Non-Abelian adiabatic geometric transformations in a cold strontium gas.

Topology, geometry, and gauge fields play key roles in quantum physics as exemplified by fundamental phenomena such as the Aharonov-Bohm effect, the integer quantum Hall effect, the spin Hall, and topological insulators. The concept of topological protection has also become a salient ingredient in many schemes for quantum information processing and fault-tolerant quantum computation. The physical properties of such systems crucially depend on the symmetry group of the underlying holonomy. Here, we study a laser-cooled gas of strontium atoms coupled to laser fields through a four-level resonant tripod scheme. By cycling the relative phases of the tripod beams, we realize non-Abelian SU(2) geometrical transformations acting on the dark states of the system and demonstrate their non-Abelian character. We also reveal how the gauge field imprinted on the atoms impact their internal state dynamics. It leads to a thermometry method based on the interferometric displacement of atoms in the tripod beams.

Coherent Backscattering Reveals the Anderson Transition.

We develop an accurate finite-time scaling analysis of the angular width of the coherent backscattering (CBS) peak for waves propagating in 3D random media. Applying this method to ultracold atoms in optical speckle potentials, we show how to determine both the mobility edge and the critical exponent of the Anderson transition from the temporal behavior of the CBS width. Our method could be used in experiments to fully characterize the 3D Anderson transition.

Coherent forward scattering peak induced by Anderson localization.

Numerical simulations show that, at the onset of Anderson localization, the momentum distribution of a coherent wave packet launched inside a random potential exhibits, in the forward direction, a novel interference peak that complements the coherent backscattering peak. An explanation of this phenomenon in terms of maximally crossed diagrams predicts that the signal emerges around the localization time and grows on the scale of the Heisenberg time associated with the localization volume. Together, coherent back and forward scattering provide evidence for the occurrence of Anderson localization.

Light transport in cold atoms and thermal decoherence.

We use the coherent backscattering interference effect to investigate experimentally and theoretically how coherent transport of light inside a cold atomic vapor is affected by the residual motion of atomic scatterers. As the temperature of the atomic cloud increases, the interference contrast decreases dramatically. This emphasizes the role of motion-induced decoherence for resonant scatterers even in the sub-Doppler regime of temperature. We derive analytical expressions for the corresponding coherence time.

Localization of matter waves in two-dimensional disordered optical potentials.

We consider ultracold atoms in 2D disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport in the noninteracting regime. We derive the diffusion constant as a function of all relevant microscopic parameters and show that coherent multiple scattering induces significant weak localization effects. In particular, we find that even the strong localization regime is accessible with current experimental techniques and calculate the corresponding localization length.

Coherent backscattering of light by nonlinear scatterers.

We theoretically study the propagation of light in a disordered medium with nonlinear scatterers. We especially focus on interference effects between reversed multiple scattering paths, which lead to weak localization and coherent backscattering. We show that, in the presence of weakly nonlinear scattering, constructive interferences exist in general between three different scattering amplitudes. This effect influences the nonlinear backscattering enhancement factor, which may thus exceed the linear barrier two.

Saturation-induced coherence loss in coherent backscattering of light.

We use coherent backscattering of light by cold strontium atoms to study phase-breaking mechanisms in the multiple-scattering regime. As the probe light intensity is increased, the atomic optical transition starts to be saturated. Nonlinearities and inelastic scattering then occur. The latter induces a characteristic phase-breaking time that reduces the wave coherence. In our experiment, this leads to a strong reduction of the enhancement factor of the coherent backscattering cone. The results at different probe detuning are also presented.

Magnetic field enhanced coherence length in cold atomic gases.

We study the effect of an external magnetic field on coherent backscattering of light from a cold rubidium vapor. We observe that the backscattering enhancement factor can be increased with B. This surprising behavior shows that the coherence length of the system can be increased by adding a magnetic field, in sharp contrast with usual situations. This is mainly due to the lifting of the degeneracy between Zeeman sublevels. We find good agreement between our experimental data and a full Monte Carlo simulation, taking into account the magneto-optical effects and the geometry of the atomic cloud.

Slow diffusion of light in a cold atomic cloud.

We study the diffusive propagation of multiply scattered light in an optically thick cloud of cold rubidium atoms illuminated by a quasiresonant laser beam. In the vicinity of a sharp atomic resonance, the energy transport velocity of the scattered light is almost 5 orders of magnitude smaller than the vacuum speed of light, reducing strongly the diffusion constant. We verify the theoretical prediction of a frequency-independent transport time around the resonance. We also observe the effect of the residual velocity of the atoms at long times.

Hanle effect in coherent backscattering.

We study the shape of the coherent-backscattering (CBS) cone obtained when resonant light illuminates a thick cloud of laser-cooled rubidium atoms in the 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).

Coherent light transport in a cold strontium cloud.

We study light coherent transport in the weak localization regime using magneto-optically cooled strontium atoms. The coherent backscattering cone is measured in the four polarization channels using light resonant with a J(g) = 0-->J(e) = 1 transition of the strontium atom. We find an enhancement factor close to 2 in the helicity preserving channel, in agreement with theoretical predictions. This observation confirms the effect of internal structure as the key mechanism for the contrast reduction observed with a rubidium cold cloud [G. Labeyrie et al., Phys. Rev. Lett. 83, 5266 (1999)]. Experimental results are in good agreement with Monte Carlo simulations taking into account geometry effects.

Chaos-assisted tunneling with cold atoms.

In the context of quantum chaos, both theory and numerical analysis predict large fluctuations of the tunneling transition probabilities when irregular dynamics is present at the classical level. Here we consider the nondissipative quantum evolution of cold atoms trapped in a time-dependent modulated periodic potential generated by two laser beams. We give some precise guidelines for the observation of chaos-assisted tunneling between invariant phase space structures paired by time-reversal symmetry.

Multiple scattering of light by atoms in the weak localization regime

Coherent backscattering is a multiple scattering interference effect which enhances the diffuse reflection off a disordered sample in the backward direction. Classically, the enhanced intensity is twice the average background under well chosen experimental conditions. We show how the quantum internal structure of atomic scatterers leads to a significantly smaller enhancement. Theoretical results for double scattering in the weak localization regime are presented which confirm recent experimental observations.