High bandwidth atomic magnetometery with continuous quantum nondemolition measurements

Quantum magnetic gradiometer with entangled twin light beams

In the past few decades, optical magnetometry has experienced remarkable development and reached to an outstanding sensitivity. For magnetometry based on optical readout of atomic ensemble, the fundamental limitation of sensitivity is restricted by spin projection noise and photon shot noise. Meanwhile, in practical applications, ambient magnetic noise also greatly limits the sensitivity. To achieve the best sensitivity, it is essential to find an efficacious way to eliminate the noises from different sources, simultaneously. Here, we demonstrate a quantum magnetic gradiometer with sub-shot-noise sensitivity using entangled twin beams with differential detection. The quantum enhancement spans a frequency range from 7 Hz to 6 MHz with maximum squeezing of 5.5 dB below the quantum noise limit. The sensitivity of gradiometer reaches 18 fT/cm[Formula: see text] at 20 Hz. Our study inspires future possibilities to use quantum-enhanced technology in developing sensitive magnetometry for practical applications in noisy and physically demanding environments.

Optimizing NV magnetometry for Magnetoneurography and Magnetomyography applications

Magnetometers based on color centers in diamond are setting new frontiers for sensing capabilities due to their combined extraordinary performances in sensitivity, bandwidth, dynamic range, and spatial resolution, with stable operability in a wide range of conditions ranging from room to low temperatures. This has allowed for its wide range of applications, from biology and chemical studies to industrial applications. Among the many, sensing of bio-magnetic fields from muscular and neurophysiology has been one of the most attractive applications for NV magnetometry due to its compact and proximal sensing capability. Although SQUID magnetometers and optically pumped magnetometers (OPM) have made huge progress in Magnetomyography (MMG) and Magnetoneurography (MNG), exploring the same with NV magnetometry is scant at best. Given the room temperature operability and gradiometric applications of the NV magnetometer, it could be highly sensitive in the pT / Hz -range even without magnetic shielding, bringing it close to industrial applications. The presented work here elaborates on the performance metrics of these magnetometers to the state-of-the-art techniques by analyzing the sensitivity, dynamic range, and bandwidth, and discusses the potential benefits of using NV magnetometers for MMG and MNG applications.

A Multi-Pass Optically Pumped Rubidium Atomic Magnetometer with Free Induction Decay

A free-induction-decay (FID) type optically-pumped rubidium atomic magnetometer driven by a radio-frequency (RF) magnetic field is presented in this paper. Influences of parameters, such as the temperature of rubidium vapor cell, the power of pump beam, and the strength of RF magnetic field and static magnetic field on the amplitude and the full width at half maximum (FWHM) of the FID signal, have been investigated in the time domain and frequency domain. At the same time, the sensitivities of the magnetometer for the single-pass and the triple-pass probe beam cases have been compared by changing the optical path of the interaction between probe beam and atomic ensemble. Compared with the sensitivity of ∼21.2 pT/Hz1/2 in the case of the single-pass probe beam, the amplitude of FID signal in the case of the triple-pass probe beam has been significantly enhanced, and the sensitivity has been improved to ∼13.4 pT/Hz1/2. The research in this paper provids a reference for the subsequent study of influence of different buffer gas pressure on the FWHM and also a foundation for further improving the sensitivity of FID rubidium atomic magnetometer by employing a polarization-squeezed light as probe beam, to achieve a sensitivity beyond the photo-shot-noise level.

Quantum-assisted distortion-free audio signal sensing

Quantum sensors are known for their high sensitivity in sensing applications. However, this sensitivity often comes with severe restrictions on other parameters which are also important. Examples are that in measurements of arbitrary signals, limitation in linear dynamic range could introduce distortions in magnitude and phase of the signal. High frequency resolution is another important feature for reconstructing unknown signals. Here, we demonstrate a distortion-free quantum sensing protocol that combines a quantum phase-sensitive detection with heterodyne readout. We present theoretical and experimental investigations using nitrogen-vacancy centers in diamond, showing the capability of reconstructing audio frequency signals with an extended linear dynamic range and high frequency resolution. Melody and speech based signals are used for demonstrating the features. The methods could broaden the horizon for quantum sensors towards applications, e.g. telecommunication in challenging environment, where low-distortion measurements are required at multiple frequency bands within a limited volume.

High sensitivity in quantum sensing comes often at the expense of other figures of merit, usually resulting in distortion. Here, the authors propose a protocol with good sensitivity, readout linearity and high frequency resolution, and benchmark it through signal measurements at audio bands with NV centers.

Squeezed-Light Enhancement and Backaction Evasion in a High Sensitivity Optically Pumped Magnetometer

We study the effect of optical polarization squeezing on the performance of a sensitive, quantum-noise-limited optically pumped magnetometer. We use Bell-Bloom (BB) optical pumping to excite a ^{87}Rb vapor containing 8.2×10^{12}  atoms/cm^{3} and Faraday rotation to detect spin precession. The sub-pT/sqrt[Hz] sensitivity is limited by spin projection noise (photon shot noise) at low (high) frequencies. Probe polarization squeezing both improves high-frequency sensitivity and increases measurement bandwidth, with no loss of sensitivity at any frequency, a direct demonstration of the evasion of measurement backaction noise. We provide a model for the quantum noise dynamics of the BB magnetometer, including spin projection noise, probe polarization noise, and measurement backaction effects. The theory shows how polarization squeezing reduces optical noise, while measurement backaction due to the accompanying ellipticity antisqueezing is shunted into the unmeasured spin component. The method is compatible with high-density and multipass techniques that reach extreme sensitivity.

All-optical intrinsic atomic gradiometer with sub-20 fT/cm/√Hz sensitivity in a 22 µT earth-scale magnetic field

In this work we demonstrate a high sensitivity atomic gradiometer capable of operation in earth-field level environments. We apply a light-pulse sequence at four times the Larmor frequency to achieve gradiometer sensitivity <20 fT/cm/Hz at the finite field strength of 22 µT. The experimental timing sequence can be tuned to the field magnitude of interest. Our all-optical scalar gradiometer performs a differential measurement between two regions of a single vapor cell on a 4 cm baseline. Our results pave the way for extensions to operation in higher dimensions, vector sensitivity, and more advanced gradiometers.

Noisy Quantum Metrology Enhanced by Continuous Nondemolition Measurement

We show that continuous quantum nondemolition (QND) measurement of an atomic ensemble is able to improve the precision of frequency estimation even in the presence of independent dephasing acting on each atom. We numerically simulate the dynamics of an ensemble with up to N=150 atoms initially prepared in a (classical) spin coherent state, and we show that, thanks to the spin squeezing dynamically generated by the measurement, the information obtainable from the continuous photocurrent scales superclassically with respect to the number of atoms N. We provide evidence that such superclassical scaling holds for different values of dephasing and monitoring efficiency. We moreover calculate the extra information obtainable via a final strong measurement on the conditional states generated during the dynamics and show that the corresponding ultimate limit is nearly achieved via a projective measurement of the spin-squeezed collective spin operator. We also briefly discuss the difference between our protocol and standard estimation schemes, where the state preparation time is neglected.

Spin squeezing of 1011 atoms by prediction and retrodiction measurements

The measurement sensitivity of quantum probes using N uncorrelated particles is restricted by the standard quantum limit¹, which is proportional to [Formula: see text]. This limit, however, can be overcome by exploiting quantum entangled states, such as spin-squeezed states². Here we report the measurement-based generation of a quantum state that exceeds the standard quantum limit for probing the collective spin of 10¹¹ rubidium atoms contained in a macroscopic vapour cell. The state is prepared and verified by sequences of stroboscopic quantum non-demolition (QND) measurements. We then apply the theory of past quantum states^3,4 to obtain spin state information from the outcomes of both earlier and later QND measurements. Rather than establishing a physically squeezed state in the laboratory, the past quantum state represents the combined system information from these prediction and retrodiction measurements. This information is equivalent to a noise reduction of 5.6 decibels and a metrologically relevant squeezing of 4.5 decibels relative to the coherent spin state. The past quantum state yields tighter constraints on the spin component than those obtained by conventional QND measurements. Our measurement uses 1,000 times more atoms than previous squeezing experiments^5-10, with a corresponding angular variance of the squeezed collective spin of 4.6 × 10^-13 radians squared. Although this work is rooted in the foundational theory of quantum measurements, it may find practical use in quantum metrology and quantum parameter estimation, as we demonstrate by applying our protocol to quantum enhanced atomic magnetometry.

RF atomic magnetometer array with over 40 dB interference suppression using electron spin resonance

An unshielded array of ⁸⁷Rb atomic magnetometers, operating close to 1 MHz, is used to attenuate interference by 42-48 dB. A sensitivity of 15 fT/Hz to a local source of signal is retained. In addition, a 2D spectroscopic technique, in which the magnetometers are repeatedly pumped and data acquired between pump times, enables a synchronously generated signal to be distinguished from an interfering signal very close in frequency; the timing and signal mimics what would be observed in a magnetic resonance echo train. Combining the interference rejection and the 2D spectroscopy techniques, a 100 fT local signal is differentiated from a 20 pT interference signal operating only 1 Hz away. A phase-encoded reference signal is used to calibrate the magnetometers in real time in the presence of interference. Key to the strong interference rejection is the accurate calibration of the reference signal across the array, obtained through electron spin resonance measurements. This calibration is found to be sensitive to atomic polarization, RF pulse duration, and direction of the excitation. The experimental parameters required for an accurate and robust calibration are discussed.

Response of a Bell⁻Bloom Magnetometer to a Magnetic Field of Arbitrary Direction

The Bell–Bloom magnetometer in response to a magnetic field of arbitrary direction is observed theoretically and experimentally. A theoretical model is built from a macroscopic view to simulate the magnetometer frequency response to an external magnetic field of arbitrary direction. Based on the simulation results, the magnetometer characteristics, including the signal phase and amplitude at resonance, the linewidth, and the magnetometer sensitivity, are analyzed, and the dependencies of these characteristics on the external magnetic field direction are obtained, which are verified by the experiment.

Signal Tracking Beyond the Time Resolution of an Atomic Sensor by Kalman Filtering

We study causal waveform estimation (tracking) of time-varying signals in a paradigmatic atomic sensor, an alkali vapor monitored by Faraday rotation probing. We use Kalman filtering, which optimally tracks known linear Gaussian stochastic processes, to estimate stochastic input signals that we generate by optical pumping. Comparing the known input to the estimates, we confirm the accuracy of the atomic statistical model and the reliability of the Kalman filter, allowing recovery of waveform details far briefer than the sensor's intrinsic time resolution. With proper filter choice, we obtain similar benefits when tracking partially known and non-Gaussian signal processes, as are found in most practical sensing applications. The method evades the trade-off between sensitivity and time resolution in coherent sensing.

Prospects for magnetic field communications and location using quantum sensors

Signal attenuation limits the operating range in wireless communications and location. To solve the reduced range problem, we can use low-frequency signals in combination with magnetic sensing. We propose the use of an optically pumped magnetometer as a sensor and realize a proof-of-principle detection of binary phase shift keying (BPSK) modulated signals. We demonstrate a ranging enhancement by exploiting both the magnetometer's intrinsic sensitivity of below 1 pT/Hz^1/2 and its 1 kHz operating bandwidth through the use of BPSK signals.

Invited Review Article: Instrumentation for nuclear magnetic resonance in zero and ultralow magnetic field

We review experimental techniques in our laboratory for nuclear magnetic resonance (NMR) in zero and ultralow magnetic field (below 0.1 μT) where detection is based on a low-cost, non-cryogenic, spin-exchange relaxation free ⁸⁷Rb atomic magnetometer. The typical sensitivity is 20-30 fT/Hz^1/2 for signal frequencies below 1 kHz and NMR linewidths range from Hz all the way down to tens of mHz. These features enable precision measurements of chemically informative nuclear spin-spin couplings as well as nuclear spin precession in ultralow magnetic fields.

Pulsed operation of a miniature scalar optically pumped magnetometer

A scalar magnetic field sensor based on a millimeter-size ⁸⁷Rb vapor cell is described. The magnetometer uses nearly copropagating pump and probe laser beams, amplitude modulation of the pump beam, and detection through monitoring the polarization rotation of the detuned probe beam. The circularly polarized pump laser resonantly drives a spin precession in the alkali atoms at the Larmor frequency. A modulation signal on the probe laser polarization is detected with a lock-in amplifier. Since the Larmor precession is driven all-optically, potential cross talk between sensors is minimized. And since the pump light is turned off during most of the precession cycle, large offsets of the resonance, typically present in a single-beam Bell-Bloom scheme, are avoided. At the same time, relatively high sensitivities can be reached even in millimeter-size vapor cells: The magnetometer achieves a sensitivity of 1 pT/Hz^1/2 in a sensitive volume of 16 mm³, limited by environmental noise. When a gradiometer configuration is used to cancel the environmental noise, the magnetometer sensitivity reaches 300 fT/Hz^1/2. We systematically study the dependence of the magnetometer performance on the optical duty cycles of the pump light and find that better performance is achieved with shorter duty cycles, with the highest values measured at 1.25% duty cycle.

The theory of spin noise spectroscopy: a review

Direct measurements of spin fluctuations are becoming the mainstream approach for studies of complex condensed matter, molecular, nuclear, and atomic systems. This review covers recent progress in the field of optical spin noise spectroscopy (SNS) with an additional goal to establish an introduction into its theoretical foundations. Various theoretical techniques that have been recently used to interpret results of SNS measurements are explained alongside examples of their applications.

Precessing Ferromagnetic Needle Magnetometer

A ferromagnetic needle is predicted to precess about the magnetic field axis at a Larmor frequency Ω under conditions where its intrinsic spin dominates over its rotational angular momentum, Nℏ≫IΩ (I is the moment of inertia of the needle about the precession axis and N is the number of polarized spins in the needle). In this regime the needle behaves as a gyroscope with spin Nℏ maintained along the easy axis of the needle by the crystalline and shape anisotropy. A precessing ferromagnetic needle is a correlated system of N spins which can be used to measure magnetic fields for long times. In principle, by taking advantage of rapid averaging of quantum uncertainty, the sensitivity of a precessing needle magnetometer can far surpass that of magnetometers based on spin precession of atoms in the gas phase. Under conditions where noise from coupling to the environment is subdominant, the scaling with measurement time t of the quantum- and detection-limited magnetometric sensitivity is t^{-3/2}. The phenomenon of ferromagnetic needle precession may be of particular interest for precision measurements testing fundamental physics.

Cavity enhanced atomic magnetometry

Atom sensing based on Faraday rotation is an indispensable method for precision measurements, universally suitable for both hot and cold atomic systems. Here we demonstrate an all-optical magnetometer where the optical cell for Faraday rotation spectroscopy is augmented with a low finesse cavity. Unlike in previous experiments, where specifically designed multipass cells had been employed, our scheme allows to use conventional, spherical vapour cells. Spherical shaped cells have the advantage that they can be effectively coated inside with a spin relaxation suppressing layer providing long spin coherence times without addition of a buffer gas. Cavity enhancement shows in an increase in optical polarization rotation and sensitivity compared to single-pass configurations.

Alkali-Metal Spin Maser

Quantum measurement is a combination of a read-out and a perturbation of the quantum system. We explore the nonlinear spin dynamics generated by a linearly polarized probe beam in a continuous measurement of the collective spin state in a thermal alkali-metal atomic sample. We demonstrate that the probe-beam-driven perturbation leads, in the presence of indirect pumping, to complete polarization of the sample and macroscopic coherent spin oscillations. As a consequence of the former we report observation of spectral profiles free from collisional broadening. Nonlinear dynamics is studied through exploring its effect on radio frequency as well as spin noise spectra.

Cross-correlation spin noise spectroscopy of heterogeneous interacting spin systems

Interacting multi-component spin systems are ubiquitous in nature and in the laboratory. As such, investigations of inter-species spin interactions are of vital importance. Traditionally, they are studied by experimental methods that are necessarily perturbative: e.g., by intentionally polarizing or depolarizing one spin species while detecting the response of the other(s). Here, we describe and demonstrate an alternative approach based on multi-probe spin noise spectroscopy, which can reveal inter-species spin interactions - under conditions of strict thermal equilibrium - by detecting and cross-correlating the stochastic fluctuation signals exhibited by each of the constituent spin species. Specifically, we consider a two-component spin ensemble that interacts via exchange coupling, and we determine cross-correlations between their intrinsic spin fluctuations. The model is experimentally confirmed using “two-color” optical spin noise spectroscopy on a mixture of interacting Rb and Cs vapors. Noise correlations directly reveal the presence of inter-species spin exchange, without ever perturbing the system away from thermal equilibrium. These non-invasive and noise-based techniques should be generally applicable to any heterogeneous spin system in which the fluctuations of the constituent components are detectable.

Fitting magnetic field gradient with Heisenberg-scaling accuracy

The linear function is possibly the simplest and the most used relation appearing in various areas of our world. A linear relation can be generally determined by the least square linear fitting (LSLF) method using several measured quantities depending on variables. This happens for such as detecting the gradient of a magnetic field. Here, we propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.

Nonlinear optical magnetometry with accessible in situ optical squeezing

We demonstrate compact and accessible squeezed-light magnetometry using four-wave mixing in a single hot rubidium vapor cell. The strong intrinsic coherence of the four-wave mixing process results in nonlinear magneto-optical rotation (NMOR) on each mode of a two-mode relative-intensity squeezed state. This framework enables 4.7 dB of quantum noise reduction while the opposing polarization rotation signals of the probe and conjugate fields add to increase the total signal to noise ratio.

Shot-noise-limited magnetometer with sub-picotesla sensitivity at room temperature

We report a photon shot-noise-limited (SNL) optical magnetometer based on amplitude modulated optical rotation using a room-temperature (85)Rb vapor in a cell with anti-relaxation coating. The instrument achieves a room-temperature sensitivity of 70 fT / √Hz at 7.6 μT. Experimental scaling of noise with optical power, in agreement with theoretical predictions, confirms the SNL behaviour from 5 μT to 75 μT. The combination of best-in-class sensitivity and SNL operation makes the system a promising candidate for application of squeezed light to a state-of-the-art atomic sensor.

Spin noise spectroscopy beyond thermal equilibrium and linear response

Per the fluctuation-dissipation theorem, the information obtained from spin fluctuation studies in thermal equilibrium is necessarily constrained by the system's linear response functions. However, by including weak radio frequency magnetic fields, we demonstrate that intrinsic and random spin fluctuations even in strictly unpolarized ensembles can reveal underlying patterns of correlation and coupling beyond linear response, and can be used to study nonequilibrium and even multiphoton coherent spin phenomena. We demonstrate this capability in a classical vapor of (41)K alkali atoms, where spin fluctuations alone directly reveal Rabi splittings, the formation of Mollow triplets and Autler-Townes doublets, ac Zeeman shifts, and even nonlinear multiphoton coherences.

Multi-channel atomic magnetometer for magnetoencephalography: a configuration study

Atomic magnetometers are emerging as an alternative to SQUID magnetometers for detection of biological magnetic fields. They have been used to measure both the magnetocardiography (MCG) and magnetoencephalography (MEG) signals. One of the virtues of the atomic magnetometers is their ability to operate as a multi-channel detector while using many common elements. Here we study two configurations of such a multi-channel atomic magnetometer optimized for MEG detection. We describe measurements of auditory evoked fields (AEF) from a human brain as well as localization of dipolar phantoms and auditory evoked fields. A clear N100m peak in AEF was observed with a signal-to-noise ratio of higher than 10 after averaging of 250 stimuli. Currently the intrinsic magnetic noise level is 4fTHz(-1/2) at 10Hz. We compare the performance of the two systems in regards to current source localization and discuss future development of atomic MEG systems.

Nonequilibrium spin noise spectroscopy

Spin noise spectroscopy is an experimental approach to obtain correlators of mesoscopic spin fluctuations in time by purely optical means. We explore the information that this technique can provide when it is applied to a weakly nonequilibrium regime when an electric current is driven through a sample by an electric field. We find that the noise power spectrum of conducting electrons experiences a shift, which is proportional to the strength of the spin-orbit coupling for electrons moving along the electric field direction. We propose applications of this effect to measurements of spin-orbit coupling anisotropy and separation of spin noise of conducting and localized electrons.

Optical spectroscopy of spin noise

Spontaneous fluctuations of the magnetization of a spin system in thermodynamic equilibrium (spin noise) manifest themselves as noise in the Faraday rotation of probe light. We show that the correlation properties of this noise over the optical spectrum can provide clear information about the composition of the spin system that is largely inaccessible for conventional linear optics. Such optical spectroscopy of spin noise, e.g., allows us to clearly distinguish between optical transitions associated with different spin subsystems, to resolve optical transitions that are unresolvable in the usual optical spectra, to unambiguously distinguish between homogeneously and inhomogeneously broadened optical bands, and to evaluate the degree of inhomogeneous broadening. These new possibilities are illustrated by theoretical calculations and by experiments on paramagnets with different degrees of inhomogeneous broadening of optical transitions [atomic vapors of 41K and singly charged (In,Ga)As quantum dots].

Subfemtotesla scalar atomic magnetometry using multipass cells

Scalar atomic magnetometers have many attractive features but their sensitivity has been relatively poor. We describe a Rb scalar gradiometer using two multipass optical cells. We use a pump-probe measurement scheme to suppress spin-exchange relaxation and two probe pulses to find the spin precession zero crossing times with a resolution of 1 psec. We realize a magnetic field sensitivity of 0.54 fT/Hz(1/2), which improves by an order of magnitude the best scalar magnetometer sensitivity and exceeds, for example, the quantum limit set by the spin-exchange collisions for a scalar magnetometer with the same measurement volume operating in a continuous regime.

Magnetic sensitivity beyond the projection noise limit by spin squeezing

We report the generation of spin squeezing and entanglement in a magnetically sensitive atomic ensemble, and entanglement-enhanced field measurements with this system. A maximal m(f) = ± 1 Raman coherence is prepared in an ensemble of 8.5 × 10(5) laser-cooled (87)Rb atoms in the f = 1 hyperfine ground state, and the collective spin is squeezed by synthesized optical quantum nondemolition measurement. This prepares a state with large spin alignment and noise below the projection-noise level in a mixed alignment-orientation variable. 3.2 dB of noise reduction is observed and 2.0 dB of squeezing by the Wineland criterion, implying both entanglement and metrological advantage. Enhanced sensitivity is demonstrated in field measurements using alignment-to-orientation conversion.

Stroboscopic backaction evasion in a dense alkali-metal vapor

We explore experimentally quantum nondemolition measurements of atomic spin in a hot potassium vapor in the presence of spin-exchange relaxation. We demonstrate a new technique for backaction evasion by stroboscopic modulation of the probe light. With this technique we study spin noise as a function of polarization for atoms with spin greater than 1/2 and obtain good agreement with a simple theoretical model. We point that, in a system with fast spin exchange, where the spin-relaxation rate is changing with time, it is possible to improve the long-term sensitivity of atomic magnetometry by using quantum nondemolition measurements.

Squeezed-light optical magnetometry

We demonstrate a light-shot-noise-limited magnetometer based on the Faraday effect in a hot unpolarized ensemble of rubidium atoms. By using off-resonant, polarization-squeezed probe light, we improve the sensitivity of the magnetometer by 3.2 dB. The technique could improve the sensitivity of the most advanced magnetometers and quantum nondemolition measurements of atomic spin ensembles.

Sub-projection-noise sensitivity in broadband atomic magnetometry

We demonstrate sub-projection-noise sensitivity of a broadband atomic magnetometer using quantum nondemolition spin measurements. A cold, dipole-trapped sample of rubidium atoms provides a long-lived spin system in a nonmagnetic environment, and is probed nondestructively by paramagnetic Faraday rotation. The calibration procedure employs as known reference state, the maximum-entropy or "thermal" spin state, and quantitative imaging-based atom counting to identify electronic, quantum, and technical noise in both the probe and spin system. The measurement achieves a sensitivity 1.6 dB (2.8 dB) better than projection-noise (thermal state quantum noise) and will enable squeezing-enhanced broadband magnetometry.