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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. The symmetry group and geometric phase of a system are responsible for many quantum properties related to non-trivial topology. Here the authors show non-Abelian geometric phase in laser-coupled ultracold strontium atoms by using a tripod scheme.

The physics of strong light-matter coupling has been addressed in different scientific communities over the last three decades. Since the early eighties, atoms coupled to optical and microwave cavities have led to pioneering demonstrations of cavity quantum electrodynamics, Gedanken experiments, and building blocks for quantum information processing, for which the Nobel Prize in Physics was awarded in 2012. In the framework of semiconducting devices, strong coupling has allowed investigations into the physics of Bose gases in solid-state environments, and the latter holds promise for exploiting light-matter interaction at the single-photon level in scalable architectures. More recently, impressive developments in the so-called superconducting circuit QED have opened another fundamental playground to revisit cavity quantum electrodynamics for practical and fundamental purposes. This book aims at developing the necessary interface between these communities, by providing future researchers with a robust conceptual, theoretical and experimental basis on strong light-matter coupling, both in the classical and in the quantum regimes. In addition, the emphasis is on new forefront research topics currently developed around the physics of strong light-matter interaction in the atomic and solid-state scenarios.

We present a detailed numerical and theoretical analysis of the recently discovered phenomenon of coherent forward scattering. This effect manifests itself as a macroscopic interference peak in the forward direction of the momentum distribution of a matter wave launched with finite velocity in a random potential. Focusing on the two-dimensional case, we show that coherent forward scattering generally arises due the confinement of the wave in a finite region of space, and explain under which conditions it can be seen as a genuine signature of Anderson localization.

Atomtronics deals with matter-wave circuits of ultra-cold atoms manipulated through magnetic or laser-generated guides with different shapes and intensities. In this way, new types of quantum networks can be constructed, in which coherent fluids are controlled with the know-how developed in the atomic and molecular physics community. In particular, quantum devices with enhanced precision, control and flexibility of their operating conditions can be accessed. Concomitantly, new quantum simulators and emulators harnessing on the coherent current flows can also be developed. Here, we survey the landscape of atomtronics-enabled quantum technology and draw a roadmap for the field in the near future. We review some of the latest progresses achieved in matter-wave circuits design and atom-chips. Atomtronic networks are deployed as promising platforms for probing many-body physics with a new angle and a new twist. The latter can be done both at the level of equilibrium and non-equilibrium situations. Numerous relevant problems in mesoscopic physics, like persistent currents and quantum transport in circuits of fermionic or bosonic atoms, are studied through a new lens. We summarize some of the atomtronics quantum devices and sensors. Finally, we discuss alkali-earth and Rydberg atoms as potential platforms for the realization of atomtronic circuits with special features.

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.

This paper investigates quantum diffusion of matter waves in two-dimensional random potentials, focussing on expanding Bose-Einstein condensates in spatially correlated optical speckle potentials. Special care is taken to describe the effect of dephasing, finite system size, and an initial momentum distribution. We derive general expressions for the interference-renormalized diffusion constant, the disorder-averaged probability density distribution, the variance of the expanding atomic cloud, and the localized fraction of atoms. These quantities are studied in detail for the special case of an inverted-parabola momentum distribution as obtained from an expanding condensate in the Thomas-Fermi regime. Lastly, we derive quantitative criteria for the unambiguous observation of localization effects in a possible 2D experiment.

The interference contrast observed in coherent backscattering by cold atoms is drastically reduced with respect to classical disordered media. We study the impact of the degeneracy of the resonant atomic dipole transition on multiple scattering of polarised photons. An analytical treatment allows to derive the diffusion coefficient and depolarisation times for the average light intensity, and dephasing times for the weak localisation corrections. The calculated CBS signals reproduce the experimental results.

An analytical microscopic theory for the resonant multiple scattering of light by cold atoms with arbitrary internal degeneracy is presented. It permits to calculate the average amplitude and the average intensity for one-photon states of the full transverse electromagnetic field in a dilute medium of unpolarized atoms. Special emphasis is laid upon an analysis in terms of irreducible representations of the rotation group. It allows to sum explicitly the ladder and maximally crossed diagrams, giving the average intensity in the Boltzmann approximation and the interference corrections responsible for weak localization and coherent backscattering. The exact decomposition into field modes shows that the atomic internal degeneracy contributes to the depolarization of the average intensity and suppresses the interference corrections. Static as well as dynamic quantities like the transport velocity, diffusion constants and relaxation times for all field modes and all atomic transitions are derived.

In a recent Letter (Phys. Rev. Lett. \\textbf{98}, 083601 (2007), arXiv:cond-mat/0610804), O. Assaf and E. Akkermans claim that the angular correlations of the light intensity scattered by a cloud of cold atoms with internal degeneracy (Zeeman sublevels) of the ground state overcome the usual Rayleigh law. More precisely, they found that they become exponentially large with the size of the sample. In what follows, we will explain why their results are wrong and, in contrary, why the internal degeneracy leads to lower intensity correlations.

Quantum Monte Carlo (QMC) techniques are used to provide an approximation-free investigation of the phases of the one-dimensional attractive Hubbard Hamiltonian in the presence of population imbalance. The temperature at which the \"Fulde-Ferrell-Larkin-Ovchinnikov\" (FFLO) phase is destroyed by thermal fluctuations is determined as a function of the polarization. It is shown that the presence of a confining potential does not dramatically alter the FFLO regime, and that recent experiments on trapped atomic gases likely lie just within the stable temperature range.