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Physical Review A

Competition of dark states: Optical resonances with anomalous magnetic field dependence

Gabriela Wa̧sik, Wojciech Gawlik, Jerzy Zachorowski, Zbigniew Kowal

Published Oct 2, 2001• 20 citations
Publisher

Abstract

A different type of optical resonance has been observed in Doppler-free saturated absorption spectroscopy when the pump beam has elliptical polarization slightly deviating from the ${\ensuremath{\sigma}}^{+}$ and the probe has ${\ensuremath{\sigma}}^{\ensuremath{-}}$ polarization. An interpretation in terms of competition between two trap states and a dressed-atom model is presented. The observed extreme sensitivity of the resonance frequency to the external magnetic field is attributed to the ``scissors effect'' of the dressed states' crossing point.

DOI
10.1103/physreva.64.051802

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A different type of optical resonance has been observed in Doppler-free saturated absorption spectroscopy when the pump beam has elliptical polarization slightly deviating from the \ensuremathσ+{\ensuremath{\sigma}}^{+}\ensuremathσ+ and the probe has \ensuremathσ\ensuremath−{\ensuremath{\sigma}}^{\ensuremath{-}}\ensuremathσ\ensuremath− polarization. An interpretation in terms of competition between two trap states and a dressed-atom model is presented. The observed extreme sensitivity of the resonance frequency to the external magnetic field is attributed to the ``scissors effect'' of the dressed states' crossing point.
In a one-dimensional model we consider the dependence of the magneto-optical force on the elliptical polarization of laser beams for different types of closed atomic transitions ${J}_{g}\ensuremath{\rightarrow}{J}_{e}$. The linear dependencies on atomic velocity and magnetic field of the magneto-optical force are found analytically. These results establish the possibility (for Jg>0{J}_{g}>0Jg​>0) to capture atoms in a magneto-optical trap even at zero detuning (i.e., at the exact resonance of atoms with laser field) in certain $(ϵ\ensuremath{-}\ensuremath{\theta}\ensuremath{-}\overline{ϵ})$ field configurations as well as in an anomalous blue-detuned region. The nonlinear dependencies of the force on atomic velocity and magnetic field are studied numerically. The capture velocity and the number of trapped atoms are estimated.
We report on cw measurements of probe beam absorption and four-wave-mixing spectra in a 85Rb^{85}\mathrm{Rb}85Rb magneto-optical trap taken while the trap is in operation. The trapping beams are used as pump light. We concentrate on the central feature of the spectra at small pump-probe detuning and attribute its narrow resonant structures to the superposition of Raman transitions between light-shifted sublevels of the ground atomic state and to atomic recoil processes. These two contributions have different dependencies on trap parameters and we show that the former is inhomogeneously broadened. The strong dependence of the spectra on the probe-beam polarization indicates the existence of large optical anisotropy of the cold-atom sample, which is attributed to the recoil effects. We point out that the recoil-induced resonances can be isolated from other contributions, making pump-probe spectroscopy a highly sensitive diagnostic tool for atoms in a working magneto-optical trap.
24 In recent years interest has been growing into the fascinating properties of dark resonances. Most of the experiments have been carried out in alkali atoms due to their favourable level structure and the commercially available diode lasers, resulting in numerous applications. Teams from Siena and Sofia developed an all-optical magnetometer based on such dark resonances. The dark-state effect was discovered in 1976 by G. Alzetta, A. Gozzini, L. Moi and G. Orriols [1], while they were working on optical-pumping experiments with a multimode dye laser. They wanted to make the observation of multi-photon radio-frequency resonances in sodium atoms easy, i.e., observable by the naked eye. To this end, they introduced a magnetic field (MF) that was constant in time but spatially inhomogeneous along the laser beam, so as to produce Zeeman splitting of groundstate hyperfine levels (Fig.1a, left). In this way, an applied radio-frequency field was resonant only if it matched the Zeeman splitting. As a result, a bright radio-frequency resonance appeared (Fig.1a, right). During these experiments, besides the bright resonances, a new “dark” resonance was observed, which does not require any radio-frequency field. In the introductory illustration only the dark resonance is shown. The new dark state (DS) effect appears in a position along the laser beam where the frequency difference (ω10-ω20) between two optical frequencies is equal to the frequency splitting ω12 between two Zeeman sublevels (Fig.1b, left). This is the resonant condition for the stimulated Raman transitions between the two longliving ground levels. Theoretical studies described the dark resonance as a coherent superposition of two long-living ground levels prepared by the bi-chromatic laser field, and ‘atomic population trapping’ was introduced, leading to the term Coherent Population Trapping (CPT) [2]. l Luigi Moi1, Stefka Cartaleva2 DOI: 10.1051/epn/2012603
We demonstrate the possibility of suppressing the linear response of the coherent population trapping resonance frequency to variations in the external magnetic field. The suppression can be achieved at a specific value of the clock magnetic field B due to the competition between the frequency pulling by neighboring resonances and the quadratic Zeeman shift. The effect is possible only with certain combinations of the optical field polarization and the direction of the magnetic field. An incorrect field configuration can significantly increase the magnetic-induced frequency shifts.
We investigate the polarization modulation between two linear orthogonal states of the laser beam that synchronously pumps time-dependent atomic alignment in caesium atoms exposed to a static magnetic field. Because of the atomic alignment symmetry two independent groups of resonances can be distinguished in the transmitted light: when modulation frequency matches either the Larmor frequency or its second harmonics, ${\ensuremath{\omega}}_{L}$ and $2{\ensuremath{\omega}}_{L}$, respectively. We report on our experiments, and discuss a model that perfectly reproduces the observed spectra. We have observed that the amplitudes and linewidths of resonances at ${\ensuremath{\omega}}_{L}$ and $2{\ensuremath{\omega}}_{L}$ show magnetic-field direction dependence. This peculiar behavior makes our approach interesting for future application to atomic magnetometry, in view of a dead-zone free high-sensitivity magnetometer.