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Physical Review A

Measurement of longitudinal and transverse spin relaxation rates using the ground-state Hanle effect

N. Castagna, Antoine Weis

Published Nov 17, 2011• 65 citations
Publisher

Abstract

We present a theoretical and experimental study of the resonant circularly-polarized-light-induced Hanle effect in the ground state of Cs vapor atoms in a paraffin-coated cell. The effect manifests itself as a narrow resonance (centered at $B=0$) in the dependence of the optical transmission coefficient of the vapor on the magnitude of an external magnetic field $\stackrel{P\vec}{B}$. We develop a theoretical model that yields an algebraic expression for the shape of these resonances for arbitrary field orientations and arbitrary angular momenta of the states coupled by the exciting light, provided that the light power is kept sufficiently small. An experimental procedure for assessing the range of validity of the model is given. Experiments were carried out on the laser-driven Cs ${D}_{1}$ transition both in longitudinal and transverse field geometries, and the observed line shapes of the corresponding bright and dark resonances give an excellent confirmation of the model predictions. The method is applied for determining the intrinsic longitudinal and transverse relaxation rates of the vector magnetization in the vapor and their dependence on light power.

DOI
10.1103/physreva.84.053421

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We present a theoretical and experimental study of the resonant circularly-polarized-light-induced Hanle effect in the ground state of Cs vapor atoms in a paraffin-coated cell. The effect manifests itself as a narrow resonance (centered at B=0B=0B=0) in the dependence of the optical transmission coefficient of the vapor on the magnitude of an external magnetic field \stackrel{P\vec}{B}. We develop a theoretical model that yields an algebraic expression for the shape of these resonances for arbitrary field orientations and arbitrary angular momenta of the states coupled by the exciting light, provided that the light power is kept sufficiently small. An experimental procedure for assessing the range of validity of the model is given. Experiments were carried out on the laser-driven Cs D1{D}_{1}D1​ transition both in longitudinal and transverse field geometries, and the observed line shapes of the corresponding bright and dark resonances give an excellent confirmation of the model predictions. The method is applied for determining the intrinsic longitudinal and transverse relaxation rates of the vector magnetization in the vapor and their dependence on light power.
The relaxation of atomic polarization in buffer-gas-free, paraffin-coated cesium vapor cells is studied using a variation on Franzen's technique of ``relaxation in the dark'' [Franzen, Phys. Rev. 115 850 (1959)]. In the present experiment, narrow-band, circularly polarized pump light, resonant with the Cs D2 transition, orients atoms along a longitudinal magnetic field, and time-dependent optical rotation of linearly polarized probe light is measured to determine the relaxation rates of the atomic orientation of a particular hyperfine level. The change in relaxation rates during light-induced atomic desorption (LIAD) is studied. No significant change in the spin relaxation rate during LIAD is found beyond that expected from the faster rate of spin-exchange collisions due to the increase in Cs density.
Abstract We present experimental and theoretical investigations of the dependence of double Hanle resonance spectrum on the light polarization angle and the direction of the applied transverse magnetic field (TMF). The experiments are done for F g = 2 → F e = 1 transition of 87Rb D1 line using a rubidium vapor cell containing buffer gas. We show that a small light polarization component along the direction of TMF introduces asymmetry in the double Hanle resonance signal. Both the magnitude and sign of asymmetry in the signal are sensitive to the TMF orientation, suggesting a possible method for in-situ measurement of the direction of the magnetic fields generated by the coils. The physical origin of this asymmetry is explained by considering the redistribution of population among the ground-state Zeeman sublevels in the presence of TMF. In addition, we systematically vary both the polarization angle and TMF direction to study their effect on the line profile of Hanle resonances. We demonstrate that a double Hanle resonance changes to a dark Hanle resonance by rotating the light polarization vector irrespective of the TMF direction. We have developed a simple theoretical model based on a degenerate two-level system to explain our experimental observations.
The ground-state Hanle effect (GSHE) in alkali-metal atomic vapor using a single circularly polarized light wave underlies one of the most reliable and simple techniques of modern atomic magnetometry. This effect causes a narrow (subnatural-width) resonance in the light wave intensity passing through the vapor cell. The GSHE-based sensors typically operate in the so-called spin-exchange relaxation-free (SERF) regime to reduce the resonance linewidth. However, this regime requires a relatively high temperature of vapors (approximately equal to $150{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$), leading to high heat release and power consumption of the sensor head. In addition, without applying special measures, the SERF regime significantly limits the dynamic range of measurements. Here we study a pump-probe scheme involving a single elliptically polarized light wave and a polarimetric detection technique. The wave is in resonance with two adjacent optical transitions in the cesium D1{D}_{1}D1​ line ($\ensuremath{\lambda}\phantom{\rule{0.16em}{0ex}}\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}894.5$ nm) due to their overlap in the presence of a buffer gas (130 Torr neon). Using a small ($V\ensuremath{\approx}0.1\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{3}$) glass vapor cell, we demonstrate the possibility to observe subnatural-width resonances with a high contrast-to-width ratio (up to 45%/mG) in low-temperature ($60{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$) operation due to strong light-induced circular dichroism in the medium. Based on the $\mathrm{\ensuremath{\Lambda}}$ scheme of atomic energy levels, we obtain explicit analytical expressions for the shape of the resonance line. The model reveals a linewidth narrowing effect due to openness of the level scheme. The observed bright features are unusual for magneto-optical atomic spectroscopy as openness is commonly considered to be an undesirable effect that degrades resonance characteristics. Measuring the noise voltage, we estimate the sensitivity of the magnetic-field measurements to be 1.8 pT/Hz\mathrm{pT}/\sqrt{\mathrm{Hz}}pT/Hz​ with a sensitivity of 60 fT/Hz\mathrm{fT}/\sqrt{\mathrm{Hz}}fT/Hz​ in the photon-shot-noise limit. In general, the results contribute to the theory of GSHE resonances and also can be applied to development of a low-temperature high-sensitivity miniaturized magnetic-field sensor with an extended dynamic range.
We have studied the ground-state Hanle effect (GSHE) excited by linearly polarized laser light on the DDD1{}_{1}1​ line of cesium atoms. We have solved algebraically the Liouville equation using the irreducible tensor formalism, and derive an analytical expression for the resonance line shapes in a magnetic field of arbitrary direction. The model predictions are in excellent agreement with experimental observations in various field geometries. Our model is valid for arbitrary $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}$ transitions in the low-power limit. We discuss the relation between the GSHE and electromagnetically induced transparency or absorption. Our approach allows a full understanding of the mechanism of the GSHE and provides tools for quantifying the resonance contrast, a crucial parameter for metrological applications of level crossing resonances.
We analyze the Hanle effect on the closed Fg equals 3 yields Fe equals 4 D2-line transition of 85Rb, by both numerical solutions of the optical Bloch equations and by experimental investigations on cell containing rubidium vapor. For laser radiation with linear polarization orthogonal to the applied magnetic field, the Hanle signal is characterized by narrow bright resonances at low laser intensities. A bright resonance Hanle signal is obtained also exciting the rubidium atoms by circularly polarized laser light and scanning a transversely applied magnetic field, at different values of an applied longitudinal magnetic field. We report experimental and numerical evidence of this new bright resonance.
The ultra-narrow resonances, obtained in the coherent spectroscopy of alkali atoms, originate from the destruction of the laser-induced coherence in the ground state. In the case of a single frequency, near-resonant excitation and a suitable geometry of irradiation and observation by scanning a weak magnetic field, one observes coherent population trapping in a Hanle - configuration. The laser field transfers the nonlinear interference resonances created in the degenerate Zeeman sublevels of the ground states to the upper level. As a result, the well-known ground state Hanle - effect is observed in the fluorescence. We investigated theoretically and experimentally the shape, amplitude and sign of these resonances and their dependence on the excitation and registration conditions. The experiment was performed on the D1 87Rb line. Results of the computations were compared with the measurements for corresponding experimental conditions.