We compare the behavior of absorption and of resonance fluorescence spectra in an extremely thin Rb vapor cell as a function of the ratio of L / , with L the cell thickness ͑L ϳ 150-1800 nm͒ and the wavelength of the Rb D 2 line ͑ = 780 mn͒. The Dicke-type coherent narrowing [G. Dutier et al., Europhys. Lett. 63, 35 (2003)] is observed only in transmission measurements, in the linear regime, with its typical collapse and revival, which reaches a maximum for L = ͑2n +1͒ /2 (n integer). It is shown not to appear in fluorescence, whose behavior-amplitude, and spectral width, is more monotonic with L. Conversely, at high-intensity, the sub-Doppler saturation effects are shown to be the most visible in transmission around L = n.
We describe a method of selective generation and study of polarization moments of up to the highest rank κ = 2F possible for a quantum state with total angular momentum F . The technique is based on nonlinear magneto-optical rotation with frequency-modulated light. Various polarization moments are distinguished by the periodicity of light-polarization rotation induced by the atoms during Larmor precession and exhibit distinct light-intensity and frequency dependences. We apply the method to study polarization moments of 87 Rb atoms contained in a vapor cell with antirelaxation coating. Distinct ultra-narrow (1-Hz wide) resonances, corresponding to different multipoles, appear in the magnetic-field dependence of the optical rotation. The use of the highest-multipole resonances has important applications in quantum and nonlinear optics and in magnetometry.PACS numbers: PACS 32.80. Bx,95.75.Hi High-rank polarization moments (PM) and associated high-order coherences have recently drawn attention (see [1,2,3,4,5,6,7,8] While signatures of high-order PM were detected in several experiments [3,4,5,6,8], the methods used in these investigations are not sufficiently selective and/or do not allow real-time manipulation of particular multipoles. Here we describe a method, based on nonlinear optical rotation with frequency-modulated light (FM NMOR) [16], by which one can selectively induce, control, and study any possible multipole moment. Applying the method to 87 Rb atoms in a paraffin-coated cell [17,18], we have verified the expected power and spectral dependences of the resonant signals and obtained a quantitative comparison of relaxation rates for the even-rank moments.The density matrix in the M, M ′ representation for a state with total angular momentum F can be decomposed into PM of rank κ = 0 . . . 2F , uncoupled under rotations, with components q = −κ . . . κ: with surfaces for which the distance to the origin in a given direction is proportional to the probability of finding the projection M = F along this direction. (a): "pure" quadrupole κ = 2, q = 0; (b): κ = 4, q = 0 hexadecapole; (c): same as in (b), but rotated by π/2 around the x-axis; (d): the average of (b) and (c), which has a 4-fold symmetry with respect to rotations aroundx. In all cases, the minimum necessary amount of ρ (0) 0 was added to ensure that all sublevel populations are non-negative [20]. Probability surfaces (a) and (d) rotating aroundx-directed magnetic field with the Larmor frequency correspond to the polarization states produced in this experiment.is uniquely associated with the highest PM for a given state, e.g., the quadrupole moment (κ = 2) for F = 1, or the hexadecapole (κ = 4) for F = 2. The method introduced here exploits the different axial symmetries of the PM (2-fold and 4-fold for the quadrupole and hexadecapole, respectively; Fig. 1) to selectively create and detect them (see also [3,4,5,6]).While multipole moments of rank κ ≤ 2 can be easily generated and detected with weak light (since a photon has spin one), higher-ra...
A low-light-power theory of nonlinear magneto-optical rotation of frequency-modulated light resonant with a J = 1 → J ′ = 0 transition is presented. The theory is developed for a Doppler-free transition, and then modified to account for Doppler broadening and velocity mixing due to collisions. The results of the theory are shown to be in qualitative agreement with experimental data obtained for the rubidium D1 line.
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