This combined investigation provides new insight into fundamental spin relaxation processes under continuous driving electromagnetic fields and paves ways to better understanding of this underexplored phenomena using single NV⁻ centers, which have shown promising applications in quantum computing and quantum metrology.

Spin-Mechanics with Nitrogen-Vacancy Centers and Trapped Particles

Controlling the motion of macroscopic oscillators in the quantum regime has been the subject of intense research in recent decades. In this direction, opto-mechanical systems, where the motion of micro-objects is strongly coupled with laser light radiation pressure, have had tremendous success. In particular, the motion of levitating objects can be manipulated at the quantum level thanks to their very high isolation from the environment under ultra-low vacuum conditions. To enter the quantum regime, schemes using single long-lived atomic spins, such as the electronic spin of nitrogen-vacancy (NV) centers in diamond, coupled with levitating mechanical oscillators have been proposed. At the single spin level, they offer the formidable prospect of transferring the spins' inherent quantum nature to the oscillators, with foreseeable far-reaching implications in quantum sensing and tests of quantum mechanics. Adding the spin degrees of freedom to the experimentalists' toolbox would enable access to a very rich playground at the crossroads between condensed matter and atomic physics. We review recent experimental work in the field of spin-mechanics that employ the interaction between trapped particles and electronic spins in the solid state and discuss the challenges ahead. Our focus is on the theoretical background close to the current experiments, as well as on the experimental limits, that, once overcome, will enable these systems to unleash their full potential.

Nitrogen-Vacancy Color Centers Created by Proton Implantation in a Diamond

We present an experimental study of the longitudinal and transverse relaxation of ensembles of negatively charged nitrogen-vacancy (NV−) centers in a diamond monocrystal prepared by 1.8 MeV proton implantation. The focused proton beam was used to introduce vacancies at a 20 µm depth layer. Applied doses were in the range of 1.5×1013 to 1.5×1017 ions/cm2. The samples were subsequently annealed in vacuum which resulted in a migration of vacancies and their association with the nitrogen present in the diamond matrix. The proton implantation technique proved versatile to control production of nitrogen-vacancy color centers in thin films.

Tailoring of Typical Color Centers in Diamond for Photonics

On the demand of single-photon entangled light sources and high-sensitivity probes in the fields of quantum information processing, weak magnetic field detection and biosensing, the nitrogen vacancy (NV) color center is very attractive and has been deeply and intensively studied, due to its convenience of spin initialization, operation, and optical readout combined with long coherence time in the ambient environment. Although the application prospect is promising, there are still some problems to be solved before fully exerting its characteristic performance, including enhancement of emission of NV centers in certain charge state (NV^- or NV⁰ ), obtaining indistinguishable photons, and improving of collecting efficiency for the photons. Herein, the research progress in these issues is reviewed and commented on to help researchers grasp the current trends. In addition, the development of emerging color centers, such as germanium vacancy defects, and rare-earth dopants, with great potential for various applications, are also briefly surveyed.

Long-Term Spin State Storage Using Ancilla Charge Memories

We articulate confocal microscopy and electron spin resonance to implement spin-to-charge conversion in a small ensemble of nitrogen-vacancy (NV) centers in bulk diamond and demonstrate charge conversion of neighboring defects conditional on the NV spin state. We build on this observation to show time-resolved NV spin manipulation and ancilla-charge-aided NV spin state detection via integrated measurements. Our results hint at intriguing opportunities in the development of novel measurement strategies in fundamental science and quantum spintronics as well as in the search for enhanced forms of color-center-based metrology down to the limit of individual point defects.

Maximal Quantum Fisher Information for Mixed States

We study quantum metrology for unitary dynamics. Analytic solutions are given for both the optimal unitary state preparation starting from an arbitrary mixed state and the corresponding optimal measurement precision. This represents a rigorous generalization of known results for optimal initial states and upper bounds on measurement precision which can only be saturated if pure states are available. In particular, we provide a generalization to mixed states of an upper bound on measurement precision for time-dependent Hamiltonians that can be saturated with optimal Hamiltonian control. These results make precise and reveal the full potential of mixed states for quantum metrology.

Engineering Electron-Phonon Coupling of Quantum Defects to a Semiconfocal Acoustic Resonator

Diamond-based microelectromechanical systems (MEMS) enable direct coupling between the quantum states of nitrogen-vacancy (NV) centers and the phonon modes of a mechanical resonator. One example, a diamond high-overtone bulk acoustic resonator (HBAR), features an integrated piezoelectric transducer and supports high-quality factor resonance modes into the gigahertz frequency range. The acoustic modes allow mechanical manipulation of deeply embedded NV centers with long spin and orbital coherence times. Unfortunately, the spin-phonon coupling rate is limited by the large resonator size, >100 μm, and thus strongly coupled NV electron-phonon interactions remain out of reach in current diamond BAR devices. Here, we report the design and fabrication of a semiconfocal HBAR (SCHBAR) device on diamond (silicon carbide) with f × Q > 10¹² (>10¹³). The semiconfocal geometry confines the phonon mode laterally below 10 μm. This drastic reduction in modal volume enhances defect center coupling to a mechanical mode by 1000 times compared to prior HBAR devices. For the native NV centers inside the diamond device, we demonstrate mechanically driven spin transitions and show a high strain-driving efficiency with a Rabi frequency of (2π)2.19(14) MHz/V_p, which is comparable to a typical microwave antenna at the same microwave power, making SCHBAR a power-efficient device useful for fast spin control, dressed state coherence protection, and quantum circuit integration.

Ultrafast Orbital Depolarization and Defect-Localized Phonon Dynamics Induced by Quantum Resonance between Multi-Nitrogen Vacancy Defects

Proximate nitrogen-vacancy (NV) defects with interdefect interaction may establish a new kind of quantum qubit network to explore controlled multibody quantum dynamics. In particular, by introducing the critical distance and favorable orientation between a pair of NV defects, the quantum resonance (QR) can be induced. Here, we present the first real-time depolarization and phonon dynamics on the excited state at ambient temperature which are intrinsic to the proximate multi-NV defects. We computationally demonstrate that the QR can effectively change the major properties of the multi-NV defects, such as orbital degeneracy, orbital delocalization, local phonon modes, electron-phonon coupling, and orbital depolarization dynamics, elucidating the physical mechanisms and finding the key factors to control them. The physical insights provide a starting point for the positioning accuracy of NV defects and creation protocols with broad implications for magnetometry, quantum information, nanophotonics, sensing, and spectroscopy, allowing the QR to be a new means of physical manipulation.

Fast and Sensitive Detection of Paramagnetic Species Using Coupled Charge and Spin Dynamics in Strongly Fluorescent Nanodiamonds

Sensing of a few unpaired electron spins, such as in metal ions and radicals, is a useful but difficult task in nanoscale physics, biology, and chemistry. Single negatively charged nitrogen-vacancy (NV^-) centers in diamond offer high sensitivity and spatial resolution in the optical detection of weak magnetic fields produced by a spin bath but often require long acquisition times on the order of seconds. Here, we present an approach based on coupled spin and charge dynamics in dense NV ensembles in strongly fluorescent nanodiamonds (NDs) to sense external magnetic dipoles. We apply this approach to various paramagnetic species, including gadolinium complexes, magnetite nanoparticles, and hemoglobin in whole blood. Taking advantage of the high NV density, we demonstrate a dramatic reduction in acquisition time (down to tens of milliseconds) while maintaining high sensitivity to paramagnetic centers. Strong luminescence, high sensitivity, and short acquisition time make dense NV^- ensembles in NDs a potentially promising tool for biosensing and bioimaging applications.

Identifying and Mitigating Charge Instabilities in Shallow Diamond Nitrogen-Vacancy Centers

The charge degree of freedom in solid-state defects fundamentally underpins the electronic spin degree of freedom, a workhorse of quantum technologies. Here we measure, analyze, and control charge-state behavior in individual near-surface nitrogen-vacancy (NV) centers in diamond, where NV^{-} hosts the metrologically relevant electron spin. We find that NV^{-} initialization fidelity varies between individual centers and over time; we alleviate the deleterious effects of reduced NV^{-} initialization fidelity via logic-based initialization. Importantly, we also show that NV^{-} can ionize in the dark on experimentally relevant timescales, and we introduce measurement protocols that mitigate the compromising effects of charge conversion on spin measurements. We identify tunneling to a single local electron trap as the mechanism for ionization in the dark, and we develop novel NV-assisted techniques to control and read out the trap charge state. Our understanding and command of the NV's local electrostatic environment will simultaneously guide materials design and provide unique functionalities with NV centers.

Probing Quantum Thermalization of a Disordered Dipolar Spin Ensemble with Discrete Time-Crystalline Order

We investigate thermalization dynamics of a driven dipolar many-body quantum system through the stability of discrete time crystalline order. Using periodic driving of electronic spin impurities in diamond, we realize different types of interactions between spins and demonstrate experimentally that the interplay of disorder, driving, and interactions leads to several qualitatively distinct regimes of thermalization. For short driving periods, the observed dynamics are well described by an effective Hamiltonian which sensitively depends on interaction details. For long driving periods, the system becomes susceptible to energy exchange with the driving field and eventually enters a universal thermalizing regime, where the dynamics can be described by interaction-induced dephasing of individual spins. Our analysis reveals important differences between thermalization of long-range Ising and other dipolar spin models.

Critical Thermalization of a Disordered Dipolar Spin System in Diamond

Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic initial conditions. This fundamental paradigm is challenged by disordered systems, in which a slowdown or even absence of thermalization is expected. We report the observation of critical thermalization in a three dimensional ensemble of ∼10^{6} electronic spins coupled via dipolar interactions. By controlling the spin states of nitrogen vacancy color centers in diamond, we observe slow, subexponential relaxation dynamics and identify a regime of power-law decay with disorder-dependent exponents; this behavior is modified at late times owing to many-body interactions. These observations are quantitatively explained by a resonance counting theory that incorporates the effects of both disorder and interactions.

Sensing Coherent Dynamics of Electronic Spin Clusters in Solids

We observe coherent spin exchange between identical electronic spins in the solid state, a key step towards full quantum control of electronic spin registers in room temperature solids. In a diamond substrate, a single nitrogen vacancy (NV) center coherently couples to two adjacent S=1/2 dark electron spins via the magnetic dipolar interaction. We quantify NV-electron and electron-electron couplings via detailed spectroscopy, with good agreement to a model of strongly interacting spins. The electron-electron coupling enables an observation of coherent flip-flop dynamics between electronic spins in the solid state, which occur conditionally on the state of the NV. Finally, as a demonstration of coherent control, we selectively couple and transfer polarization between the NV and the pair of electron spins. Our observations enable the realization of fast quantum gate operations and quantum state transfer in a scalable, room temperature, quantum processor.

Bounds on Energy Absorption and Prethermalization in Quantum Systems with Long-Range Interactions

Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general rigorous bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as 1/r^{α} with α>d/2. We show that the disorder averaged energy absorption rate at high temperatures decays exponentially with the driving frequency. This strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times, and we provide numerical evidence to support such a statement. Our results are relevant for understanding timescales of heating and new dynamical regimes described by effective Hamiltonians in such long-range systems.

High-Density Quantum Sensing with Dissipative First Order Transitions

The sensing of external fields using quantum systems is a prime example of an emergent quantum technology. Generically, the sensitivity of a quantum sensor consisting of N independent particles is proportional to sqrt[N]. However, interactions invariably occurring at high densities lead to a breakdown of the assumption of independence between the particles, posing a severe challenge for quantum sensors operating at the nanoscale. Here, we show that interactions in quantum sensors can be transformed from a nuisance into an advantage when strong interactions trigger a dissipative phase transition in an open quantum system. We demonstrate this behavior by analyzing dissipative quantum sensors based upon nitrogen-vacancy defect centers in diamond. Using both a variational method and a numerical simulation of the master equation describing the open quantum many-body system, we establish the existence of a dissipative first order transition that can be used for quantum sensing. We investigate the properties of this phase transition for two- and three-dimensional setups, demonstrating that the transition can be observed using current experimental technology. Finally, we show that quantum sensors based on dissipative phase transitions are particularly robust against imperfections such as disorder or decoherence, with the sensitivity of the sensor not being limited by the T_{2} coherence time of the device. Our results can readily be applied to other applications in quantum sensing and quantum metrology where interactions are currently a limiting factor.

First-Principles Study of Charge Diffusion between Proximate Solid-State Qubits and Its Implications on Sensor Applications

Solid-state qubits from paramagnetic point defects in solids are promising platforms to realize quantum networks and novel nanoscale sensors. Recent advances in materials engineering make it possible to create proximate qubits in solids that might interact with each other, leading to electron spin or charge fluctuation. Here we develop a method to calculate the tunneling-mediated charge diffusion between point defects from first principles and apply it to nitrogen-vacancy (NV) qubits in diamond. The calculated tunneling rates are in quantitative agreement with previous experimental data. Our results suggest that proximate neutral and negatively charged NV defect pairs can form a NV-NV molecule. A tunneling-mediated model for the source of decoherence of the near-surface NV qubits is developed based on our findings on the interacting qubits in diamond.

Observation of discrete time-crystalline order in a disordered dipolar many-body system

Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. Out-of-equilibrium systems can display a rich variety of phenomena, including self-organized synchronization and dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter; for example, the interplay between periodic driving, disorder and strong interactions has been predicted to result in exotic 'time-crystalline' phases, in which a system exhibits temporal correlations at integer multiples of the fundamental driving period, breaking the discrete time-translational symmetry of the underlying drive. Here we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of about one million dipolar spin impurities in diamond at room temperature. We observe long-lived temporal correlations, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions. This order is remarkably stable to perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.

Cooling a mechanical resonator with nitrogen-vacancy centres using a room temperature excited state spin-strain interaction

Cooling a mechanical resonator mode to a sub-thermal state has been a long-standing challenge in physics. This pursuit has recently found traction in the field of optomechanics in which a mechanical mode is coupled to an optical cavity. An alternate method is to couple the resonator to a well-controlled two-level system. Here we propose a protocol to dissipatively cool a room temperature mechanical resonator using a nitrogen-vacancy centre ensemble. The spin ensemble is coupled to the resonator through its orbitally-averaged excited state, which has a spin–strain interaction that has not been previously studied. We experimentally demonstrate that the spin–strain coupling in the excited state is 13.5±0.5 times stronger than the ground state spin–strain coupling. We then theoretically show that this interaction, combined with a high-density spin ensemble, enables the cooling of a mechanical resonator from room temperature to a fraction of its thermal phonon occupancy.

An efficient cooling mechanism for nanoscale mechanical resonators would help improve their properties for use in sensing applications. Here, the authors demonstrate a strong interaction between NV centres and a resonator and show how it could be harnessed to achieve a large cooling rate.