Hanle Effect in Coherent Backscattering

Abstract

We study the shape of the coherent backscattering (CBS) cone obtained when resonant light illuminates a thick cloud of laser-cooled rubidium atoms in presence of a homogenous magnetic field. We observe new magnetic field-dependent anisotropies in the CBS signal. We show that the observed behavior is due to the modification of the atomic radiation pattern by the magnetic field (Hanle effect in the excited state). 32.80.Pj When a multiply scattering medium is illuminated by a laser beam, the scattered intensity results from the interference between the amplitudes associated with the various scattering paths; for a disordered medium, the interference terms are washed out when averaged over many sample configurations, except in a narrow angular range around exact backscattering where the average intensity is enhanced. This phenomenon, known as coherent backscattering (CBS), is due to a two-wave constructive interference (at exact back-scattering) between waves following a given scattering path and the associated reverse path, where exactly the same scatterers are visited in the reversed order [1]. The maximum enhancement is obtained when the amplitudes of the interfering paths are exactly balanced. For a convenient choice of polarization, time-reversal symmetry directly implies the equality of the interfering amplitudes. More generally, the interference phenomenon is very robust and qualitatively insensitive to most characteristics of the sample and illuminating wave.However, applying a magnetic field on the sample breaks the time-reversal invariance. It was predicted [2], then experimentally observed [3] and theoretically studied [4,5] that it results in a decrease of the CBS enhancement as well as some rather complicated behavior of the cone shape. In our current understanding of CBS, two ingredients are essential : the individual scattering event, characterized for example by the radiation pattern of each scatterer (this is the single scattering ingredient), and the propagation in the medium between scattering events (this is the "average effective medium" ingredient). Of course, these two ingredients are not independent since the optical theorem links the propagation in the medium to the individual scattering. In the presence of a magnetic field, both ingredients can be affected. For the propagation, this is well known under the name of Faraday effect (and the Voigt or Cotton-Mouton effect) and can be described by the modification of the complex refractive index by the magnetic field. The magnetic field-induced variation of the radiation pattern is much less studied, because it is very small in usual magnetooptically active materials; it is responsible for the "photonic Hall effect" predicted by van Tiggelen [6] and later observed experimentally [7]. In this paper, we show a novel situation where it is experimentally and theoretically possible to discriminate between the two ingredients and where the modification of the radiation pattern dominates the propagation effects.In our experiment, we analyze coheren...

Coherent backscattering of light by cold atoms: Theory meets experiment

“…In the circular polarization channels, this proves to be safe since the recorded cones are isotropic (although the scattering medium itself has not a perfect cylindrical symmetry around the probe propagation axis). In the lin lin channel, the cone shape is anisotropic (roughly an elliptical shape, see table I) and the widths are different along the direction of the incoming polarization and perpendicular to it [13]. In the lin ⊥ lin channel, the CBS cone has a four-fold symmetry [13] and two different widths can be measured, either along one of the polarization axes or at 45…”

“…Complementary Monte-Carlo calculations, discussed in [12], show that the angular width is rather sensitive to the detailed shape of the medium, especially in the external layers of the atomic cloud. Keeping the same optical thickness, but changing the density of the medium from a Gaussian density exp(−r 2 /2r 2 0 ) to a exp(−r 4 /4r 4 0 ) density (i.e.…”

“…We choose to perform the average over the positions of the scatterers with a Monte-Carlo method and to use an internal analytical average by employing the average atomic scattering vertex [9,11]. The details of the method are given in [12]. The essential assumption is that all Zeeman sublevels in the ground-state are equally populated, without any coherence between sub-levels.…”

Analogue of the Quantum Hanle Effect and Polarization Conversion in Non-Hermitian Plasmonic Metamaterials

“…The main advantage for typical measurements of this kind is a very high spectral resolution and sensitivity to magnetic fields, since the level crossings are not limited by the Doppler width of the spectral lines, but solely by the coherence in individual atoms. The observation of the Hanle effect is possible in the presence of a magnetic field which violates the time-reversal symmetry as was observed in the experiments on coherent backscattering 9 and can contribute to parity symmetry breaking 10 .…”

Light trapping in high-density ultracold atomic gases for quantum memory applications

“…Multiple light scattering in atomic gases is quasielastic, and so the scattered light can remain in a coherent state. This situation corresponds in the lower density case to the so-called weak localization regime, where such scattering can produce macroscopic observables such as the coherent backscattering cone [11][12][13][14][15][16][17][18][19][20][21][22]. The weak localization case is characterized by the inequality kl ≫ 1, where k = 2π/λ is the light wave vector, and l is the meanfree path for light scattering.…”