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arXiv:0906.3586 · Journal of Applied Physics

Magnetometric sensitivity optimization for nonlinear optical rotation with frequency-modulated light: Rubidium D2 line

Derek F. Jackson Kimball, Louis Jacome, Srikanth Guttikonda, Eric J. Bahr, Lok Fai Chan

Published Sep 15, 2009• 32 citations
arXivHTMLPDF

Abstract

Atomic spin polarization of alkali atoms in the ground-state can survive thousands of collisions with paraffin-coated cell walls. The resulting long spin-relaxation times achieved in evacuated, paraffin-coated cells enable precise measurement of atomic spin precession and energy shifts of ground-state Zeeman sublevels. In the present work, nonlinear magneto-optical rotation with frequency-modulated light (FM NMOR) is used to measure magnetic field-induced spin precession for rubidium atoms contained in a paraffin-coated cell. The magnetometric sensitivity of FM NMOR for the rubidium D2 line is studied as a function of light power, detuning, frequency-modulation amplitude, and rubidium vapor density. For a 5-cm-diameter cell at temperature T≈35 °C, the optimal shot-noise-projected magnetometric sensitivity is found to be 2×10−11 G/Hz (corresponding to a sensitivity to spin precession frequency of ≈10 μHz/Hz or a sensitivity to Zeeman sublevel shifts of ≈4×10−20 eV/Hz).

DOI
10.1063/1.3225917

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Atomic spin polarization of alkali atoms in the ground-state can survive thousands of collisions with paraffin-coated cell walls. The resulting long spin-relaxation times achieved in evacuated, paraffin-coated cells enable precise measurement of atomic spin precession and energy shifts of ground-state Zeeman sublevels. In the present work, nonlinear magneto-optical rotation with frequency-modulated light (FM NMOR) is used to measure magnetic field-induced spin precession for rubidium atoms contained in a paraffin-coated cell. The magnetometric sensitivity of FM NMOR for the rubidium D2 line is studied as a function of light power, detuning, frequency-modulation amplitude, and rubidium vapor density. For a 5-cm-diameter cell at temperature T≈35 °C, the optimal shot-noise-projected magnetometric sensitivity is found to be 2×10−11 G/Hz (corresponding to a sensitivity to spin precession frequency of ≈10 μHz/Hz or a sensitivity to Zeeman sublevel shifts of ≈4×10−20 eV/Hz).
Application of nonlinear magneto-optical (Faraday) rotation to magnetometry is investigated. Our experimental setup consists of a modulation polarimeter that measures rotation of the polarization plane of a laser beam resonant with transitions in Rb. Rb vapor is contained in an evacuated cell with antirelaxation coating that enables atomic ground-state polarization to survive many thousand wall collisions. This leads to ultranarrow features $(\ensuremath{\sim}{10}^{\ensuremath{-}6} \mathrm{G})$ in the magnetic-field dependence of optical rotation. The potential sensitivity of this scheme to sub-$\ensuremath{\mu}\mathrm{G}$ magnetic fields as a function of atomic density, light intensity, and light frequency is investigated near the D1D1D1 and D2D2D2 lines of 85Rb.{}^{85}\mathrm{Rb}.85Rb. It is shown that through an appropriate choice of parameters the shot-noise-limited sensitivity to small magnetic fields can reach $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{G}/\sqrt{\mathrm{Hz}}.$
Nonlinear magneto-optical Faraday rotation (NMOR) on the potassium D1 and D2 lines was used to study Zeeman relaxation rates in an antirelaxation paraffin-coated $3\text{\ensuremath{-}}\mathrm{cm}$-diameter potassium vapor cell. Intrinsic Zeeman relaxation rates of ${\ensuremath{\gamma}}^{NMOR}∕2\ensuremath{\pi}=2.0(6)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ were observed. The relatively small hyperfine intervals in potassium lead to significant differences in NMOR in potassium compared to rubidium and cesium. Using laser optical pumping, widths and frequency shifts were also determined for transitions between ground-state hyperfine sublevels of 39K^{39}\mathrm{K}39K atoms contained in the same paraffin-coated cell. The intrinsic hyperfine relaxation rate of ${\ensuremath{\gamma}}_{\mathit{expt}}^{\mathit{hf}}∕2\ensuremath{\pi}=10.6(7)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ and a shift of $\ensuremath{-}9.1(2)\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$ were observed. These results show that adiabatic relaxation gives only a small contribution to the overall hyperfine relaxation in the case of potassium, and the relaxation is dominated by other mechanisms similar to those observed in previous studies with rubidium.
A self-oscillating magnetometer based on nonlinear magneto-optical rotation using amplitude-modulated pump light and unmodulated probe light (AM-NMOR) in 87Rb has been constructed and tested towards a goal of airborne detection of magnetic anomalies. In AM-NMOR, stroboscopic optical pumping via amplitude modulation of the pump beam creates alignment of the ground electronic state of the rubidium atoms. The Larmor precession causes an ac rotation of the polarization of a separate probe beam; the polarization rotation frequency provides a measure of the magnetic field. An anti-relaxation coating on the walls of the atomic vapor cell results in a long lifetime of 56 ms for the alignment, which enables precise measurement of the precession frequency. Light is delivered to the magnetometer by polarization-maintaining optical fibers. Tests of the sensitivity include directly measuring the beat frequency between the magnetometer and a commercial instrument and measurements of Earth's field under magnetically quiet conditions, indicating a sensitivity of at least 5 pT/νHz. Rotating the sensor indicates a heading error of less than 1 nT, limited in part by residual magnetism of the sensor.
An atomic magnetometer detects atomic responses to the magnetic field, and its sensitivity is ultimately limited by quantum noise fluctuations. For magnetometers based on nonlinear magneto-optical rotation (NMOR), the possible concurrent generation of light squeezing due to polarization self-rotation complicates the optimization for magnetometer sensitivity. Here, we study NMOR magnetometers with frequency-modulated light in a paraffin coated 87Rb vapor cell in the low and high power regimes corresponding to situations with and without light squeezing, respectively, with detection observables being different Stokes components reflecting the magnetic-field-induced atomic circular dichroism or birefringence. We found that the overall best sensitivity is achieved in the low power regime when there is no light squeezing and for circular dichroism measurement. We provide a general insight on parameter optimization and the choice of detection observables, from the delicate trade-off between the atomic responses and the noises including the technical and quantum optical noises. Our results could have practical significance in optical atomic magnetometry.
Recent work investigating resonant nonlinear magneto-optical rotation (NMOR) related to long-lived $({\ensuremath{\tau}}_{\mathrm{rel}}\ensuremath{\sim}1\mathrm{s})$ ground-state atomic coherences has demonstrated potential magnetometric sensitivities exceeding ${10}^{\ensuremath{-}11}\phantom{\rule{0.3em}{0ex}}\mathrm{G}∕\sqrt{\mathrm{Hz}}$ for small $(\ensuremath{\lesssim}1\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}\mathrm{G}$) magnetic fields. In the present work, NMOR using frequency-modulated light (FM NMOR) is studied in the regime where the longitudinal magnetic field is in the geophysical range$(\ensuremath{\sim}500\mathrm{mG})$, of particular interest for many applications. In this regime a splitting of the FM NMOR resonance due to the nonlinear Zeeman effect is observed. At sufficiently high light intensities, there is also a splitting of the FM NMOR resonances due to ac Stark shifts induced by the optical field, as well as evidence of alignment-to-orientation conversion type processes. The consequences of these effects for FM-NMOR-based atomic magnetometry in the geophysical field range are considered.
A magnetometric technique is demonstrated that may be suitable for precision measurements of fields ranging from the submicrogauss level to above the earth field. It is based on resonant nonlinear magneto-optical rotation caused by atoms contained in a vapor cell with antirelaxation wall coating. Linearly polarized, frequency-modulated laser light is used for optical pumping and probing. If the time-dependent optical rotation is measured at the first harmonic of the modulation frequency, ultra-narrow (\ensuremath{\sim} a few hertz) resonances are observed at near-zero magnetic fields, and at fields where the Larmor frequency coincides with half the light modulation frequency. Upon optimization, the sensitivity of the technique is expected to exceed ${10}^{\ensuremath{-}11} G/\sqrt{\mathrm{Hz}}.$