Chapter 4 extends the previous chapter by scaling up by a factor of ten the number of barriers in the quantum wire, thus forming a one-dimensional lattice site by site.For the first time in a cold-atom experiment, we characterize the appearance of an insulating phase via transport measurements, here visible as a conductance minimum at chemical potentials in the expected band gap of the infinite lattice.This length scaling gives insights on how the transmission of a finite lattice maps to band theory in the thermodynamic limit.We furthermore study the influence of non-uniformity, lattice height and temperature on the apparent transition between conductor and band insulator.-Chapter 5 reproduces the previous measurements on a mesoscopic lattice with stronger attractive interactions spanning the BCS and unitary regimes.Surprisingly, we observe the persistence of an insulating gap in the conductance, although one could expect superfluidity in the wire and the neighboring reservoirs to dominate transport properties.This behavior is attributed to the formation of a Luther-Emery liquid, a strongly correlated phase characteristic of the one-dimensional physics of the channel, for which we provide a detailed introduction.Numerical simulations based on Tomonaga-Luttinger theory support this interpretation.-Chapter 6 finally investigates transport in a short quantum point contact through a spin-dependent obstacle produced by an optical tweezer at frequencies close to the transitions of two different hyperfine states.The micron-wide footprint of the tweezer
Chapter 4 extends the previous chapter by scaling up by a factor of ten the number of barriers in the quantum wire, thus forming a one-dimensional lattice site by site.For the first time in a cold-atom experiment, we characterize the appearance of an insulating phase via transport measurements, here visible as a conductance minimum at chemical potentials in the expected band gap of the infinite lattice.This length scaling gives insights on how the transmission of a finite lattice maps to band theory in the thermodynamic limit.We furthermore study the influence of non-uniformity, lattice height and temperature on the apparent transition between conductor and band insulator.-Chapter 5 reproduces the previous measurements on a mesoscopic lattice with stronger attractive interactions spanning the BCS and unitary regimes.Surprisingly, we observe the persistence of an insulating gap in the conductance, although one could expect superfluidity in the wire and the neighboring reservoirs to dominate transport properties.This behavior is attributed to the formation of a Luther-Emery liquid, a strongly correlated phase characteristic of the one-dimensional physics of the channel, for which we provide a detailed introduction.Numerical simulations based on Tomonaga-Luttinger theory support this interpretation.-Chapter 6 finally investigates transport in a short quantum point contact through a spin-dependent obstacle produced by an optical tweezer at frequencies close to the transitions of two different hyperfine states.The micron-wide footprint of the tweezer
In a first part, I study the electronic transport through a one-dimensional, finite-length quantum wire of correlated electrons (Luttinger liquid) coupled at arbitrary position via tunnel barriers to two semi-infinite, one-dimensional as well as stripe-like (two-dimensional) leads, thereby bringing theory closer towards systems resembling setups realized in experiments. In particular, I compute the temperature dependence of the linear conductance of a system without bulk impurities. The appearance of new temperature scales introduced by the lengths of the overhanging parts of the leads and the wire implies a conductance function which is much more complex than the simple power-law behavior obtained in earlier approaches. My results can be used to optimize the experimental setups designed for a verification of Luttinger-liquid scaling. In a second part, I suggest a setup to study Luttinger-liquid behavior in quantum wires which allows to determine the Luttinger-liquid parameter from two independent measurements: transport through a quantum dot embedded in the wire and the charge on the dot. To this end, I identified novel Luttinger-liquid power-laws in the charging of the dot. In a more technical part, I extended an adaption of the functional renormalization group such that it can be used on correlated electrons in complex geometries like the wire-lead structures described above and arbitrary dot structures coupled to Luttinger-liquid leads.
The Chapter 2 is devoted to the study of the transport properties of a quantum wire, described by the Tomonaga-Luttinger model, in the presence of a backscattering potential provided by several point-like or extended time-dependent impurities (barriers) and find regimes of conductance enhancement. In Chapte 3 we study a set of crossed 1D systems, which are coupled with each other via tunnelling at the crossings. Concentrating on the case of a single crossing, we were able to explain recent experiments on crossed metallic and semiconducting nanotubes, which showed the presence of localized states in the region of crossing. The Chapter 4 treats the effects of disorder and interactions in a quantum Hall ferromagnet. We study the problem by projecting the original fermionic Hamiltonian into magnon states, which behave as bosons in the vicinity of the ferromagnetic ground state. The approach permits the reformulation of a strongly interacting model into a non-interacting one. The latter is a non-perturbative scheme that consists in treating the two-particle neutral excitations of the electron system as a bosonic single-particle. Indeed, the employment of bosonization facilitates the inclusion of disorder in the study of the system. It has been shown previously that disorder may drive a quantum phase transition in the Hall ferromagnet. However, such studies have been either carried out in the framework of the nonlinear sigma model, as an effective low-energy theory, or included the long-range Coulomb interaction in a quantum description only up to the Hartree-Fock level. Here, we establish the occurrence of a disorder-driven quantum phase transition from a ferromagnetic 2DEG to a spin glass phase by taking into account interactions between electrons up to the random phase approximation level in a fully quantum description. In the Chapter 5 we derive and discuss an experimentally realistic model describing ultracold atoms in an optical lattice including a commensurate, but staggered, Zeeman field. The resulting band structure is quite exotic; fermions in the third band have an unusual rounded picture-frame Fermi surface (essentially two concentric squircles), leading to imperfect nesting. We develop a generalized theory describing the spin and charge degrees of freedom simultaneously, and show that the system can develop a coupled spin-charge-density wave order. This ordering is absent in studies of the Hubbard model that treat spin and charge density separately.
A system of ultracold atoms in an optical lattice provides a powerful platform for quantum simulation. In our laboratory, we use a quantum gas microscope to tune lattice parameters not only in a global scale but also at the level of individual sites. This allows us to control and detect the quantum state of interacting many-body systems as well as to engineer a broad class of Hamiltonians with high fidelity. Leveraging this versatility, we can realize several types of strongly correlated bosonic systems, which present intriguing behaviors and implement novel phases of matter. Analyzing snapshots of the atomic distribution with single-site resolution, we measure correlations and entanglement within these systems to reveal their main features, including non-equilibrium dynamics and quantum phase transitions. In this thesis, I present the works performed by our team for four different types of systems. First of all, I briefly introduce the behavior of a 1D disordered system in the critical regime between the thermal and the many-body-localized phases. In particular, we discuss what happens when a disordered and a non-disordered region are coupled via a single site. We find evidence for accelerated transport of thermal inclusion into the localized region, which shows the existence of a quantum avalanche, i.e. thermalization via accelerated transport throughout the localized system. In the second part, we realize a fractional quantum Hall state using an artificial gauge field, by implementing an adiabatic preparation protocol. We identify a topological phase transition in our system and characterize several key physical features expected for a Laughlin state by measuring density correlations and Hall conductivity. The next topic of this thesis relates to quantum magnetism. Mapping nearest hopping in a tilted optical lattice to spin flips, we realize a finite one-dimensional chain of 1/2-spins with closed boundary conditions. We perform an in-depth investigation on behaviors shown across the quantum phase transition between paramagnetic and antiferromagnetic ground states, including the evolution of the magnetization and Néel order parameter. Also, we find evidence for quantum superposition at the many-body level as a result of geometric frustration. In the last chapter, I report the experimental realization of a novel dipolar Bose-Hubbard Hamiltonian, based on a strongly tilted lattice system. When the tilt becomes the dominant energy scale, the Hamiltonian is fragmented, and the system behaves in a way that conserves dipole moment. Starting from a 1D chain of unity filled sites, we generate individual dipolar and anti-dipolar excitations at desired pinpoints. We observe quantum walks of these dipolar quasi-particles as well as their scattering dynamics, which allows us to study this new type of Hamiltonian using a bottom-up approach.
Transport measurements provide a powerful probe of quantum manybody systems, offering insights into the non-equilibrium dynamics of particles, spin, and entropy. Because transport inherently probes many-body systems away from equilibrium, its theoretical description remains a significant challenge, particularly in the presence of strong correlations or beyond the linear response regime. A close interplay between theoretical efforts and systematic experiments is therefore essential to deepen our understanding. In this thesis, we extend and employ a cold-atom transport setup to investigate the flow of a unitary Fermi gas through a mesoscopic channel connecting two superfluid reservoirs. The present work focuses on residual dissipative processes occurring in superfluid flow away from equilibrium. Specifically, we investigate how the geometry and dimensionality of the channel influence the mechanisms of dissipation under an applied chemical-potential bias. This system serves as a highly tunable quantum simulator of a voltage-biased superconducting wire. We resolve distinct dissipative regimes as the channel is tuned from the quasi-one-dimensional to the quasi-two-dimensional limit. In narrow channels, dissipation is driven by phase slips described by the Langer–Ambegaokar–McCumber–Halperin theory. In wide channels, dissipation is instead dominated by vortex dynamics, consistent with a finite-size vortex model. In the dimensional crossover between these limits, we observe a non-monotonic dependence of dissipation on channel width, characterized by a local minimum. These measurements provide a systematic experimental validation of theoretically predicted scaling laws in both the one- and two-dimensional limits. Beyond establishing a quantitative benchmark for theoretical descriptions of the delicate dimensional crossover, our findings suggest strategies for minimizing dissipation in mesoscopic superconducting devices.
We study theoretically the transport of the one-dimensional single-channel interacting electron gas through a strong potential barrier in the parameter regime where the spin sector of the low-energy theory is gapped by interaction (Luther-Emery liquid). There are two distinct phases of this nature, of which one is of particular interest as it exhibits nontrivial interaction-induced topological properties. Focusing on this phase and using bosonization and an expansion in the tunneling strength we calculate the conductance through the barrier as a function of the temperature as well as the local density of states (LDOS) at the barrier. Our main result concerns the mechanism of bound-state-mediated tunneling. The characteristic feature of the topological phase is the emergence of protected zero-energy bound states with fractional spin located at the impurity position. By flipping this fractional spin, single electrons can tunnel across the impurity even though the bulk spectrum for spin excitations is gapped. This results in a finite LDOS below the bulk gap and in a nonmonotonic behavior of the conductance. The system represents an important physical example of an interacting symmetry-protected topological phase, which combines features of a topological spin insulator and a topological charge metal, in which the topology can be probed by measuring transport properties.