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arXiv:quant-ph/0001072 · Physical Review A

Quantum limit of optical magnetometry in the presence of ac Stark shifts

Michael Fleischhauer, Andrey B. Matsko, Marlan O. Scully

Published Jun 14, 2000• 128 citations

Abstract

We analyze systematic (classical) and fundamental (quantum) limitations of the sensitivity of optical magnetometers resulting from ac Stark shifts. We show that in contrast to absorption-based techniques, the signal reduction associated with classical broadening can be compensated in magnetometers based on phase measurements using electromagnetically induced transparency (EIT). However due to ac Stark--associated quantum noise the signal-to-noise ratio of EIT-based magnetometers attains a maximum value at a certain laser intensity. This value is independent on the quantum statistics of the light and defines a standard quantum limit of sensitivity. We demonstrate that an EIT-based optical magnetometer in Faraday configuration is the best candidate to achieve the highest sensitivity of magnetic-field detection and give a detailed analysis of such a device.

DOI: 10.1103/physreva.62.013808

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We analyze systematic (classical) and fundamental (quantum) limitations of the sensitivity of optical magnetometers resulting from ac Stark shifts. We show that in contrast to absorption-based techniques, the signal reduction associated with classical broadening can be compensated in magnetometers based on phase measurements using electromagnetically induced transparency (EIT). However due to ac Stark--associated quantum noise the signal-to-noise ratio of EIT-based magnetometers attains a maximum value at a certain laser intensity. This value is independent on the quantum statistics of the light and defines a standard quantum limit of sensitivity. We demonstrate that an EIT-based optical magnetometer in Faraday configuration is the best candidate to achieve the highest sensitivity of magnetic-field detection and give a detailed analysis of such a device.

The ac Stark shift of the resonance frequency of the nonlinear magneto-optic effect (NMOE) results in a fundamental broadening of this resonance which limits the precision of optical magnetometry based on NMOE. We have studied the dependence of the ac Stark shift versus frequency of the probing laser for the

{D}_{1}

and

{D}_{2}

lines of

{}^{87}\mathrm{Rb},

and have shown that there exists a frequency where the shifts from different hyperfine components of the upper level cancel each other. This holds promise for an in-principle increase in the sensitivity of optical magnetometers. The influence of buffer gas on Faraday rotation and ac Stark shifts is also considered.

Optical magnetometers based on electromagnetically induced transparency (EIT) in atomic vapor can in principle achieve outstanding sensitivity and accuracy in a small volume. Up until now, however, the predicted fundamental quantum-noise-limited sensitivity has not been achieved in practice due to various technical limitations associated with the measurement apparatus. Here we analyze these restrictions and propose viable mitigation strategies for performance optimization. As an example, we show that an EIT magnetometer can theoretically achieve sensitivity better than 100 fT at 1 s measurement time under realistic conditions.

We develop a generalized principle of electromagnetically induced transparency (EIT) vector magnetometry based on high-contrast EIT resonances and the symmetry of atom-light interaction in the linearly polarized bichromatic fields. Operation of such vector magnetometer on the

{D}_{1}

line of

^{87}\mathrm{Rb}

has been demonstrated. The proposed compass-magnetometer has an increased immunity to shifts produced by quadratic Zeeman and ac-Stark effects, as well as by atom-buffer gas and atom-atom collisions. In our proof-of-principle experiment the detected angular sensitivity to magnetic field orientation is ${10}^{\ensuremath{-}3}$ deg/Hz

{}^{1/2}

, which is limited by laser intensity fluctuations, light polarization quality, and magnitude of the magnetic field.

In a recent letter [Auzinsh {\it{et. al.}} (physics/0403097)] we have analyzed the noise properties 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 probe light. Here we consider maximally squeezed probe light, and carry out a detailed derivation of the contribution to the noise in a magnetometric measurement due to the differential AC Stark shift between Zeeman sublevels arising from quantum fluctuations of the probe polarization.