We have studied the ground-state Hanle effect (GSHE) excited by linearly polarized laser light on the $D$${}_{1}$ line of cesium atoms. We have solved algebraically the Liouville equation using the irreducible tensor formalism, and derive an analytical expression for the resonance line shapes in a magnetic field of arbitrary direction. The model predictions are in excellent agreement with experimental observations in various field geometries. Our model is valid for arbitrary $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}$ transitions in the low-power limit. We discuss the relation between the GSHE and electromagnetically induced transparency or absorption. Our approach allows a full understanding of the mechanism of the GSHE and provides tools for quantifying the resonance contrast, a crucial parameter for metrological applications of level crossing resonances.
We have studied the ground-state Hanle effect (GSHE) excited by linearly polarized laser light on the D$${}_{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→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.
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 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 with a sensitivity of 60 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.
The optical Hanle effect (light-shift-induced zero-field level crossing) has been investigated theoretically and experimentally. In the case of a $J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0$ three-level system and of a $J=0\ensuremath{\rightarrow}1$ two-level system, the resonance line shape has been obtained using a nonlinear-response-function method. Approximate expressions, valid under the conditions for the observation of light shifts, are obtained and compared with exact calculations as well as with the corresponding expression for the magnetic Hanle effect. As concerns the weak laser beam which produces the coherent excitation of atomic substates, we have calculated the linear response in the limiting case of monochromatic and of broad-band excitation. The experimental investigation has been performed for the Ba resonance line using two cw dye lasers at $\ensuremath{\lambda}=5535$ \AA{} and an atomic beam. The absorption- and dispersion-shaped level crossing resonances have been observed, for narrow- and broad-band excitation, by varying the power of the strong nonresonant laser beam. We have checked that the line shapes are only dependent upon the reduced variable $\frac{{P}_{L}}{\ensuremath{\delta}}$ (PL; beam power; $\ensuremath{\delta}$: frequency detuning). Using the theoretical expressions, we have tried to fit the experimental curves. Provided that the Gaussian distribution of the beams is taken into account, we have obtained a good agreement between theory and experiment for the whole set of experimental data.
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 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.
Bright and dark nonlinear magneto-optical resonances associated with the ground state Hanle effect have been studied experimentally and theoretically for D1 excitation of atomic cesium. This system offers the advantage that the separation between the different hyperfine levels exceeds the Doppler width, and hence transitions between individual levels can be studied separately. At the same time, the system retains the advantages offered by ordinary glass cells, including simplicity and subnatural width Hanle resonances. Experimental measurements for various laser power densities and transit relaxation times are compared with a model based on the optical Bloch equations, which averages over the Doppler contour of the absorption line and simultaneously takes into account all hyperfine levels, as well as mixing of magnetic sublevels in an external magnetic field. In contrast to previous studies, which could not resolve the hyperfine transitions because of Doppler broadening, in this study there is excellent agreement between experiment and theory regarding the sign (bright or dark), contrast and width of the resonance. The results support the traditional theoretical interpretation, according to which these effects are related to the relative strengths of transition probabilities between different magnetic sublevels in a given hyperfine transition.
In a previous paper, I have presented a general theory of the optical pumping of atoms by a polarized multimode-laser beam, in the presence of a magnetic field. Equations of motion, valid at arbitrary laser intensities for the density matrix of the atomic system, have been obtained. In this paper, these equations are exactly solved for a linearly $\ensuremath{\sigma}$-polarized laser and levels having small angular momenta. More precisely, I consider the laser transitions ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=0$, ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=1$, and ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$. Two particular results are emphasized: (i) For $J=1\ensuremath{-}J=0$ and $J=1\ensuremath{-}J=1$ transitions and for the J=2 level of a $J=1\ensuremath{-}J=2$ transition, the laser-induced Hanle effects keep a Lorentzian shape, independent of the laser intensity. For the $J=1\ensuremath{-}J=1$ transition, it is shown that the depolarizing relaxation processes play a leading part in the coupling induced by the laser between the transverse alignments of the two levels. On the other hand, the power broadenings of the Hanle effects are shown to be similar. For the J=1 level of a $J=1\ensuremath{-}J=2$ transition, the Hanle-effect shape presents a departure from the Lorentzian one, owing to a coupling with the laser-induced hexadecapole moment in the J=2 level. (ii) The populations of the levels exhibit a "zero-field saturation resonance" which is due to the coupling with the Zeeman coherences. These resonances, which reproduce the Hanle effects of the transition, can be observed on the $\ensuremath{\pi}$-polarized fluorescence from the levels. In general, these resonances appear as a saturation effect, i.e., they reduce the laser-induced fluorescence of the levels in zero magnetic field. However, for the ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$ transition, the ${J}_{a}=2\ensuremath{\rightarrow}{J}_{f}=2 \ensuremath{\pi}$ fluorescence presents an anomalous behavior; the saturation resonance increases the zero-field laser-induced fluorescence. The theoretical study shows the prominent part played by the value of the Jb=1 level lifetime in the interpretation of this anomaly. Other results, such as the laser-induced depolarization of the fluorescence, are also obtained. All the theoretical predictions have been experimentally checked and will be presented in forthcoming papers.
The ultra narrow resonances, obtained by means of polarization spectroscopy of alkali atoms, originate from the destruction of the laser-induced coherence in the ground state. In the case of single-frequency, near resonance excitation and suitable geometry the well-known ground state Hanle effect is observed. Coherent population trapping in Hanle configuration is a nonlinear modification of this effect, observed in the fluorescence from the upper level. The ground state coherence is transmitted from the laser field and higher rank polarization moments are created. Using the irreducible tensor operator formal- ism programs for numerical modelling of this effect has been developed and presented here. The velocity distribution of the atoms, the Gaussian distribu- tion of the laser beam, stray magnetic field, and the experimental geometry are taken into account. The scheme of conversion of the octupole (� = 3) and hex- adecapole (� = 4) polarization moments (PM) through the laser and magnetic fields into the upper level quadropoles f 2 q is proposed. The conversion of the high-rank polarization moments (PM) into observable components is also dis- cussed. The results of the modelling are compared with the measured ones at different experimental conditions.