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Scientific Reports

A self-sustaining atomic magnetometer with τ−1 averaging property

Chi Xu, Shiguang Wang, Y. Y. Feng, Luodi Zhao, L. J. Wang

Published Jun 30, 2016• 16 citations
Publisher

Abstract

Quantum measurement using coherent superposition of intrinsic atomic states has the advantage of being absolute measurement and can form metrological standards. One example is the absolute measurement of magnetic field by monitoring the Larmor precession of atomic spins whilst another being the Ramsey type atomic clock. Yet, in almost all coherent quantum measurement, the precision is limited by the coherence time beyond which, the uncertainty decreases only as τ(-1/2). Here we show that by non-destructively measuring the phase of the Larmor precession and regenerating the coherence via optical pumping, the self-sustaining Larmor precession signal can persist indefinitely. Consequently, the precision of the magnetometer increases with time following a much faster τ(-1) rule. A mean sensitivity of 240 from 1 Hz to 10 Hz is realized, being close to the shot noise level. This method of coherence regeneration may also find important applications in improving the performance of atomic clocks.

DOI
10.1038/srep28169

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•Aug 18, 2011•1 citation
Quantum measurement using coherent superposition of intrinsic atomic states has the advantage of being absolute measurement and can form metrological standards. One example is the absolute measurement of magnetic field by monitoring the Larmor precession of atomic spins whilst another being the Ramsey type atomic clock. Yet, in almost all coherent quantum measurement, the precision is limited by the coherence time beyond which, the uncertainty decreases only as τ(-1/2). Here we show that by non-destructively measuring the phase of the Larmor precession and regenerating the coherence via optical pumping, the self-sustaining Larmor precession signal can persist indefinitely. Consequently, the precision of the magnetometer increases with time following a much faster τ(-1) rule. A mean sensitivity of 240 from 1 Hz to 10 Hz is realized, being close to the shot noise level. This method of coherence regeneration may also find important applications in improving the performance of atomic clocks.
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.
The magnetic field is one of the most important physical observables with about all electromagnetic information. Larmor precession atomic magnetometers based on optical pumping experienced considerable attention recently. However, the sensitivity of this kind of atomic magnetometers is limited by their spin coherence time and the systematic noise. Here, we propose a self-sustaining atomic magnetic gradiometer that shows a superior 1/τ behavior in the magnetic field uncertainty measurement over time. The gradiometer is implemented by mixing and filtering the different frequency signals from two adjacent spin self-sustaining magnetometers with a baseline equal to 1 cm. The common-mode noise is suppressed and a gradient sensitivity of 200 fT/(√Hz=cm) is realized, being close to the shot noise limit.
The spin self-sustaining atomic magnetometer has the advantage of 1/τ measurement and great development potential in many applications. In this paper, we investigated the main elements that affect the stability and accuracy of the self-sustaining magnetometer and proposed the methods to improve its performance based on the measurement results. The correlation coefficient between fluctuations of the magnetic field generated by coils and the spin Larmor precession frequency is 0.97, which mainly dominates the stability in a short term. The accuracy of the magnetometer is affected by the power and frequency of the pump light. The Larmor precession frequency coefficient related to the pump light power is 26 mHz/mW, and the effect on the Larmor precession frequency is minimized when the pump light frequency is red detuned by 200 MHz from the 85Rb transition D1 line F = 3 to F′ = 3. The 1/τ measurement time after these corrections can be extended to 10 s, and the sensitivity achieved is 149 fT/Hz, which is close to the quantum projection noise limit of the system.
We consider the limitations due to noise (e.g., quantum projection noise and photon shot-noise) on the sensitivity of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of N atomic spins by detecting optical rotation of far-detuned light. We show that for very short measurement times, the optimal sensitivity scales as N-3/4; if strongly squeezed probe light is used, the Heisenberg limit of N-1 scaling can be achieved. However, if the measurement time exceeds tau(rel)/N-1/2 in the former case, or tau(rel)/N in the latter, where tau(rel) is the spin relaxation time, the scaling becomes N-1/2, as for a standard shot-noise-limited magnetometer.
We demonstrate a precise magnetic microscope based on direct imaging of the Larmor precession of a 87Rb^{87}\mathrm{Rb}87Rb spinor Bose-Einstein condensate. This magnetometer attains a field sensitivity of 8.3  pT/Hz1/28.3\text{ }\text{ }\mathrm{pT}/{\mathrm{Hz}}^{1/2}8.3  pT/Hz1/2 over a measurement area of $120\text{ }\text{ }\ensuremath{\mu}{\mathrm{m}}^{2}$, an improvement over the low-frequency field sensitivity of modern SQUID magnetometers. The achieved phase sensitivity is close to the atom shot-noise limit, estimated as 0.15  pT/Hz1/20.15\text{ }\text{ }\mathrm{pT}/{\mathrm{Hz}}^{1/2}0.15  pT/Hz1/2 for a unity duty cycle measurement, suggesting the possibilities of spatially resolved spin-squeezed magnetometry. This magnetometer marks a significant application of degenerate atomic gases to metrology.
Optically pumped radio frequency (RF) atomic magnetometers have been shown to have an improved sensitivity over standard tuned coils for frequencies less than 50 MHz, making these RF magnetometers attractive for the detection of nuclear quadrupole resonance (NQR) and low-field nuclear magnetic resonance (NMR) signals. In an atomic magnetometer a linearly polarized probe beam measures, through Faraday rotation, the transverse atomic magnetization induced by the resonant RF signal. The resonance, or Larmor, frequency of the magnetometer is easily tuned with a small magnetic field. We construct an atomic magnetometer based on a potassium vapor cell with a measured sensitivity of 0.22 ± 0.02 fT/ √ Hz and a detection bandwidth of 334 ± 11 Hz when tuned to 423 kHz, giving a Q of over 1200. While high Q magnetometers are sensitive to weak magnetic fields, they are also sensitive to magnetic transients, such as those associated with the excitation pulses needed for magnetic resonance. The ringing created by such transients can obscure the signal of interest. This is particularly detrimental for magnetic resonance signals that decay faster than the transverse relaxation rate. We demonstrate that by feeding back part of the optical signal to orthogonal electromagnetic coils, this unwanted ringing can be quickly damped out leaving the magnetometer ready for the detection of the signal. This negative feedback as applied to the K spins is called spin-damping and can be used to relax the K atoms faster by more than two orders of magnitude. Using spin-damping we reduce the dead-time before data acquisition from 0.8 to 0.2 ms in the detection of NQR signals from ammonium nitrate, one of the so-called fertilizer bomb explosives with an NQR frequency of 423 kHz. Furthermore, we discover that spin-damping can not only be used to suppress signals, it can also be used to suppress noise. We show that it can be used to suppress both environmental noise and more fundamental quantum noise, such as photon shot and spin projection noise. The latter suppression opens the door for its use in quantum control to initialize spin systems before measurements. For phase-sensitive detection, as is often used in magnetic resonance, spin-damping suppresses signal and noise in such a way as to increase the sensitivity bandwidth of the magnetometer. We prove, both theoretically and experimentally, that it is possible to increase the magnetometer detection bandwidth by a factor of 3 or more without significant loss in sensitivity. Such gains in bandwidth for a high Q magnetometer translate into savings in detection time, particularly for substance detection where the frequency of the signal of interest may not be completely known.