Measurement Of Magnetic Field Gradients Research Articles

A protocol to create a multi-particle entangled state for quantum-enhanced sensing

We propose a protocol for generating multi-particle entangled states using coherent manipulation of atoms trapped in an optical cavity. We show how entanglement can be adiabatically produced with two control beams and by exploiting cavity-mediated interactions between the atoms. Our methods will allow for optimal generation of entanglement for the measurement protocol we propose. We discuss a possible experimental implementation and compare the performance of the states produced with those of classical states and ideal maximally-entangled Dicke states. We find that our states always feature metrological gain and even outperform ideal Dicke states in the measurement of magnetic field gradients. Due to the easy scalability, our entanglement protocol is a promising tool for quantum state engineering.

High Sensitivity Planar Hall Effect Magnetic Field Gradiometer for Measurements in Millimeter Scale Environments.

We report a specially designed magnetic field gradiometer based on a single elliptical planar Hall effect (PHE) sensor, which allows measuring magnetic field at nine different positions in a 4 mm length scale. The gradiometer detects magnetic field gradients with equivalent gradient magnetic noises of ∼958, ∼192, ∼51, and ∼26 nT/m√ Hz (pT/mm√Hz) at 0.1, 1, 10, and 50 Hz, respectively. The performance of the gradiometer is tested in ambient conditions by measuring the field gradient induced by electric currents driven in a long straight wire. This gradiometer is expected to be highly useful for the measurement of magnetic field gradients in confined areas for its small footprint, low noise, scalability, simple design, and low costs.

Single-beam highly sensitive magnetic field gradiometer based on the atomic spin-exchange relaxation-free effect.

This paper presents a single-beam atomic magnetic field measurement gradiometer, which is a highly sensitive magnetic field gradient measuring instrument based on the atom spin-exchange relaxation-free (SERF) effect. The reflective detection optical path structure is adopted. The spin precession signals of an atom under incident and reflected light are different. There is also a difference in the corresponding magnetic field distribution. The final measurement of magnetic field gradients is conducted based on the different magnetic field distributions. The single-beam high-sensitive magnetic field gradiometers based on the atomic SERF effect are more sensitive than conventional two-probe magnetic field gradiometers or two-beam magnetic field gradiometers. The gradiometers are not affected by a difference in the detected optical power in the single-beam detection light measurements. The reflector uses an angular cone prism for two-dimensional magnetic field gradient measurements and is simple to construct. The single-beam highly sensitive magnetic field gradient measurement instrument based on the atomic SERF effect has a reflective detection optical path structure. It uses a quarter-wave plate to achieve the initial signal phase elimination of both incident and reflected signal and an angular cone prism as a reflector to achieve two-dimensional measurement.

Direct measurement of focusing fields in active plasma lenses

Active plasma lenses have the potential to enable broad-ranging applications of plasma-based accelerators owing to their compact design and radially symmetric kT/m-level focusing fields, facilitating beam-quality preservation and compact beam transport. We report on the direct measurement of magnetic field gradients in active plasma lenses and demonstrate their impact on the emittance of a charged particle beam. This is made possible by the use of a well-characterized electron beam with 1.4 mm mrad normalized emittance from a conventional accelerator. Field gradients of up to 823 T/m are investigated. The observed emittance evolution is supported by numerical simulations, which suggest the potential for conservation of the core beam emittance in such a plasma lens setup.

Aeromagnetic Gradiometry and Its Application to Navigation

Modern methods of airborne magnetic field measurements are described. A stochastic algorithm to compensate the deviations between the indications of an aeromagnetometer and an aeromagnetic gradiometer is considered. An integration algorithm for the inertial and correlation-extremal navigation systems is briefly described. An advantage of using magnetic field gradient measurements as navigational data is justified. The performance of the integration algorithm is illustrated by numerical simulation.

Entanglement distribution in star network based on spin chain in diamond

After star network of spins was proposed, generating entanglement directly through spin interactions between distant parties became possible. We propose an architecture which involves coupled spin chains based on nitrogen-vacancy centers and nitrogen defect spins to expand star network. The numerical analysis shows that the maximally achievable entanglement Em exponentially decays with the length of spin chains M and spin noise. The entanglement capability of this configuration under the effect of disorder and spin loss is also studied. Moreover, it is shown that with this kind of architecture, star network of spins is feasible in measurement of magnetic-field gradient.

Note: An atomic self-sustaining magnetic gradiometer with a 1/τ uncertainty property based on Larmor precession.

We demonstrate an atomic magnetic gradiometer based on self-sustaining Larmor precession. By coherent optical pumping, we measure the phase of the Larmor precession directly and observe that the gradiometer shows a 1/τ improvement in magnetic field gradient uncertainty over time τ. Since the measurement gives frequency signals, the gradiometer can be easily implemented by mixing and filtering the different frequency signals from two adjacent magnetometers. A gradient sensitivity of 186 fT/Hz/cm-1) is realized, which is close to the shot-noise limit. In a noisy environment, the gradiometer can still maintain its 1/τ behavior by suppressing 90% of the common-mode noise. This method should be widely applicable to the measurement of magnetic field gradients owing to its simplicity and outstanding performance.

Detection of applied and ambient forces with a matter-wave magnetic gradiometer

An atom interferometer using a Bose-Einstein condensate of $^{87}$Rb atoms is utilized for the measurement of magnetic field gradients. Composite optical pulses are used to construct a spatially symmetric Mach-Zehnder geometry. Using a biased interferometer we demonstrate the ability to measure small residual forces in our system at the position of the atoms. These are a residual magnetic field gradient of 15$\pm$2 mG/cm and and an inertial acceleration of 0.08$\pm$0.02 m/s$^2$. Our method has important applications in the calibration of precision measurement devices and the reduction of systematic errors.

Efficient generation of many-body singlet states of spin-1 bosons in optical superlattices

We propose an efficient stepwise adiabatic merging (SAM) method to generate many-body singlet states in antiferromagnetic spin-1 bosons in concatenated optical superlattices with isolated double-well arrays, by adiabatically ramping up the double-well bias. With an appropriate choice of bias sweeping rate and magnetic field, the SAM protocol predicts a fidelity as high as 90% for a sixteen-body singlet state and even higher fidelities for smaller even-body singlet states. During their evolution, the spin-1 bosons exhibit interesting squeezing dynamics, manifested by an odd-even oscillation of the experimentally observable squeezing parameter. The generated many-body singlet states may find practical applications in precision measurement of magnetic field gradient and in quantum information processing.

Precise measurement of magnetic field gradients from free spin precession signals of 3He and 129Xe magnetometers

We report on precise measurements of magnetic field gradients extracted from transverse relaxation rates of precessing spin samples. The experimental approach is based on the free precession of gaseous, nuclear spin polarized $^3$He and $^{129}$Xe atoms in a spherical cell inside a magnetic guiding field of about 400 nT using LT$_C$ SQUIDs as low-noise magnetic flux detectors. The transverse relaxation rates of both spin species are simultaneously monitored as magnetic field gradients are varied. For transverse relaxation times reaching 100 h, the residual longitudinal field gradient across the spin sample could be deduced to be$|\vec{\nabla}B_z|=(5.6 \pm 0.4)$ pT/cm. The method takes advantage of the high signal-to-noise ratio with which the decaying spin precession signal can be monitored that finally leads to the exceptional accuracy to determine magnetic field gradients at the sub pT/cm scale.

In-situ measurement of magnetic field gradient in a magnetic shield by a spin-exchange relaxation-free magnetometer**Project supported by the National Natural Science Foundation of China (Grant Nos. 61227902, 61374210, and 61121003).

A method of measuring in-situ magnetic field gradient is proposed in this paper. The magnetic shield is widely used in the atomic magnetometer. However, there is magnetic field gradient in the magnetic shield, which would lead to additional gradient broadening. It is impossible to use an ex-situ magnetometer to measure magnetic field gradient in the region of a cell, whose length of side is several centimeters. The method demonstrated in this paper can realize the in-situ measurement of the magnetic field gradient inside the cell, which is significant for the spin relaxation study. The magnetic field gradients along the longitudinal axis of the magnetic shield are measured by a spin-exchange relaxation-free (SERF) magnetometer by adding a magnetic field modulation in the probe beam’s direction. The transmissivity of the cell for the probe beam is always inhomogeneous along the pump beam direction, and the method proposed in this paper is independent of the intensity of the probe beam, which means that the method is independent of the cell’s transmissivity. This feature makes the method more practical experimentally. Moreover, the AC-Stark shift can seriously degrade and affect the precision of the magnetic field gradient measurement. The AC-Stark shift is suppressed by locking the pump beam to the resonance of potassium’s D1 line. Furthermore, the residual magnetic fields are measured with σ+- and σ–-polarized pump beams, which can further suppress the effect of the AC-Stark shift. The method of measuring in-situ magnetic field gradient has achieved a magnetic field gradient precision of better than 30 pT/mm.

In situ MEMS gradiometer with nanometer-resolution optical detection system

Mechanically resonant ferromagnetic MEMS sensors intended for magnetic field gradient measurements are presented. Suspended quad-beams with proof mass have been designed to improve their sensitivity and to simplify the detection. Fabricated devices exhibit the compact size of current MEMS technologies and are built within a simple deep-reactive-ion etching-based process. Nanometer-resolution detection based on optical interferometry and signal processing techniques have been employed to find out dynamic-mode transformation factors of 6.25 × 10 −3 T/m/Hz with 0.1-Hz resolution. The device performs in situ gradiometry with a single-sensor structure, which represents a technological advance to current-art gradiometers.

Higher Order HTSC Gradiometer for Measurements in Unshielded Environment

We present a new higher order gradiometer layout for bicrystal Josephson junctions based on high-temperature superconducting thin films. Our single layer gradiometers are suitable for the simultaneous measurement of magnetic field gradients with different spatial orientations. The sophisticated technology for bicrystal Josephson junctions is combined with custom substrates with two crossing 30 degree grain boundaries. We present the technological challenges focusing on the low ohmic contact resistance using gold nanoparticles embedded in the thin film. The sensor performance is characterized using SQUID electronics. Its main parameters such as critical current and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ICRN</i> -product are compared with parameters of first order gradiometers on single 30 degree bicrystal substrates. Special emphasis is put on the optimization of the noise properties in unshielded environment.

Inductive measurement of magnetic field gradients for magnetic resonance imaging

A simple device for highly accurate and real-time measurement of magnetic field gradient pulses is presented. It uses analog integration of the differential voltage induced in a pair of sensor coils placed along the investigated gradient direction. By this principle, the method is insensitive to static magnetic field inhomogeneities. It does not need either a main field or imaging apparatus and hence can be used in the process of gradient system design and optimization. Two different solutions for analog integration are suggested. The measurement accuracy is analyzed, taking into account errors due to the sensor coils and to both analog integration schemes. Sensor coils and integrators have been built to perform measurements on various gradient systems. Measurements of an actual whole-body gradient system are presented. The measurement accuracy is in the 5–10−4 range, and the reproducibility is better than 10−4, relative to the maximum gradient amplitude. These performances are better than any other presented in literature. They have allowed precise adjustment of a preemphasis unit so as to suppress eddy currents influence below 0.01%, and placed into evidence the thermal drift of standard power amplifier.

Spatial Structure of Solar Coronal Magnetic Loops Revealed by Transient Microwave Brightenings

We present the measurement of magnetic field gradient in magnetic loops in the solar corona, based on the multi-wavelength Very Large Array observations of two transient microwave brightenings (TMBs) in the solar active region 7135. The events were observed at 2 cm (spatial resolution ∼ 2=) and 3.6 cm (spatial resolution ∼ 3=) with a temporal resolution of 3.3 s in a time-sharing mode. Soft X-ray data (spatial resolution ∼ 2.5=) were available from the Soft X-ray Telescope on board the Yohkoh satellite. The three-dimensional structure of simple magnetic loops, where the transient brightenings occurred, were traced out by these observations. The 2-cm and 3.6-cm sources were very compact, located near the footpoint of the magnetic loops seen in the X-ray images. For the two events reported in this paper, the projected angular separation between the centroids of 2 and 3.6-cm sources is about 2.3= and 3.1=, respectively. We interpret that the 2 and 3.6-cm sources come from thermal gyro-resonance emission. The 2-cm emission is at the 3rd harmonic originating from the gyro-resonance layer where the magnetic field is 1800 G. The 3.6-cm emission is at the 2nd harmonic, originating from the gyro-resonance layer with a magnetic field of 1500 G. The estimated magnetic field gradient near the footpoint of the magnetic loop is about 0.09 G km=1 and 0.12 G km=1 for the two events. These values are smaller than those observed in the photosphere and chromosphere by at least a factor of 2.

Magnetic Field Gradients and Their Uses in the Study of the Earth's Magnetic Field.

Magnetic field gradient measurements for geophysical purposes have been made with much less frequency than total field observations. Yet there are considerable advantages in gradient measurements, especially if the objective is to study magnetic anomalies produced by magnetization contrasts in the crust and possibly upper mantle of the Earth. This is because gradient measurements enhance short wavelength signals relative to long wavelength signals. The power spectrum of a magnetic gradient measurement along any line is the same as the power spectrum of the field measured along the same line multiplied by the wavenumber. This means that signals from crustal sources are greatly enhanced over those from core sources, and also that diurnal variations of the field, which appear as very long wavelength features in most observations, are heavily attenuated compared with the crustal signal. To make full use of gradient measurements it is desirable to orient the gradient instrument. If orientation can be achieved, then it is possible to determine the lineation direction of lineated features using just one profile running at some angle to the feature lineation. This is similar to the technique for determining lineation direction from the measurement of field components, but the requirement for orientation is much less severe. Even if orientation cannot be achieved, there are rotationally invariant quantities which can be formulated from the gradient tensor which are of potential use in the interpretation of magnetic anomaly sources.

Measurement of magnetic field gradient by its effect on the NMR free induction decay

The technique of measuring a magnetic field gradient from the FID signal of a right cylindrical sample is analyzed for sources of systematic error. The sources include the resonance condition, nonorthogonality of gradient and cylinder axes, time delays from electronic time constants and finite RF pulses, choice of signal baseline, menisci of the sample, background gradients, and inhomogeneities in the applied gradient. Corrections to reduce the errors are provided where possible.