Atomic sensing is, at large, based on measuring energy differences. Specifically, magnetometry is typically performed by using a superposition of two quantum states, the energy difference of which depends linearly on the magnetic field due to the Zeeman effect. The magnetic field is then evaluated from repeated measurements of the accumulated dynamic phase between the two Zeeman states. Here we show that atomic clock states, with an energy separation that is independent of the magnetic field, can nevertheless acquire a phase that is magnetic field dependent. We experimentally demonstrate this on an ensemble of optically trapped ^{87}Rb atoms. Finally, we use this effect to propose a magnetic field sensing method for static and time-dependent magnetic fields and analyze its sensitivity, showing it essentially allows for high-sensitivity magnetometery.
Atomic sensing is, at large, based on measuring energy differences. Specifically, magnetometry is typically performed by using a superposition of two quantum states, the energy difference of which depends linearly on the magnetic field due to the Zeeman effect. The magnetic field is then evaluated from repeated measurements of the accumulated dynamic phase between the two Zeeman states. Here we show that atomic clock states, with an energy separation that is independent of the magnetic field, can nevertheless acquire a phase that is magnetic field dependent. We experimentally demonstrate this on an ensemble of optically trapped ^{87}Rb atoms. Finally, we use this effect to propose a magnetic field sensing method for static and time-dependent magnetic fields and analyze its sensitivity, showing it essentially allows for high-sensitivity magnetometery.
Magnetic field sensing utilizing Bose-condensed atomic gases can achieve both high sensitivity and spatial resolution. Employing two-photon transitions from F=1, mF=1→F=2, mF=-1 (F is the quantum number of total atomic angular momentum, mF is the magnetic quantum number of F level) of Bose-condensed 87Rb atomic gases in one-dimensional optical lattice, the precision magnetic field measurement with phase Ramsey interference has been demonstrated. Utilizing single-photon transitions from F=1, mF=1→F=2, mF=0 of Bose-condensed 87Rb atomic gases in a crossed optical dipole trap, we experimentally study frequency domain Ramsey interference, time domain Ramsey interference, and phase domain Ramsey interference. Based on phase Ramsey interference, the sensitivity and spatial resolution of static magnetic field measurement are evaluated. The comparison of these three typical Ramsey interferences reveals that phase Ramsey interference can effectively avoid the fringe distortion in frequency-domain interference and the decoherence effects in time-domain interference, thereby improving the sensitivity and accuracy of the static magnetic field measurement. Utilizing Bose-condensed 87Rb atomic gases with the volume of 1.31±0.03×10-9 cm3 in an unshielded environment, a sensitivity of 130 nT/Hz for static magnetic fields can be achieved. By reducing the preparation time of the atomic gases and increasing the signal interrogation time, the sensitivity has the potential to be further improved.
We present a method for magnetic field measurement by the weak magnetic-sensitive Zeeman splitting based on stimulated Raman transition. The magnetic field intensity measured by our proposed method is consistent with that by the magnetic-sensitive method in the error range of 0.5%. Compared with the traditional measurement, the contrast of the weak magnetic-sensitive resonance signal is improved significantly for gradient field. The dependence of the Raman transitions on polarization schemes is analyzed. The cancellation of the differential light shift between the separated peaks is demonstrated by proper choice of polarization configuration. The presented method is applicable to measuring the magnetic field with large gradient, such as 2–40 mG/mm in our clock, where the traditional method is unsuitable.
The comagnetometer has been one of the most sensitive devices with which to test new physics related to spin-dependent interactions, but the comagnetometers based on overlapping ensembles of multiple spin species usually suffer from systematic errors due to magnetic field gradients. Here, we propose a comagnetometer based on the Zeeman transitions of the dual hyperfine levels in ground-state ^{87}Rb atoms, which shows nearly negligible sensitivity to variations of laser power and frequency, magnetic field, and magnetic field gradients. We measured the hypothetical spin-dependent gravitational energy of the proton with the comagnetometer, which is smaller than 4×10^{-18} eV, comparable to the most stringent existing constraint. Through optimizing the system parameters such as cell temperature, laser power, amplitude of driving magnetic field, as well as choosing better current source, it is possible to improve the sensitivity of the comagnetometer further.
During recent years, interest has been rising for applications of vector light beams toward magnetic field sensing. A series of experiments were performed to extract information about properties of static magnetic fields from absorption profiles of light passing through an atomic gas target. In this paper, we propose an extension to this method for oscillating magnetic fields. To investigate this scenario, we carried out theoretical analysis based on the time-dependent density matrix theory. We found that absorption profiles, even when averaged over typical observation times, are indeed sensitive to both strength and frequency of the time-dependent field, thus opening the prospect for a powerful diagnostic technique. To illustrate this sensitivity, we performed detailed calculations for the $5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\phantom{\rule{0.16em}{0ex}}(F=1)\ensuremath{-}5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}\phantom{\rule{0.16em}{0ex}}(F=0)$ transition in rubidium atoms, subject to a superposition of an oscillating (test) and a static (reference) magnetic field.
Magnetometry utilizing a spin qubit in a solid state possesses high sensitivity. In particular, a magnetic sensor with a high spatial resolution can be achieved with the electron-spin states of a nitrogen-vacancy (NV) center in the diamond. In this study, we demonstrated that NV quantum sensing based on multiple-pulse decoupling sequences can sensitively measure not only the amplitude but also the phase shift of an alternating-current (AC) magnetic field. In the AC magnetometry based on decoupling sequences, the maximum phase accumulation of the NV spin due to an AC-field can be generally obtained when the π-pulse period in the sequences matches the half time period of the field and the relative phase difference between the sequences and the field is zero. By contrast, the NV quantum sensor acquires no phase accumulation if the relative phase difference is π/2. Thus, this phase-accumulation condition does not have any advantage for the magnetometry. However, we revealed that the nonphase-accumulation condition is available for detecting a very small phase shift of an AC-field from its initial phase. Measurements of the real part and the imaginary part of AC impedance require the amplitude and the phase information of an AC-field, and thus, this finding is expected to provide a guide for realizing sensitive measurement of AC impedance in the micrometer and nanometer scales.
Introduction The rapid development in recent decades of techniques for producing, trapping, and manipulating cold atoms has, as a side-benefit, made possible new methods of atomic magnetometry. The properties of cold atoms, including long coherence times and excellent spatial localization, are often desirable for high-precision magnetic sensing and allow the techniques of atomic magnetometry to be extended to previously inaccessible regions of parameter space. Specifically, the appeal of cold atoms for magnetometry lies in the demonstrated potential for high sensitivity at high spatial resolution. Magnetic-field measurements with atoms at finite temperature are generally characterized by motional averaging, in which atoms statistically sample a volume of space determined by the measurement time, the velocity distribution, and, if present, the confinement. For high-spatial-resolution magnetometry, atomic motion must be limited. The average displacement of atoms can be reduced by decreasing the measurement time, but a shorter measurement time is unappealing because it degrades the sensitivity of the measurement. Tighter confinement is an alternative means of reducing atomic motion, and is indeed attractive provided the confinement does not adversely affect the atomic spin coherence. The use of buffer gases in vapor-cell magnetometers is effectively a form of confinement, and indeed allows magnetometry with millimeter-scale spatial resolution. However, buffer gases are not entirely benign for atomic spins, having small but finite spin-destruction collisional cross-sections [1], whose effects would be increasingly deleterious at the high pressures necessary to achieve micrometer-scale resolution. A final alternative is to reduce the velocity spread by cooling the atomic ensemble; indeed, the use of cold atoms permits a significant reduction in motional averaging, and can be achieved with no loss (and potentially an increase) in spin-coherence time.