arXiv subjects
Publications and source records attributed to Dominique Delande.
We show that optical beams propagating in transversally disordered materials exhibit a spin Hall effect and a spin-to-orbital conversion of angular momentum as they deviate from paraxiality. We theoretically describe these phenomena on the basis of the microscopic statistical approach to light propagation in random media, and show that they can be detected via polarimetric measurements under realistic experimental conditions
We calculate the relative permittivity of a cold atomic gas under weak probe illumination, up to second order in the density. Within the framework of a diagrammatic representation method, we identify all the second order diagrams that enter into the description of the relative permittivity for coherent light transmission. These diagrams originate from pairwise position correlation and recurrent scattering. Using coupled dipole equations, we numerically simulate the coherent transmission with scalar and vector waves, and find good agreement with the perturbative calculations. We applied this perturbative expansion approach to a classical gas at rest, but the method is extendable to thermal gas with finite atomic motion and to quantum gases where non-trivial pair correlations can be naturally included.
The atomic Quantum Kicked Rotor is an outstanding "quantum simulator" for the exploration of transport in disordered quantum systems. Here we study experimentally the phase-shifted quantum kicked rotor, which we show to display properties close to an ideal disordered quantum system, opening new windows into the study of Anderson physics.
The two-component Fermi gas with contact attractive interactions between different spin components can be described by the Yang-Gaudin model. Applying the Bethe ansatz approach, one finds analytical formulae for the system eigenstates that are uniquely parametrized by the solutions of the corresponding Bethe equations. Recent numerical studies of the so-called yrast eigenstates, i.e. lowest energy eigenstates at a given non-zero total momentum, in the Yang-Gaudin model show that their spectrum resembles yrast dispersion relation of the Lieb-Liniger model which in turn matches the dark soliton dispersion relation obtained within the nonlinear Schrödinger equation. It was shown that such conjecture in the case of the Lieb-Liniger model was not accidental and that dark soliton features emerged in the course of measurement of positions of particles, when the system was initially prepared in an yrast eigenstate. Here, we demonstrate that, starting with yrast eigenstates in the Yang-Gaudin model, the key soliton signatures are revealed by the measurement of pairs of fermions. We study soliton signatures in a wide range of the interaction strength.
We study many-body localization for a disordered chain of spin 1/2 fermions. In [Phys. Rev. B \textbf{94}, 241104 (2016)], when both down and up components are exposed to the same strong disorder, the authors observe a power law growth of the entanglement entropy that suggests that many-body localization is not complete; the density (charge) degree of freedom is localized, while the spin degree of freedom is apparently delocalized. We show that this power-like behavior is only a transient effect and that, for longer times, the growth is logarithmic in time suggesting that the spin degree of freedom is also localized, so that the system follows the standard many-body localization scenario. We also study the experimentally relevant case of quasiperiodic disorder.
We study experimentally a quantum kicked rotor with broken parity symmetry, supporting a ratchet effect due to the presence of a classical accelerator mode. We show that the short-time dynamics is very well described by the classical dynamics, characterized by a strongly asymmetric momentum distribution with directed motion on one side, and an anomalous diffusion on the other. At longer times, quantum effects lead to dynamical localization, causing an asymptotic resymmetrization of the wave function.
Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and compare the results with the standard uniform distribution. Both statistical properties of energy levels and the long time non-ergodic behavior are discussed. The results for different discrete distributions are essentially identical to those obtained for the continuous distribution, provided the disorder strength is rescaled by the standard deviation of the random distribution. Only for the binary distribution significant deviations are observed.
We report on the measurement of the spectral functions of noninteracting ultracold atoms in a three-dimensional disordered potential resulting from an optical speckle field. Varying the disorder strength by 2 orders of magnitude, we observe the crossover from the "quantum" perturbative regime of low disorder to the "classical" regime at higher disorder strength, and find an excellent agreement with numerical simulations. The method relies on the use of state-dependent disorder and the controlled transfer of atoms to create well-defined energy states. This opens new avenues for experimental investigations of three-dimensional Anderson localization.
Systems which can spontaneously reveal periodic evolution are dubbed time crystals. This is in analogy with space crystals that display periodic behavior in configuration space. While space crystals are modelled with the help of space periodic potentials, crystalline phenomena in time can be modelled by periodically driven systems. Disorder in the periodic driving can lead to Anderson localization in time: the probability for detecting a system at a fixed point of configuration space becomes exponentially localized around a certain moment in time. We here show that a three-dimensional system exposed to a properly disordered pseudo-periodic driving may display a localized-delocalized Anderson transition in the time domain, in strong analogy with the usual three-dimensional Anderson transition in disordered systems. Such a transition could be experimentally observed with ultra-cold atomic gases.
Anderson localization, the absence of diffusion in disordered media, draws its origins from the destructive interference between multiple scattering paths. The localization properties of disordered systems are expected to be dramatically sensitive to their symmetry characteristics. So far however, this question has been little explored experimentally. Here, we investigate the realization of an artificial gauge field in a synthetic (temporal) dimension of a disordered, periodically-driven (Floquet) quantum system. Tuning the strength of this gauge field allows us to control the time-reversal symmetry properties of the system, which we probe through the experimental observation of three symmetry-sensitive `smoking-gun' signatures of localization. The first two are the coherent backscattering, marker of weak localization, and the coherent forward scattering, genuine interferential signature of Anderson localization, observed here for the first time. The third is the direct measurement of the $β(g)$ scaling function in two different symmetry classes, allowing to demonstrate its universality and the one-parameter scaling hypothesis.
We study many-body localization in a one dimensional optical lattice filled with bosons. The interaction between bosons is assumed to be random, which can be realized for atoms close to a microchip exposed to a spatially fluctuating magnetic field. Close to a Feshbach resonance, such controlled fluctuations can be transfered to the interaction strength. We show that the system reveals an inverted mobility edge, with mobile particles at the lower edge of the spectrum. A statistical analysis of level spacings allows us to characterize the transition between localized and excited states. The existence of the mobility edge is confirmed in large systems, by time dependent numerical simulations using tDMRG. A simple analytical model predicts the long time behavior of the system.
We show that the coherent forward scattering (CFS) interference peak amplitude sharply jumps from zero to a finite value upon crossing a metal-insulator transition. Extensive numerical simulations reveal that the CFS peak contrast obeys the one-parameter scaling hypothesis and gives access to the critical exponents of the transition. We also discover that the critical CFS peak directly controls the spectral compressibility at the transition where eigenfunctions are multifractal, and we demonstrate the universality of this property with respect to various types of disorder.
The possibility of observing many body localization of ultracold atoms in a one dimensional optical lattice is discussed for random interactions. In the non-interacting limit, such a system reduces to single-particle physics in the absence of disorder, i.e. to extended states. In effect the observed localization is inherently due to interactions and is thus a genuine many-body effect. In the system studied, many-body localization manifests itself in a lack of thermalization visible in temporal propagation of a specially prepared initial state, in transport properties, in the logarithmic growth of entanglement entropy as well as in statistical properties of energy levels.
We study the critical dynamics of matter waves at the 3D Anderson mobility edge in cold-atom disorder quench experiments. General scaling arguments are supported by precision numerics for the spectral function, diffusion coefficient, and localization length in isotropic blue-detuned speckle potentials. We discuss signatures of critical slowdown in the time-dependent central column density of a spreading wave packet, and evaluate the prospects of observing anomalous diffusion right at criticality.
Recent experiments on non-interacting ultra-cold atoms in correlated disorder have yielded conflicting results regarding the so-called mobility edge, i.e. the energy threshold separating Anderson localized from diffusive states. At the same time, there are theoretical indications that the experimental data overestimate the position of this critical energy, sometimes by a large amount. The non-trivial effect of anisotropy in the spatial correlations of experimental speckle potentials have been put forward as a possible cause for such discrepancy. Using extensive numerical simulations we show that the effect of anisotropy alone is not sufficient to explain the experimental data. In particular, we find that, for not-too-strong anisotropy, realistic disorder configurations are essentially identical to the isotropic case, modulo a simple rescaling of the energies.
In analogy with usual Anderson localization taking place in time-independent disordered quantum systems where the disorder acts in configuration space, systems exposed to temporally disordered potentials can display Anderson localization in the time domain. We demonstrate this phenomenon with one-dimensional examples where a temporally disordered potential induces localization during the quantum evolution of wave-packets, in contrast with a fully delocalized classical dynamics. This is an example of a time crystal phenomenon, i.e., a crystalline behavior in the time domain.
We develop a perturbative treatment of induced dipole-dipole interactions in the diffusive transport of electromagnetic waves through disordered atomic clouds. The approach is exact at order two in the atomic density and accounts for the vector character of light. It is applied to the calculation of the electromagnetic energy stored in the atomic cloud - which modifies the energy transport velocity - and of the light scattering and transport mean free paths. Results are compared to those obtained from a purely scalar model for light.
We present a novel analytical method for calculating the spectral function and the density of states in speckle potentials, valid in the semiclassical regime. Our approach relies on stationary phase approximations, allowing us to describe the singular quantum corrections at low energies. We apply it to the calculation of the spectral function and the density of states in one and two-dimensional speckle potentials. By connecting our results with those of previous work valid in the high energy sector, we end up with a consistent description of the whole energy spectrum, in good agreement with numerical simulations.