Spin Ensemble Research Articles

Calibration of the Solid‐State Nuclear Magnetic Resonance Search for Axion‐Like Dark Matter

AbstractCalibration of nuclear‐magnetic‐resonance‐based searches for axion‐like dark matter can be performed by free induction decay (FID) measurements. This manu‐ script describes FID experiments on several solid materials, motivated by the Cosmic Axion Spin Precession Experiment (CASPEr) program. Experiments with207Pb nuclear spins in ferroelectrics, lead magnesium niobate‐lead titanate (PbMg1/3Nb2/3O3) (PbTiO3)1/3 (PMN‐PT) and lead zirconium titante PbZr0.52Ti0.48O3 (PZT) are directly relevant to the CASPEr‐electric search for the electric dipole moment interaction of axion‐like dark matter. Experiments with 31P nuclear spins in gadolinium‐doped hydroxypyromorphite Pb4.95Gd0.05(PO4)3OH (HPM:Gd) are used for apparatus calibration. The measurements characterized the nuclear spin ensemble coherence time and the magnetic resonance detection sensitivity for these samples. Calibration is performed using small tip‐angle pulses.

Design and simulation of an accelerometer based on NV center spin–strain coupling

The nitrogen-vacancy (NV) center quantum systems have emerged as versatile tools in the field of precision measurement because of their high sensitivity in spin state detection and miniaturization potential as solid-state platforms. In this paper, an acceleration sensing scheme based on NV spin–strain coupling is proposed, which can effectively eliminate the influence of the stray noise field introduced by traditional mechanical schemes. Through the finite element simulation, it is found that the measurement bandwidth of this ensemble NV spin system ranges from 3 kHz to hundreds of kHz with structure optimization. The required power is at the sub-μW level, corresponding to a noise-limited sensitivity of 6.7×10−5g/Hz . Compared with other types of accelerometers, this micro-sized diamond sensor proposed here has low power consumption, exquisite sensitivity, and integration potential. This research opens a fresh perspective to realize an accelerometer with appealing comprehensive performance applied in biomechanics and inertial measurement fields.

Quantum Phase Transitions in a Generalized Dicke Model.

We investigate a generalized Dicke model by introducing two interacting spin ensembles coupled with a single-mode bosonic field. Apart from the normal to superradiant phase transition induced by the strong spin-boson coupling, interactions between the two spin ensembles enrich the phase diagram by introducing ferromagnetic, antiferromagnetic and paramagnetic phases. The mean-field approach reveals a phase diagram comprising three phases: paramagnetic-normal phase, ferromagnetic-superradiant phase, and antiferromagnetic-normal phase. Ferromagnetic spin-spin interaction can significantly reduce the required spin-boson coupling strength to observe the superradiant phase, where the macroscopic excitation of the bosonic field occurs. Conversely, antiferromagnetic spin-spin interaction can strongly suppress the superradiant phase. To examine higher-order quantum effects beyond the mean-field contribution, we utilize the Holstein-Primakoff transformation, which converts the generalized Dicke model into three coupled harmonic oscillators in the thermodynamic limit. Near the critical point, we observe the close of the energy gap between the ground and the first excited states, the divergence of entanglement entropy and quantum fluctuation in certain quadrature. These observations further confirm the quantum phase transition and offer additional insights into critical behaviors.

Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach

We introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. This certification task allows one to quantify the resource content of a quantum system for metrology applications without complete knowledge of the quantum state. We implement the algorithm to study quantum spin ensembles. We first focus on Dicke states, where our findings challenge and complement previous results in the literature. We then investigate states generated during the one-axis twisting dynamics, where in particular we find that the metrological power of the so-called multi-headed cat states can be certified using simple collective spin observables, such as fourth-order moments for small systems, and parity measurements for arbitrary system sizes.

The squeezed dark nuclear spin state in lead halide perovskites

Coherent many-body states are highly promising for robust quantum information processing. While far-reaching theoretical predictions have been made for various implementations, direct experimental evidence of their appealing properties can be challenging. Here, we demonstrate optical manipulation of the nuclear spin ensemble in the lead halide perovskite semiconductor FAPbBr3 (FA = formamidinium), targeting a long-postulated collective dark state that is insensitive to optical pumping after its build-up. Via optical orientation of localized hole spins we drive the nuclear many-body system into this entangled state, requiring a weak magnetic field of only a few milli-Tesla strength at cryogenic temperatures. During its fast establishment, the nuclear polarization along the optical axis remains small, while the transverse nuclear spin fluctuations are strongly reduced, corresponding to spin squeezing as evidenced by a strong violation of the generalized nuclear squeezing-inequality with ξs < 0.5. The dark state corresponds to an ~35-body entanglement between the nuclei. Dark nuclear spin states can be exploited to store quantum information benefiting from their long-lived many-body coherence and to perform quantum measurements with a precision beyond the standard limit.

Realization of the unidirectional amplification in a cavity magnonic system

We experimentally demonstrate the nonreciprocal microwave amplification using a cavity magnonic system, consisting of a passive cavity (i.e., the split-ring resonator), an active feedback circuit integrated with an amplifier, and a ferromagnetic spin ensemble (i.e., a yttrium–iron–garnet sphere). Combining the amplification provided by the active circuit and the nonreciprocity supported by the cavity magnonics, we implement a nonreciprocal amplifier with the functions of both unidirectional amplification and reverse isolation. The microwave signal is amplified by 11.5 dB in the forward propagating direction and attenuated in the reverse direction by −34.7 dB, giving an isolation ratio of 46.2 dB. Such a unidirectional amplifier can be readily employed in quantum technologies, where the device can simultaneously amplify the weak signal output by the quantum system and isolate the sensitive quantum system from the backscattered external noise. Also, it is promising to explore more functions and applications using a cavity magnonic system with a real gain.

Long-Lived Squeezed Ground States in a Quantum Spin Ensemble.

We generate spin squeezed ground states in an atomic spin-1 Bose-Einstein condensate tuned near the quantum-critical point separating the different spin phases of the interacting ensemble using a novel nonadiabatic technique. In contrast to typical nonequilibrium methods for preparing atomic squeezed states by quenching through a quantum phase transition, squeezed ground states are time stationary with a constant quadrature squeezing angle. A squeezed ground state with 6-8dB of squeezing and a constant squeezing angle is demonstrated. The long-term evolution of the squeezed ground state is measured and shows gradual decrease in the degree of squeezing over 2s that is well modeled by a slow tuning of the Hamiltonian due to the loss of atomic density. Interestingly, modeling the gradual decrease does not require additional spin decoherence models despite a loss of 75% of the atoms.

14N Hyperfine and nuclear interactions of axial and basal NV centers in 4H-SiC: A high frequency (94 GHz) ENDOR study

The nitrogen-vacancy (NV) centers (NCVSi)− in 4H silicon carbide (SiC) constitute an ensemble of spin S = 1 solid state qubits interacting with the surrounding 14N and 29Si nuclei. As quantum applications based on a polarization transfer from the electron spin to the nuclei require the knowledge of the electron–nuclear interaction parameters, we have used high-frequency (94 GHz) electron–nuclear double resonance spectroscopy combined with first-principles density functional theory to investigate the hyperfine and nuclear quadrupole interactions of the basal and axial NV centers. We observed that the four inequivalent NV configurations (hk, kh, hh, and kk) exhibit different electron–nuclear interaction parameters, suggesting that each NV center may act as a separate optically addressable qubit. Finally, we rationalized the observed differences in terms of distinctions in the local atomic structures of the NV configurations. Thus, our results provide the basic knowledge for an extension of quantum protocols involving the 14N nuclear spin.

In-Situ Detection for Atomic Density in the K-Rb-21Ne Co-Magnetometer via an Optical Heterodyne Interferometry

The low-frequency fluctuations of the atomic density within the cell can induce the longterm drift of the K-Rb-21Ne spin-exchange relaxation-free (SERF) co-magnetometer output, such that the accurate measurement of in situ atomic density is of great significance for improving the performance of co-magnetometer. In this paper, the complex refractive index model of the spin ensembles under the hybrid optical pumping condition is established first, according to which the relation between atomic density and its complex refractive index is revealed and an optical heterodyne-based scheme for atomic density detection is proposed. The dependence of the atomic density on the demodulated phase signal from the optical heterodyne-based scheme is provided by numerical simulations. After that, a dual acousto-optics frequency shifter (AOFS)-based optical heterodyne interferometry is constructed with a noise level below 1 mrad/Hz for frequencies &gt; 1 Hz, and a compact SERF co-magnetometer is implemented as the testing medium, by which the atomic density detection with resolution of 0.40 K @ 473 K is reached and the experimental results agree well with theoretical simulations. Moreover, the detection scheme proposed in this paper has the properties of high detection sensitivity and immunity to laser power fluctuation, which are also proved experimentally.

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.

Microwave Fluorescence Detection of Spin Echoes.

Counting the microwave photons emitted by an ensemble of electron spins when they relax radiatively has recently been proposed as a sensitive method for electron paramagnetic resonance spectroscopy, enabled by the development of operational single microwave photon detectors at millikelvin temperature. Here, we report the detection of spin echoes in the spin fluorescence signal. The echo manifests itself as a coherent modulation of the number of photons spontaneously emitted after a π/2_{X}-τ-π_{Y}-τ-π/2_{Φ} sequence, dependent on the relative phase Φ. We demonstrate experimentally this detection method using an ensemble of Er^{3+} ion spins in a scheelite crystal of CaWO_{4}. We use fluorescence-detected echoes to measure the erbium spin coherence time, as well as the echo envelope modulation due to the coupling to the ^{183}W nuclear spins surrounding each ion. We finally compare the signal-to-noise ratio of inductively detected and fluorescence-detected echoes, and show that it is larger with the fluorescence method.

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.

Hybrid quantum systems with high-T_c superconducting resonators

Superconducting microwave resonators are crucial elements of microwave circuits, offering a wide range of potential applications in modern science and technology. While conventional low-T_c superconductors are mainly employed, high-T_c cuprates could offer enhanced temperature and magnetic field operating ranges. Here, we report the realization of textrm{YBa}_2textrm{Cu}_3textrm{O}_{7-delta } superconducting coplanar waveguide resonators, and demonstrate a continuous evolution from a lossy undercoupled regime, to a lossless overcoupled regime by adjusting the device geometry, in good agreement with circuit model theory. A high-quality factor resonator was then used to perform electron spin resonance measurements on a molecular spin ensemble across a temperature range spanning two decades. We observe spin-cavity hybridization indicating coherent coupling between the microwave field and the spins in a highly cooperative regime. The temperature dependence of the Rabi splitting and the spin relaxation time point toward an antiferromagnetic coupling of the spins below 2 K. Our findings indicate that high-Tc superconducting resonators hold great promise for the development of functional circuits. Additionally, they suggest novel approaches for achieving hybrid quantum systems based on high-T_c superconductors and for conducting electron spin resonance measurements over a wide range of magnetic fields and temperatures.

Improved Limits on an Exotic Spin- and Velocity-Dependent Interaction at the Micrometer Scale with an Ensemble-NV-Diamond Magnetometer.

Searching for exotic interactions provides a path for exploring new particles beyond the standard model. Here, we used an ensemble-NV-diamond magnetometer to search for an exotic spin- and velocity-dependent interaction between polarized electron spins and unpolarized nucleons at the micrometer scale. A thin layer of nitrogen-vacancy electronic spin ensemble in diamond is utilized as both the solid-state spin quantum sensor and the polarized electron source, and a vibrating lead sphere serves as the moving unpolarized nucleon source. The exotic interaction is searched by detecting the possible effective magnetic field induced by the moving unpolarized nucleon source using the ensemble-NV-diamond magnetometer. Our result establishes new bounds for the coupling parameter f_{⊥} within the force range from 5 to 400 μm. The upper limit of the coupling parameter at 100 μm is |f_{⊥}|≤1.1×10^{-11}, which is 3 orders of magnitude more stringent than the previous constraint. This result shows that NV ensemble can be a promising platform to search for hypothetical particles beyond the standard model.

Squeezed Superradiance Enables Robust Entanglement-Enhanced Metrology Even with Highly Imperfect Readout.

Quantum metrology protocols using entangled states of large spin ensembles attempt to achieve measurement sensitivities surpassing the standard quantum limit (SQL), but in many cases they are severely limited by even small amounts of technical noise associated with imperfect sensor readout. Amplification strategies based on time-reversed coherent spin-squeezing dynamics have been devised to mitigate this issue, but are unfortunately very sensitive to dissipation, requiring a large single-spin cooperativity to be effective. Here, we propose a new dissipative protocol that combines amplification and squeezed fluctuations. It enables the use of entangled spin states for sensing well beyond the SQL even in the presence of significant readout noise. Further, it has a strong resilience against undesired single-spin dissipation, requiring only a large collective cooperativity to be effective.

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.

Multiparameter quantum metrology and mode entanglement with spatially split nonclassical spin ensembles

We identify the multiparameter sensitivity of entangled spin states, such as spin-squeezed and Dicke states that are spatially distributed into several addressable spatial modes. Analytical expressions for the spin-squeezing matrix of families of states that are accessible by current atomic experiments reveal the quantum gain in multiparameter metrology, as well as the optimal strategies to maximize the sensitivity gain for the estimation of any linear combination of parameters. We further study the mode entanglement of these states by deriving a witness for genuine k-partite mode entanglement from the spin-squeezing matrix. Our results highlight the advantage of mode entanglement for distributed sensing, and outline optimal protocols for multiparameter estimation with nonclassical spatially-distributed spin ensembles. We illustrate our findings with the design of a protocol for gradient sensing with a Bose–Einstein condensate in an entangled spin state in two modes.

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.

All-optical nuclear quantum sensing using nitrogen-vacancy centers in diamond

Solid state spins have demonstrated significant potential in quantum sensing with applications including fundamental science, medical diagnostics and navigation. The quantum sensing schemes showing best performance under ambient conditions all utilize microwave or radio-frequency driving, which poses a significant limitation for miniaturization, energy efficiency, and non-invasiveness of quantum sensors. We overcome this limitation by demonstrating a purely optical approach to coherent quantum sensing. Our scheme involves the 15N nuclear spin of the Nitrogen-Vacancy (NV) center in diamond as a sensing resource, and exploits NV spin dynamics in oblique magnetic fields near the NV’s excited state level anti-crossing to optically pump the nuclear spin into a quantum superposition state. We demonstrate all-optical free-induction decay measurements—the key protocol for low-frequency quantum sensing—both on single spins and spin ensembles. Our results pave the way for highly compact quantum sensors to be employed for magnetometry or gyroscopy applications in challenging environments.

The optimization and stabilization of detuned probe light frequency to suppress electron spin polarization error in SERF co-magnetometer

Spin-exchange free-relaxation (SERF) co-magnetometer has promising applications in the field of inertial navigation and fundamental physics experiments since its coupled spin ensemble is capable of measuring rotation with ultra-high sensitivity. Electron spin polarization determines the performance of the SERF co-magnetometer directly. In this paper, it is found that there is a non-negligible coupling between the probe light frequency and electron spin polarization. A model of the polarization in relation to the probe light frequency for a hybrid pumping cell is established. This paper discovers the existence of a theoretical optimum frequency that enables a more stable polarization in the model, and an experimental verification is carried out. Experiments results show that when the SERF co-magnetometer operates at this optimization frequency, its short- and long-term stability is significantly enhanced. Further, based on this model, the detuned frequency stabilization technique is proposed. The long-term stability of the probe light frequency is also improved by 43.85% after closing the loop.