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arXiv:physics/0302079 · Physical Review Letters

Selective Addressing of High-Rank Atomic Polarization Moments

Valeriy V. Yashchuk, Dmitry Budker, Wojciech Gawlik, Derek F. Jackson Kimball, Yu. P. Malakyan, Simon Rochester

Published Jun 26, 2003• 65 citations
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Abstract

We describe a method of selective generation and study of polarization moments of up to the highest-rank kappa=2F possible for a quantum state with total angular momentum F. The technique is based on nonlinear magneto-optical rotation with frequency-modulated light. Various polarization moments are distinguished by the periodicity of light-polarization rotation induced by the atoms during Larmor precession and exhibit distinct light-intensity and frequency dependences. We apply the method to study polarization moments of 87Rb atoms contained in a vapor cell with antirelaxation coating. Distinct ultranarrow (1-Hz wide) resonances, corresponding to different multipoles, appear in the magnetic-field dependence of the optical rotation. The use of the highest-multipole resonances supported by a given system has important applications in quantum and nonlinear optics and in magnetometry.

DOI
10.1103/physrevlett.90.253001

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We describe a method of selective generation and study of polarization moments of up to the highest-rank kappa=2F possible for a quantum state with total angular momentum F. The technique is based on nonlinear magneto-optical rotation with frequency-modulated light. Various polarization moments are distinguished by the periodicity of light-polarization rotation induced by the atoms during Larmor precession and exhibit distinct light-intensity and frequency dependences. We apply the method to study polarization moments of 87Rb atoms contained in a vapor cell with antirelaxation coating. Distinct ultranarrow (1-Hz wide) resonances, corresponding to different multipoles, appear in the magnetic-field dependence of the optical rotation. The use of the highest-multipole resonances supported by a given system has important applications in quantum and nonlinear optics and in magnetometry.
Larmor precession of laser-polarized atoms contained in antirelaxation-coated cells, detected via nonlinear magneto-optical rotation (NMOR), is a promising technique for a new generation of ultrasensitive atomic magnetometers. For magnetic fields directed along the light propagation direction, resonances in NMOR appear when linearly polarized light is frequency or amplitude modulated at twice the Larmor frequency. Because the frequency of these resonances depends on the magnitude but not the direction of the field, they are useful for scalar magnetometry. Additional NMOR resonances at the Larmor frequency appear when the magnetic field is tilted away from the light propagation direction in the plane defined by the light propagation and polarization vectors. These resonances, studied both experimentally and with a density matrix calculation in the present work, offer a convenient method of achieving additional information about a direction of the magnetic field.
A precise, accurate, and relatively straightforward in situ method to measure and control the ellipticity of light resonantly interacting with an atomic vapor is described. The technique can be used to minimize vector light shifts. The method involves measurement of ellipticity-induced resonances in the magnetic-field dependence of nonlinear magneto-optical rotation of frequency-modulated light. The light propagation direction is orthogonal to the applied magnetic field B\mathbf{B}B and the major axis of the light polarization ellipse is along B\mathbf{B}B. When the light modulation frequency matches the Larmor frequency, elliptically polarized light produces a precessing atomic spin orientation transverse to B\mathbf{B}B via synchronous optical pumping. The precessing spin orientation causes optical rotation oscillating at the Larmor frequency by modulating the atomic vapor's circular birefringence. Based on this technique's precision, in situ nature (which avoids systematic errors arising from optical interfaces) and independent control of the most important systematic errors, it is shown that the accuracy of light ellipticity measurements achievable with this technique can exceed that of existing methods by orders of magnitude.
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 ${10}^{\ensuremath{-}11} G/\sqrt{\mathrm{Hz}}.$
Abstract Polarization moments play a crucial role in measuring magnetic fields for nonlinear magneto‐optical rotation (NMOR) atomic magnetometers. However, it is challenging to distinguish between each polarization moment and evaluate its effect on the magnetic resonance response signal in an alkali vapor cell with buffer gas. To address this issue, a method is proposed to identify different polarization moments through the frequency shift of the magnetic resonance response signal. The proportion of each polarization moment is determined, and it is demonstrated that the magnetic resonance response signal is affected by the hexadecapole moment, resulting in a frequency shift and a decrease in signal amplitude. To mitigate this effect, an approach is investigated to manipulate the polarization moments by flipping the phase of the pump light. Ultimately, a 15.19% increase in response amplitude is achieved in the simulated geomagnetic environment within the magnetic shield barrel. The theory and method presented here provide strong support for the study of the polarization moments in an alkali vapor cell with buffer gas, which potentially enhance the performance of NMOR atomic magnetometers.
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 $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{G}/\sqrt{\mathrm{Hz}}.$
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).