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.
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.
Cutting-edge technology needs small, ultrafast devices, operational in a wide range of regimes. This calls for solids with novel, unconventional and tailorable properties. Great progress is expected from materials in which electron-electron and electron-phonon correlations strongly affect the dynamics ( i.e. "unforeseen" useful properties are expected to be most likely found in systems with complex behavior). In spite of the potentially huge technological pay-off, our understanding of these systems is rather incomplete, especially in non-equilibrium. Often, with knowledge of systems or phenomena at an early stage, it is rewarding to resort to model, simplified descriptions. This strategy is used in this thesis, where we study several models lattice systems via density-functional theory. The latter is a well established approach (in fact, it is the current method of choice) for investigations of real materials. In our research, we focussed on little understood properties of interacting many-particle systems, such as the time-dependent conduction properties of electronic devices in the presence of interactions, disorder, and lattice vibrations, or the expansion of ultracold fermion clouds in 3D optical lattices. All these systems were described in terms of Hubbard-type interactions for the electrons, and Holstein-type electron-phonon interactions. Our results show interesting features due to the interactions which depend on dimensionality; they also show a dynamical crossover for several properties, due to the competition between disorder and interaction. Finally, when lattice vibrations are included, we showed how it is possible to manipulate in a controlled way the nuclear dynamics of molecular device via fast electronic external fields, of potential interest for technologies employing nanomolecular motors.
This thesis presents a series of theoretical studies of ultra cold atomic systems which model and propose experiments, and develop new computational techniques in order to elucidate aspects of many-body physics and non-equilibrium dynamics. In the first two studies I model the dynamics of nonlinear solitonic excitations in ultracold fermionic superfluids: the first simulates recent experiments and supports the hypothesis that the solitons generated in those experiments are unstable to the formation of vortex rings; the second demonstrates how population imbalance between up and down spin fermions can be used to prevent this instability. In the next study I discuss a method for generating and probing topologically protected edge states using periodically driven optical lattices potentials. Next I use a perturbative approach to study the spectral density of fermions with strong attractive interactions in the normal phase. After that I develop a novel cluster expansion technique to model the dynamics of interacting fermions in a disordered optical lattice. Finally I apply a Ginzurg-Landau theory to model experimental studies of superfluid 3He embedded in nematically ordered aerogel, finding evidence for a new phase of matter --the ``polar phase"-- which is not seen in bulk 3He.
This thesis highlights the versatility of ultracold atoms as quantum simulators by utilizing Bose gases and engineered light-induced Hamiltonians to investigate quantum phenomena across multiple areas of physics.As a high-energy simulator, an analog experiment simulating particle–antiparticle pair creation from the quantum vacuum, emulated these strong-field effects at energy scales accessible in the laboratory. The Dirac picture of particle-antiparticle vacuum and the concept of optical lattice band theory was the foundation of our approach. In this framework, we readily measured pair creation and demonstrated that this high-field phenomenon is well-characterized by Landau-Zener tunneling. Within condensed matter physics, ultracold atoms were employed to study topological dynamics of periodically driven Floquet systems. Using a Floquet “switching” protocol in a one-dimensional bipartite magnetic lattice, we realized a periodically driven Su–Schrieffer–Heeger model that maps onto a massless Dirac Hamiltonian. By alternating between two lattice configurations with near-optimal timing, we observed spin–momentum–locked transport characterized by well-defined drift velocities and with spatial displacement linearly increasing over many Floquet periods, establishing a platform for exploring topological band dynamics. The culminating focus of this thesis is localization physics in Rb-87 Bose-Einstein condensates subjected to disordered artificial gauge fields over a range of energy and time scales, in both equilibrium and out-of-equilibrium settings. The effective Hamiltonian was implemented by driving two-photon Raman transitions with laser fields, while disordered vector potential landscapes were independently generated using tunable intensity patterns projected by a digital micromirror device (DMD). By varying the experimental protocols—including the turn on times of the Raman coupling and disorder, as well as the disorder strength—we obtained insight into quantum dynamics in the presence of disordered gauge fields. The resulting dynamics revealed rich behavior: including spatially inhomogeneous magnetization for high-energy dynamics and increases in the condensate width after time-of-flight for pulsed disorder in lower energy and near-equilibrium conditions; lastly, signatures of localization, in the form of damped oscillations, were observed as the system was driven out-of-equilibrium.
In this thesis, both experimental studies and numerical simulations of ultracold atoms in optical potentials are presented in a collection of nine scientific papers. In particular, noise-induced transport in dissipative optical lattices and superfluid properties of Bose-Einstein condensates have been studied. Noise is usually regarded as a complication to most systems and as something that needs to be minimized. However, in a series of experiments at Umeå University, noise has been shown to play a key role for laser-cooled cesium atoms trapped in dissipative optical lattices. By using a combination of two dissipative optical lattices, where the relative spatial phase between them can be controlled, a so-called Brownian motor can be realized, where energy can be extracted from the inherent noise. In the experiment, this energy is used to control the transport of the laser-cooled atoms in real time and along pre-designed paths. This thesis also presents a way to characterize this system in terms of energy conversion efficiency and coherence of the transport, which may allow for a more straightforward comparison with other systems that rely on noise rectification. In the studies, it is also shown that the noise triggers a downward drift due to gravity, even though the optical potential should support the atoms. Further investigation of this might help to understand the underlying principles of laser cooling, as well as showing that the system might be suitable as a flexible test bed for statistical physics. In close relation to the experimental system, two numerical simulations are also presented, one in which different ways to induce asymmetries between two periodic potentials are investigated, and one in which a proposal for detecting quantum walks is explored. In the second part of the thesis, a work from the Joint Quantum Institute is presented, where a long-lived persistent current in a toroidal Bose-Einstein condensate, held in an all-optical trap, is created. The critical velocity of the superflow is measured in the presence of a tunable barrier. The system can be seen as a first realization of an elementary closed-loop atom circuit. Finally a theoretical study of the crossover between one- and two-dimensional systems is presented, in particular the transition between a two-dimensional superfluid to a one-dimensional Mott insulator is investigated.
The transport of quantum particles in non ideal material media (eg the conduction of electrons in an imperfect crystal) is strongly affected by scattering from impurities of the medium. Even for a weak disorder, semi-classical theories, such as those based on the Boltzmann equation for matter-waves scattering from the impurities, often fail to describe transport properties and full quantum approaches are necessary. The properties of the quantum systems are of fundamental interest as they show intriguing and non-intuitive phenomena that are not yet fully understood such as Anderson localization, percolation, disorder-driven quantum phase transitions and the corresponding Bose-glass or spin-glass phases. Understanding quantum transport in amorphous solids is one of the main issues in this context, related to electric and thermal conductivities. Ultracold atomic gases can now be considered to revisit the problem of quantum conductivity and quantum transport under unique control possibilities. Dilute atomic Bose-Einstein condensates (BEC) and degenerate Fermi gases (DFG) are produced routinely taking advantage of the recent progress in cooling and trapping of neutral atoms. Transport has been widely investigated in controlled potentials with no defects, for instance periodic potentials (optical lattices). Controlled disordered potentials can also be produced with various techniques such as the use of magnetic traps designed on atomic chips with rough wires, the use of localized impurity atoms, the use of radio-frequency fields or the use of optical potentials. This recently lead to the observation of the Anderson Localisation of a BEC and the measurement of the diffusion coefficient of a 2D gaz in the presence of disorder.
In this thesis, we study the coherence and the dynamics of ultracold atomic quantum gases, with a particular regard on Fermi gases. For what concerns the coherence, we study a Fermi gas confined on a ring threaded by an artificial gauge field. First, we show that the persistent current flowing in the ring can be used as probe for the different regimes of the BCS-BEC crossover. We propose a readout protocol for our results, based on the co-expansion of the gas trapped on the ring and a reference gas placed in the center of the ring itself. Next, we show that using the same expansion protocol we can extract information about the phase of the quantum gas. At intermediate times, the expanding cloud provides information about the first order coherence of the Fermi gas. In few-body systems, we can also access the number of particles in the system. At long times, we extract information about the many-body coherence coherence of the gas. Subsequently we focus on the dynamics of a strongly interacting two-component Fermi gas trapped in a harmonic potential. We consider a spin-separated state and then we follow the dynamics until long times. At short times, the dynamics is superdiffusive with dynamical exponents of the Kardar-Parisi-Zhang universality class. At intermediate times, the dynamics is dominated by damped spin oscillations unveleing a spin-drag effect. At long times, we observe thermalization. Ultimately, we study a multicomponent Bose gas in the strongly interacting regime. We first provide the exact solution for the wavefunction and we discuss its symmetry. Afterwards, we study the response of the gas to an artificial gauge field, with particular regard to the period of the persistent current as a function of the gauge flux.