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Ultracold fermionic atoms in disordered potentials

Stanimir Kondov

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

This thesis describes the construction of an experimental apparatus to study disorder physics using ultracold fermionic atomic gases. We use this apparatus to realize 3D Ander-son localization for the first time for quantum matter waves. We provide the first measure-ment of how the mobility edge—a hallmark of 3-dimensionality—and of localization lengths depend on the disorder strength. In a second experimental study, we add an optical lattice to the disorder potential to realize the disordered Fermi-Hubbard model, which is a minimal model for strongly correlated electronic solids. The interplay of interactions and disorder is investigated. We find an Anderson-like disorder-driven metal-to-insulator transition as well as disorder-induced breaking of the Mott gap in the strongly interacting regime. ii To my Parents and to Sveta iii Acknowledgements I first want to thank Brian, who taught me the important notion that experimental physics lives in the intersection space between equations and reality, and that both will gladly turn around and bite off your finger if you are not careful. In this dangerous situation, it is the necessity that one becomes a better scientist, and it is also the hope that one becomes a better human being. I would like to thank my family and friends, and I would like to point out that, for many of us, graduate school is a rather self-centered experience in which we are only left to worry about ourselves while we do what we love among people whom we appreciate. Yet those who inspire and sustain us are left out of the author lists and honorable mentions. In summary, graduate school is a wonderful place and a privilege, and I am grateful that the fundamental laws of the universe have so conspired that I’ve had the chance to be here.

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This thesis describes the construction of an experimental apparatus to study disorder physics using ultracold fermionic atomic gases. We use this apparatus to realize 3D Ander-son localization for the first time for quantum matter waves. We provide the first measure-ment of how the mobility edge—a hallmark of 3-dimensionality—and of localization lengths depend on the disorder strength. In a second experimental study, we add an optical lattice to the disorder potential to realize the disordered Fermi-Hubbard model, which is a minimal model for strongly correlated electronic solids. The interplay of interactions and disorder is investigated. We find an Anderson-like disorder-driven metal-to-insulator transition as well as disorder-induced breaking of the Mott gap in the strongly interacting regime. ii To my Parents and to Sveta iii Acknowledgements I first want to thank Brian, who taught me the important notion that experimental physics lives in the intersection space between equations and reality, and that both will gladly turn around and bite off your finger if you are not careful. In this dangerous situation, it is the necessity that one becomes a better scientist, and it is also the hope that one becomes a better human being. I would like to thank my family and friends, and I would like to point out that, for many of us, graduate school is a rather self-centered experience in which we are only left to worry about ourselves while we do what we love among people whom we appreciate. Yet those who inspire and sustain us are left out of the author lists and honorable mentions. In summary, graduate school is a wonderful place and a privilege, and I am grateful that the fundamental laws of the universe have so conspired that I’ve had the chance to be here.
We experimentally study localization and dynamics of ultracold fermions in speckle and optical lattice potentials to explore Anderson localization, many-body localization, and relaxation dynamics in strongly correlated systems. Anderson localization is probed by releasing non-interacting, spin-polarized gases into three dimensional, anisotropic disordered potentials produced from optical speckle. A fraction of the atoms are localized by the disorder, and a mobility edge is found separating localized from extended states. The length scale of the speckle is varied, and the localized state is found to scale linearly with the geometric mean of the speckle autocorrelation length. We realize the Fermi Hubbard model by loading atoms in a cubic optical lattice. Non-equilibrium momentum distributions are created via Raman transitions, and the excitation relaxation rate is measured in the lattice. Transport experiments were performed in a disordered optical lattice to explore the disordered Hubbard model. These experiments reveal localization in the presence of strong interactions and an interaction driven metal-to-insulator transition. The localized state is found to be insensitive to a doubling in the temperature of the gas and is consistent with predictions of many-body localization.
Ultracold fermionic atoms in a disordered optical lattice can realize the disordered Fermi-Hubbard model, allowing investigations of the nature of strongly-correlated fermions in a minimal setting. This thesis describes two such studies. In the first, we observe the momentum relaxation of strongly-correlated fermions in the absence of disorder. We find a violation of the weak-scattering prediction for the scaling with temperature, which is analogous to the linear-in-temperature scaling of resistivity in substances called ``bad metals.'' In the second, we probe a disordered and strongly-correlated system using quenches of the interaction strength that take it far from equilibrium. We find that the relaxation of double occupancies following the quenches has distinct dynamical regimes controlled by the interplay of interactions and disorder. We present a minimal picture of the relaxation process that illustrates the origin of these regimes, which are related to the Mott--metal--Anderson transitions of the ground state at half-filling.
Disorder plays a fundamental role in many fields of physics such as condensed-matter physics, optics, acoustics, or atomic physics. It is responsible for a number of surprizing effects, such as Anderson localization, metal-insulator transitions and intriguing glass phases. The inherent complexity of disordered systems poses outstanding challenges to the full understanding of these phenomena. In the last years, disorder has emerged as a major line of research in the field of ultracold quantum gases. The latter offer fascinating perspectives to better understand the effects of disorder in quantum systems, thanks not only to an unprecedented control of parameters, but also to their original properties. This Habilitation thesis reviews our recent contributions to the theory of disordered quantum gases along three main lines: - Anderson localization in disordered quantum gases; - Disorder in interacting Bose gases; - Simulating extended Hubbard and spin models with ultracold gases. On the one hand, we propose and analyze experiments aiming at realizing quantum simulators to address open questions of fundamental importance for the field of disordered systems. In this respect, we show that quantum gases offer promising perspectives. On the other hand, we lead prospective works, which in particular show that quantum gases have original properties. They hence shed new light on issues of broad interest in the field of disordered systems.
A new millennia ushered in novel experimental capabilities to investigate engineered quantum systems. Gases consisting of charge neutral atoms are cooled to the ground state and by exploiting the dipole interaction can be trapped by laser light. In ultracold atomic systems the tunneling and interactions are controllable, and the system is absent of disorder. Disorder and interactions in solid-state systems inhibits a complete understanding of transport phenomena. Theoretical investigations into non-equilibrium and equilibrium dynamics of fermions in discretized potentials and in continuum are presented. The affect of controllable, external system parameters is evaluated and exploited to reveal new properties of fermion dynamics. My thesis will begin with an overview of the physics associated with many-body fermion and the models used to obtain results, followed by my thesis research on how matter-waves can be manipulated by lattice geometry and tunneling strengths. Next, I present how dissipation affects current in a continuous ring, demonstrating rate-dependent hysteresis as the particles are driven by an artificial gauge field. After presenting the continuous ring, I will then focus on persistent current and corresponding quantum current fluctuations in a discretized ring. Lissajous curves are found in the system whose area strongly depends on the presence and absence of interactions. Lastly, I will discuss dynamical detection methods for one-dimensional topological insulators using ultracold fermions. All of the results are supported with discussion on how they can be realized using current experimental technology.
In this thesis we address relevant problems of the physics of quantum disordered systems from a numerical and theoretical point of view, with specific attention to the connection of our findings with ultracold atomic gases experiments. We concentrate on two main issues: the interplay between localization and interaction in disordered systems and the problem of localization in correlated random potentials. The first problem is investigated considering the expansion of a weakly interacting Bose gas in a bichromtic optical lattice. We observe that interaction has a destructive effect on the disorder-induced localization and leads to a subdiffusive expansion of the atomic gas. By comparing three characteristic energy scales of the system one can identify three different spreading regimes: weak chaos, strong chaos and self-trapping. The spreading behaviour in these regimes is predicted theoretically and verified numerically. We also interpreted existing experimental data on the basis of our findings and showed that there is a qualitative agreement between our numerical simulations and experiments. The second problem is investigated proposing a new model of correlated disorder that can be implemented experimentally using ultracold dipolar gases. We show that this model is characterized by the presence of both short and long range correlations. We study the localization properties of the model and highlight the role played by short and long range correlations in the determination of those properties. In particular we show that when short-range correlations are dominant, extended states can appear in the spectrum. The effect of long-range correlations is instead to restore localization over the whole spectrum and lead to counterintuitive behaviours of the localization length. More precisely, depending on the localization regime they can enhance or reduce the localization length at the centre of the band.
We study the interplay of disorder localization and strong local interactions within the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. For fermions, we find rich nonmonotonic behavior of the localization length ξ, particularly in two-dimensional systems, including an interaction-induced exponential enhancement of ξ for small and intermediate disorders and a strong reduction of ξ due to hopping suppression by strong interactions. In three dimensions, we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbardgapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase. For bosons, the unrestricted particle occupation number per lattice site yields a monotonic enhancement of ξ as a function of decreasing interaction, which we assume to persist until the superfluid Bose- Einstein condensate phase is entered. Besides, we study cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.