-0.05 0.00 0.05 Faraday rotation [rad] 5 0 -5 Magnetic field [G] M FGLYPH<.notdef>=GLYPH<.notdef>3 -3 -2 -1 0 1 2 3 m = F F’ =GLYPH<.notdef>4 M MOTGLYPH<.notdef>beams BGLYPH<.notdef>field λ/4 λ/4 λ/4 λ/4 -3 -4 -2 -1 0 1 2 3 4 m = F’ λ/2 M Probe PBS a) PD1 PD2 PBS b) FIG. 2: Linear (wide) and nonlinear (narrow) Faraday rota- tion resonances centered at B = 0 . NFR resonance is power broadened for a better visibility. The probe power is 64 µ W. FIG. 1: (a) The setup of the experiment for the balanced po- larimeter arrangement. M are mirrors, PBS polarizing beam splitters, PD photodetectors, λ/ 2 , λ/ 4 waveplates. Direc- tion of the magnetic field B necessary for the observation of the Faraday rotation is indicated. (For FS scheme the λ/ 2 plate is removed and PD2 is not used). (b) Energy level-structure with the Zeeman-coherences established by a linearly-polarized light. scheme which for resonant light is sensitive to the square of the rotation angle. For non-resonant case, circular dichroism contributes also to the observed signal. In the experiment atoms were collected and cooled in the MOT. This phase was periodically interrupted for the measurement of optical rotation: the MOT lasers and the quadrupole magnetic field were switched off and a homogenous magnetic field B of a controlled value was applied along the probe beam. After 2 ms (required for complete decay of the eddy currents induced by turning off the quadrupole field) the probe beam was switched on and polarization rotation was recorded for the next 5 ms. Finally, the MOT fields were switched back for 50–200 ms and the atomic cloud was recaptured and cooled. This procedure allowed recording polarization rotation signals as a function of time for each value of the B field. The experiment was controlled by a PC, which also digitized, stored, and averaged (typically 20 times) the data. Typical signals (rotation angle vs. B ) associated with linear and nonlinear Faraday effect have the form of dis- persive resonances nested at B = 0 , as shown in Fig. 2. The narrow feature is the nonlinear resonance (NFR); it appears when the probe beam is sufficiently intense. Hereinafter, we refer to this nonlinear resonance as the zero-field resonance. The width of the linear resonance amounts to several G and corresponds to the natural linewidth of the studied transition. It also depends on the detuning of the probe beam from resonance condi- tion and initial Zeeman-sublevel populations, as has been shown in [2]. That situation is prominently different from the case of vapor cells, where LFR resonance is two orders of magnitude broader, because of the Doppler effect In Fig. 3 we depict the evolution of the Faraday rota- tion signals with the increase of the light power. While the wide structure associated with the linear Faraday ef- fect represent rotation angle independent on the light in- tensity, the central narrow feature clearly exhibits non- atoms is that at light intensity required for creation of the Zeeman coherence the laser beam may mechanically perturb the cold-atom sample. In our study this adverse effect is reduced by retroreflection of the light beam and careful optimization of the experimental conditions to minimize the light power. The experiment (see the setup shown in Fig. 1a) was performed with about 10 $^{7 85}$Rb atoms using a standard MOT. In addition to the trapping and repumping lasers we used a separate probe laser whose frequency was tuned around the F = 3 → F ′ = 4 hyperfine transition of the D2 line (780nm). Fig. 1b depicts the Zeeman structure of the F = 3 and F ′ = 4 states with the transitions induced by linearly polarized light (superposition of σ ± polariza- tions). A weak linearly polarized probe beam of several µ W in power and 2 mm in diameter was sent through the atom cloud and then retroreflected to partially reduce light pressure effects. The probe-beam frequency 14 MHz below the line center proved to be optimal from the point of view of atomic loss which we attribute to extra Doppler-cooling mechanism by two counter-propagating beams. The double passage of light through the sample doubled the acquired Faraday rotation. The light polar- ization was measured in two arrangements: using bal- anced polarimeter (direct rotation angle measurement) and in a crossed polarizers or forward-scattering (FS) 2