Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets.

We identify the key features of Kardar-Parisi-Zhang (KPZ) universality class in the fluctuations of the wave density logarithm in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit an algebraic scaling with distance characterized by an exponent of 1/3, and a Tracy-Widom probability distribution of the fluctuations. Additionally, within a directed polymer picture of KPZ physics, we identify the dominant contribution of a directed path to the wave packet density and find that its transverse fluctuations are characterized by a roughness exponent 2/3.

Critical dynamics of long-range quantum disordered systems.

Long-range hoppings in quantum disordered systems are known to yield quantum multifractality, the features of which can go beyond the characteristic properties associated with an Anderson transition. Indeed, critical dynamics of long-range quantum systems can exhibit anomalous dynamical behaviors distinct from those at the Anderson transition in finite dimensions. In this paper, we propose a phenomenological model of wave packet expansion in long-range hopping systems.

Chaos-Assisted Long-Range Tunneling for Quantum Simulation.

We present an extension of the chaos-assisted tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with chaos-induced long-range hoppings t_{n}∝1/n between sites at a distance n. We provide a numerical demonstration of the robustness of the results and derive an analytical prediction for the hopping term law.

Controlling symmetry and localization with an artificial gauge field in a disordered quantum system.

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 symmetries. So far, this question has been little explored experimentally.

Chaos-assisted tunneling in the presence of Anderson localization.

Tunneling between two classically disconnected regular regions can be strongly affected by the presence of a chaotic sea in between. This phenomenon, known as chaos-assisted tunneling, gives rise to large fluctuations of the tunneling rate. Here we study chaos-assisted tunneling in the presence of Anderson localization effects in the chaotic sea.

Return to the Origin as a Probe of Atomic Phase Coherence.

We report on the observation of the coherent enhancement of the return probability ["enhanced return to the origin" (ERO)] in a periodically kicked cold-atom gas. By submitting an atomic wave packet to a pulsed, periodically shifted, laser standing wave, we induce an oscillation of ERO in time that is explained in terms of a periodic, reversible dephasing in the weak-localization interference sequences responsible for ERO. Monitoring the temporal decay of ERO, we exploit its quantum-coherent nature to quantify the decoherence rate of the atomic system.

Critical properties of the superfluid-bose-glass transition in two dimensions.

We investigate the superfluid (SF) to Bose-glass (BG) quantum phase transition using extensive quantum Monte Carlo simulations of two-dimensional hard-core bosons in a random box potential. T=0 critical properties are studied by thorough finite-size scaling of condensate and SF densities, both vanishing at the same critical disorder Wc=4.80(5).

Thermal enhancement of interference effects in quantum point contacts.

We study an electron interferometer formed with a quantum point contact and a scanning probe tip in a two-dimensional electron gas. The images giving the conductance as a function of the tip position exhibit fringes spaced by half the Fermi wavelength. For a contact opened at the edges of a quantized conductance plateau, the fringes are enhanced as the temperature T increases and can persist beyond the thermal length l(T).

Critical state of the Anderson transition: between a metal and an insulator.

Using a three-frequency one-dimensional kicked rotor experimentally realized with a cold atomic gas, we study the transport properties at the critical point of the metal-insulator Anderson transition. We accurately measure the time evolution of an initially localized wave packet and show that it displays at the critical point a scaling invariance characteristic of this second-order phase transition. The shape of the momentum distribution at the critical point is found to be in excellent agreement with the analytical form deduced from the self-consistent theory of localization.

Experimental observation of the Anderson metal-insulator transition with atomic matter waves.

We realize experimentally an atom-optics quantum-chaotic system, the quasiperiodic kicked rotor, which is equivalent to a 3D disordered system that allows us to demonstrate the Anderson metal-insulator transition. Sensitive measurements of the atomic wave function and the use of finite-size scaling techniques make it possible to extract both the critical parameters and the critical exponent of the transition, the latter being in good agreement with the value obtained in numerical simulations of the 3D Anderson model.