Many-body quantum tunneling of ultracold bosonic gases: quantum phase transitions, bosonic Josephson junctions, and Mott switch atomtronics

Abstract

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 result of the confining potential and corresponds with critical phenomena in transport properties as measured via transmission and fidelity. g^(2) two-point correlators provide an experimentally viable means of identifying superfluid fragments as a means of identifying switching state. Finally, the research presented in this dissertation provides a foundation for many-body quantum tunneling that can be further expanded to the emerging field of quantum atomtronics. The highly precise architectures needed for such technologies are conducive to understanding many-body phenomena for the creation of quantum-engineered devices, from atomic clocks and simulation techniques to biomedical magnetic sensors and secure communications.