Weak localisation in the transport of interacting Bose-Einstein condensates across random media

Abstract

Quantum simulation with ultracold atoms gained a lot of traction recently by proposing a framework with a lot of flexibility, versatility and tunability to emulate diverse quantum ef- fects. It indeed provides the ideal playground to study many–body effects in a well–controlled environment and is particularly useful in the domain of quantum coherent transport of waves in random media. The purpose of this thesis is to study several configurations of coher- ent transport within random media with Bose–Einstein condensates and to investigate the interplay between coherence and interaction effects. In particular, we start by numerically studying Aharonov–Bohm oscillations in the transmission of particles across the eponymous rings in a 1D configuration. When exposed to a suitably chosen disorder potential, those rings yield oscillations with double frequency, which are routinely encountered in solid–state physics where they are referred to as Al’tshuler–Aronov–Spivak oscillations, similar in essence to coherent backscattering and weak localisation. We then study the behaviour of those os- cillations in the presence of interaction within Aharonov–Bohm rings and find that in the mean–field regime, they are inverted for finite interaction. Truncated Wigner simulations are then carried out in the same scenario and indicate that the inversion should be observ- able for realistic atomic and experimental parameters with 39 K atoms, although dephasing of the oscillations is observed at strong interaction owing to interaction–induced inelastic scattering. A first–order nonlinear diagrammatic theory is then presented and benchmarks our numerical findings. The question of the inversion prevalence is then investigated in a 2D scenario, following state–of–the–art observations in the literature. It has indeed been nu- merically observed that coherent backscattering is inverted in the mean–field approximation for finite interaction strength. We numerically confirm this observation with our study and extend it beyond the mean–field approximation by applying the truncated Wigner method. These simulations show that the inversion prevails beyond the mean–field regime and should moreover be observable experimentally with 87 Rb atoms for realistic parameters, despite a partial dephasing. This dephasing however completely eclipses interference effects and washes out this signature of antilocalisation for stronger interaction.