The origin of recently discovered reverse (opposite-sign) dark resonances has been explained theoretically and verified experimentally. It is shown that the reason for these resonances is a specific optical pumping of the ground state magnetic sublevel in a transition when the ground state angular momentum is smaller than the excited state momentum. An experiment was conducted on 85 Rb atoms in a cell, when a diode laser using the ground state hyperfine level F g = 3 simultaneously excites spectrally unresolved hyperfine levels with total angular momentum quantum numbers F e = 2,3 and 4. It is shown that due to differences in the transition probabilities the dominant role in total absorption and fluorescence signals is played by absorption on a transition F g = 3→ F e = 4.
The origin of recently discovered reverse (opposite-sign) dark resonances has been explained theoretically and verified experimentally. It is shown that the reason for these resonances is a specific optical pumping of the ground state magnetic sublevel in a transition when the ground state angular momentum is smaller than the excited state momentum. An experiment was conducted on 85 Rb atoms in a cell, when a diode laser using the ground state hyperfine level F g = 3 simultaneously excites spectrally unresolved hyperfine levels with total angular momentum quantum numbers F e = 2,3 and 4. It is shown that due to differences in the transition probabilities the dominant role in total absorption and fluorescence signals is played by absorption on a transition F g = 3→ F e = 4.
Subnatural-width resonances due to coherent effects in optical pumping at hyperfine (hf) transitions of Rb are investigated using a linearly or circularly polarized single-frequency diode laser beam. The sign and amplitude of the resonances in the fluorescence are measured by scanning the laser frequency over the hf transitions of the Rb D 1 and D 2 lines. The fluorescence perpendicular to the laser beam is detected as a function of magnetic field parallel to the beam propagation and scanned around zero value. In the case of linear polarization of the field, dark resonances are observed for hf transitions with F g → F e = F g -1 and F g → F e = F g , and bright resonances are observed for transitions with F g → F e = F g + 1. This is in agreement with the recently developed theories. For all (except F g = 2→ F e = 3, 85 Rb, D 1 line) hf transitions the sign of the resonances reverses when the polarization of the field changes to circular. The amplitudes of the resonances correspond to the probability of the hf transitions and to the calculated loss rate of the population to the ground hf level not excited by the laser field. The observed narrow resonances (FWHM: few tens of kHz) and their sensitivity to weak magnetic fields are interesting for high-resolution spectroscopy and for development of simple and precise magnetometers.
Nonlinear magneto-optical resonances on the hyperfine transitions belonging to the D2 line of rubidium were changed from bright to dark resonances by changing the laser power density of the single exciting laser field or by changing the vapor temperature in the cell. In one set of experiments atoms were excited by linearly polarized light from an extended cavity diode laser with polarization vector perpendicular to the light's propagation direction and magnetic field, and laser-induced fluorescence was observed along the direction of the magnetic field, which was scanned. A low-contrast bright resonance was observed at low laser power densities when the laser was tuned to the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of 87Rb and near to the ${F}_{g}=3\ensuremath{\rightarrow}{F}_{e}=4$ transition of 85Rb. The bright resonance became dark as the laser power density was increased above 0.6 mW/cm2 or 0.8 mW/cm2, respectively. When the ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition of 87Rb was excited with circularly polarized light in a second set of experiments, a bright resonance was observed, which became dark when the temperature was increased to around 50${}^{\phantom{\rule{0.16em}{0ex}}\ensuremath{\circ}}$C. The experimental observations at room temperature could be reproduced with good agreement by calculations based on a theoretical model, although the theoretical model was not able to describe measurements at elevated temperatures, where reabsorption was thought to play a decisive role. The model was derived from the optical Bloch equations and included all nearby hyperfine components, averaging over the Doppler profile, mixing of magnetic sublevels in the external magnetic field, and a treatment of the coherence properties of the exciting radiation field.
We measure and simulate numerically the Hanle effect and non-zero field level crossing signals in 85 Rb and 87 Rb atoms in a magnetic field at room temperature. Diode laser radiation from 4 mW cm −2 to 3.3 W cm −2 tuned to the D 2 absorption line of each isotope excites atoms into all the excited-state hyperfine levels simultaneously inside the unresolved Doppler profile. Polarization fluorescence detection is used to observe dark and bright resonances, as well as non-zero field level crossing resonances, for several excitation lines. A broad spectral line excitation model is applied to analyse the measured signals. The non-linear Zeeman effect is included in the model for both ground and excited states. Although the applied magnetic field does not exceed 80 G, several hyperfine levels of the excited state show a substantial deviation from the linear Zeeman effect.
Nonlinear magneto-optical resonances have been measured in an extremely thin cell (ETC) for the D1 transition of rubidium in an atomic vapor of natural isotopic composition. All hyperfine transitions of both isotopes have been studied for a wide range of laser power densities, laser detunings, and ETC wall separations. Dark resonances in the laser induced fluorescence (LIF) were observed as expected when the ground-state total angular momentum Fg was greater than or equal to the excited-state total angular momentum Fe. Unlike the case of ordinary cells, the width and contrast of dark resonances formed in the ETC dramatically depended on the detuning of the laser from the exact atomic transition. A theoretical model based on the optical Bloch equations was applied to calculate the shapes of the resonance curves. The model, which had been developed previously for ordinary vapor cells, averaged over the contributions from different atomic velocity groups, considered all neighboring hyperfine transitions, took into account the splitting and mixing of magnetic sublevels in an external magnetic field, and included a detailed treatment of the coherence properties of the laser radiation. Such a theoretical approach had successfully described nonlinear magneto-optical resonances in ordinary vapor cells. However, to describe the resonances in the ETC, key parameters such as the ground-state relaxation rate, excited-state relaxation rate, Doppler width, and Rabi frequency had to be modified significantly in accordance with the ETC's unique features. The level of agreement between the measured and calculated resonance curves achieved for the ETC was similar to what could be accomplished for ordinary cells. However, in the case of the ETC, it was necessary to fine-tune parameters such as the background and the Rabi frequency for different transitions, whereas for the ordinary cells, these parameters were identical for all transitions.
The detection of narrow and high-amplitude optical resonances in atomic cells is of crucial importance for the development of compact and high-stability lasers or vapor-cell optical references. In this work, using monochromatic light and appropriate polarization settings for the counterpropagating pump and probe beams, we demonstrate the detection of enhanced-absorption sub-Doppler resonances on the D1 line of the Rb atom. We report a theoretical model showing that the Zeeman coherence induced between magnetic sublevels---especially in the $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=F\ensuremath{-}1$ systems, with F and ${F}^{\ensuremath{'}}$ being the hyperfine quantum numbers of the ground and excited states, respectively---plays a key role in the observed enhanced-absorption process. The theoretically predicted behavior matches the experimental observations well. The impact of light polarization, laser intensity, magnetic field, and cell temperature on the Doppler-free resonance features is experimentally investigated. For application, two identical diode lasers are frequency-stabilized onto enhanced-absorption sub-Doppler resonances. The fractional frequency stability of the laser beatnote is measured to be $1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 1s and $8.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 104s. These results demonstrate the potential of this scheme for the implementation of a compact or even chip-scale optical frequency reference, which might find applications in instrumentation, navigation, and metrology.
We present the results of an experimental as well as a theoretical study of nonlinear magneto-optical resonances in diatomic potassium molecules in the electronic ground state with large values of the angular momentum quantum number $J\ensuremath{\sim}100$. At zero magnetic field, the absorption transitions are suppressed because of population trapping in the ground state due to Zeeman coherences between magnetic sublevels of this state along with depopulation pumping. The destruction of such coherences in an external magnetic field was used to study the resonances in this work. K2 molecules were formed in a glass cell filled with potassium metal at a temperature above 150 ${}^{\ensuremath{\circ}}$C. The cell was placed in an oven and was located in a homogeneous magnetic field B, which was scanned from 0 to 0.7 T. Q-type and R-type transitions were excited with a tunable, single-mode diode laser with a central wavelength of 660 nm. Well-pronounced nonlinear Hanle effect signals were observed in the intensities of the linearly polarized components of the laser-induced fluorescence (LIF) detected in the direction parallel to the B field with polarization vectors parallel (Ipar) and perpendicular (Iper) to the polarization vector of the exciting laser radiation, which was orthogonal to B. The intensities of the LIF components were detected for different experimental parameters, such as laser power density and vapor temperature, in order to compare them with numerical simulations that were based on the optical Bloch equations for the density matrix. We report good agreement of our measurements with numerical simulations. Narrow, subnatural linewidth dark resonances in Iper(B) were detected and explained.