Quantum diffusion with disorder, noise and interaction

Abstract

Disorder, noise and interaction play a crucial role in the transport properties of real systems, but they are typically hard to control and study, both theoretically and experimentally, especially in the quantum case. Here, we explore a paradigmatic problem, the diffusion of a wavepacket, by employing ultra-cold atoms in a quasi-periodic lattice with controlled noise and tunable interaction. The presence of quasi-disorder leads to Anderson localization, while both interaction and noise tend to suppress localization and restore transport, although with completely different mechanisms. When only noise or interaction is present, we observe a diffusion dynamics that can be explained by existing microscopic models. When noise and interaction are combined, we observe instead a complex anomalous diffusion. By combining experimental measurements with numerical simulations, we show that such anomalous behavior can be modeled with a generalized diffusion equation in which the noise-and interaction-induced diffusions enter in an additive manner. Our study reveals also a more complex interplay between the two diffusion mechanisms in the regimes of strong interaction or narrowband noise.

Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials

“…With the help of the available experimental apparatus, one aims at simulating in great detail the transition from microscopic to macroscopic scales while accurately adjusting the interaction between the particles, the effect of external (disorder) potentials and/or sources of noise, cf. [14,15] and Section 2.1. Additionally, as the transition towards macroscopic scales involves irreversibility, i. e. an increase of entropy, the question arises under which condition and how a certain system reaches (thermal) equilibrium [16].…”

“…In addition to (15), an evolution equation for the non-condensate density ρ nc (r, t) has to be stated in order to solve the coupled equations simultaneously. We will consider such an equation further down.…”

“…We will consider such an equation further down. However, due to the very structure of (15), the number of particles N 0 (t) = dr |φ(r, t)| 2 inside the condensate remains fixed. (Dynamical) scenarios, where the condensate can grow or shrink as a consequence of collisions, require a treatment beyond the Hartree-Fock approximation and the explicit inclusion of contributions that mimic particle exchange -a situation that is also covered within the next section.…”

“…(15), and corrections to the Hamiltonian are added sequentially, a general quantum kinetic theory has been developed which upon necessary approximations reproduces the results of [128] in a "top-down" approach. We will briefly introduce the main ideas of the quantum kinetic theory and also comment on the method of non-equilibrium Green's functions (which is also able to reproduce [128]) before we state what path we decide to follow within this thesis.…”

Probing the effect of interaction in Anderson localization using linear photonic lattices

“…In fact, Anderson himself first noticed the importance of interaction in localization phenomena [8] and launched a theoretical investigation in collaboration with Fleishman [9]. Recently, advances in technology have reinvigorated theoretical [10,11] and experimental [12][13][14][15][16][17][18][19] interest on this subject. For the special case of two interacting particles in a random one-dimensional (1D) potential, Shepelyansky has investigated the interplay of disorder and interaction and concluded that interaction modifies (weakens) localization [20].…”