Abstract Typical treatments of superconducting or superfluid Josephson junctions rely on mean-field or two-mode models; we explore many-body dynamics of an isolated, ultracold, Bose-gas long Josephson junction using time-evolving block decimation simulations. We demonstrate that with increasing repulsive interaction strength, localized dynamics emerge that influence macroscopic condensate behavior and can lead to the formation of solitons that directly oppose the symmetry of the junction. Initial state population and phase yield insight into dynamic tunneling regimes of a quasi one-dimensional double well potential, from Josephson oscillations to macroscopic-self-trapping. Population imbalance simulations reveal substantial deviation of many-body dynamics from mean-field Gross–Pitaevskii predictions, particularly as the barrier height and interaction strength increase. In addition, the sudden approximation supports localized particle–hole formation after a diabatic quench, and correlation measures unveil a new dynamic regime: the Fock flashlight.
Abstract Typical treatments of superconducting or superfluid Josephson junctions rely on mean-field or two-mode models; we explore many-body dynamics of an isolated, ultracold, Bose-gas long Josephson junction using time-evolving block decimation simulations. We demonstrate that with increasing repulsive interaction strength, localized dynamics emerge that influence macroscopic condensate behavior and can lead to the formation of solitons that directly oppose the symmetry of the junction. Initial state population and phase yield insight into dynamic tunneling regimes of a quasi one-dimensional double well potential, from Josephson oscillations to macroscopic-self-trapping. Population imbalance simulations reveal substantial deviation of many-body dynamics from mean-field Gross–Pitaevskii predictions, particularly as the barrier height and interaction strength increase. In addition, the sudden approximation supports localized particle–hole formation after a diabatic quench, and correlation measures unveil a new dynamic regime: the Fock flashlight.
Ultracold Bose gases as precise quantum simulators have emerged amongst the leaders in the current race – a second quantum revolution – toward the promise of unfathomable sensitivity, scope, and speed of a new era of technology. The only path leading to these advancements is through many-body descriptions, especially in regimes where interatomic interactions render many approximations incompatible with the physics. The research in this dissertation unlocks a piece of this mystery through investigations of many-body quantum tunneling of ultracold bosons in optical lattices. A key mechanism to characterizing the dynamics, matrix product state simulations equip the many-body toolbox with efficient optimization of large Hilbert spaces together with correlation and entropy measures that help clarify when semiclassical or mean-field approximations fail. In this thesis we obtain the following results. Macroscopic quantum tunneling escape of a Bose-Einstein condensate – comprised of tens of thousands of 87Rb atoms – from a single well, as portrayed through both experiment and theory, highlights non-exponential decay in the number of atoms trapped behind the barrier. Additionally, explicit symmetry breaking of a biperiodic optical lattice ring trap to a uniform one illustrates a critical symmetry-breaking strength at which the system transitions from a state of remembering to a state of forgetting its initial symmetry state; this symmetry memory indicates a new form of quantum dynamics that requires the quantum advantage for scaling up particle number and lattice sites. Extensive characterization of dynamical regimes in a bosonic Josephson junction – underlaid by an optical lattice as described by the Bose-Hubbard model – reveal substantial deviation of many body dynamics from the mean field or semiclassical predictions underlying the usual operating regime of Josephson junctions. Initial state population and phase yield insight into dynamic tunneling regimes of a quasi one-dimensional double well potential, through the Z2 spontaneous symmetry-breaking phase transition from Josephson oscillations to macroscopic self-trapping. We demonstrate that with increasing repulsive interaction strength, the U(1) superfluid-Mott insulator phase transition induces localized dynamics in the number density, such as particle-hole and soliton formation. Moreover, g^(2) correlations unveil a new dynamic regime – the Fock flashlight. The new field of atomtronics – or atomic circuits – has emerged with many studies of weakly-interacting condensates. In contrast, and building on our work on many-body effects in the double wells underlying Josephson junctions, we present a proof-of-principle of a Mott-insulating atomtronic switch that requires strongly-interacting bosons. Through transient analysis, we reveal that hole conductance can be modulated via tuning interaction strength through a critical value, thus propelling the state to the next ``wedding cake'' layer of the Mott insulating structure. This critical interaction strength is a…
We investigate the fully quantum evolution of the population imbalance in a perfectly symmetric Bose-Josephson junction modeled by a two-mode Bose-Hubbard Hamiltonian, focusing on the validity of macroscopic quantum self-trapping beyond the mean-field theory. We show that for any finite number of particles, the exact quantum dynamics leads to the breakdown of macroscopic quantum self-trapping after a finite time, regardless of the initial state. Using the symmetries of the Bose-Hubbard Hamiltonian, we provide a mathematical demonstration of this result and analyze the spectral properties governing the dynamics. We identify a branching behavior in the eigenvalue differences and a nontrivial structure of the population-imbalance amplitudes. These features allow us to distinguish two clearly different dynamical regimes and to elucidate the mechanism leading to the emergence of a quasi–macroscopic quantum self-trapping regime for large particle numbers. These findings bridge the gap between mean-field predictions and exact quantum dynamics and provide insight into the emergence of classical nonlinear behavior from finite quantum many-body systems.
We explore the interplay between tunneling and interatomic interactions in the dynamics of a bosonic Josephson junction. We tune the scattering length of an atomic ^{39}K Bose-Einstein condensate confined in a double-well trap to investigate regimes inaccessible to other superconducting or superfluid systems. In the limit of small-amplitude oscillations, we study the transition from Rabi to plasma oscillations by crossing over from attractive to repulsive interatomic interactions. We observe a critical slowing down in the oscillation frequency by increasing the strength of an attractive interaction up to the point of a quantum phase transition. With sufficiently large initial oscillation amplitude and repulsive interactions, the system enters the macroscopic quantum self-trapping regime, where we observe coherent undamped oscillations with a self-sustained average imbalance of the relative well population. The exquisite agreement between theory and experiments enables the observation of a broad range of many body coherent dynamical regimes driven by tunable tunneling energy, interactions and external forces, with applications spanning from atomtronics to quantum metrology.
Understanding how coherent quantum dynamics give way to correlation-dominated behavior in low-dimensional systems remains a central challenge in quantum many-body physics. Here, we investigate a one-dimensional Bose-Josephson junction confined in a box trap using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). By varying the interaction strength and initial population imbalance, we identify distinct dynamical regimes governed by the competition between coherence and correlation-induced fragmentation. Weak interactions support coherent Josephson oscillations, whereas increasing imbalance leads to damping. At intermediate interaction strength, varying only the initial imbalance induces a crossover from nearly pure coherent oscillations to many-body dephasing with collapse-and-revival dynamics, and ultimately to equilibration accompanied by strong fragmentation and the saturation of many-body observables. In the strongly interacting regime, the system enters a dynamical freezing regime characterized by pronounced fragmentation, well-separated particle-resolved density peaks, and strongly suppressed tunneling. A systematic comparison with the Bose-Hubbard model reveals excellent agreement in the weakly interacting regime, while progressively larger deviations emerge as higher-orbital occupations beyond the two-mode approximation become significant. These results provide a unified picture of the emergence and competition of coherence, many-body dephasing, equilibration, and dynamical freezing, while delineating the regime of validity of the Bose-Hubbard description.
We study atomic Josephson junctions (AJJs) with one and two bosonic species confined by a double-well potential. Proceeding from the second quantized Hamiltonian, we show that it is possible to describe the zero-temperature AJJ microscopic dynamics by means of extended Bose–Hubbard (EBH) models, which include usually neglected nonlinear terms. Within the mean-field approximation, the Heisenberg equations derived from such two-mode models provide a description of AJJ macroscopic dynamics in terms of ordinary differential equations (ODEs). We discuss the possibility of distinguishing the Rabi, Josephson and Fock regimes in terms of the macroscopic parameters which appear in the EBH Hamiltonians, and then in the ODEs. We compare the predictions for the relative populations of the Bose gas atoms in the two wells obtained from the numerical solutions of the two-mode ODEs, with those deriving from the direct numerical integration of the Gross–Pitaevskii equations (GPEs). Our investigations show that the nonlinear terms of the ODEs are crucial to achieve a good agreement between the ODE and GPE approaches, and in particular to give quantitative predictions of the self-trapping regime.
In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.