The tunneling process in a many-body system is a phenomenon which lies at the very heart of quantum mechanics. It appears in nature in the form of α-decay, fusion and fission in nuclear physics, and photoassociation and photodissociation in biology and chemistry. A detailed theoretical description of the decay process in these systems is a very cumbersome problem, either because of very complicated or even unknown interparticle interactions or due to a large number of constituent particles. In this work, we theoretically study the phenomenon of quantum many-body tunneling in a transparent and controllable physical system, an ultracold atomic gas. We analyze a full, numerically exact many-body solution of the Schrödinger equation of a one-dimensional system with repulsive interactions tunneling to open space. We show how the emitted particles dissociate or fragment from the trapped and coherent source of bosons: The overall many-particle decay process is a quantum interference of single-particle tunneling processes emerging from sources with different particle numbers taking place simultaneously. The close relation to atom lasers and ionization processes allows us to unveil the great relevance of many-body correlations between the emitted and trapped fractions of the wave function in the respective processes.
The tunneling process in a many-body system is a phenomenon which lies at the very heart of quantum mechanics. It appears in nature in the form of α-decay, fusion and fission in nuclear physics, and photoassociation and photodissociation in biology and chemistry. A detailed theoretical description of the decay process in these systems is a very cumbersome problem, either because of very complicated or even unknown interparticle interactions or due to a large number of constituent particles. In this work, we theoretically study the phenomenon of quantum many-body tunneling in a transparent and controllable physical system, an ultracold atomic gas. We analyze a full, numerically exact many-body solution of the Schrödinger equation of a one-dimensional system with repulsive interactions tunneling to open space. We show how the emitted particles dissociate or fragment from the trapped and coherent source of bosons: The overall many-particle decay process is a quantum interference of single-particle tunneling processes emerging from sources with different particle numbers taking place simultaneously. The close relation to atom lasers and ionization processes allows us to unveil the great relevance of many-body correlations between the emitted and trapped fractions of the wave function in the respective processes.
The creation of tunable open quantum systems is becoming feasible in current experiments with ultracold atoms in low-dimensional traps. In particular, the high degree of experimental control over these systems allows detailed studies of tunneling dynamics, e.g., as a function of the trapping geometry and the interparticle interaction strength. In order to address this exciting opportunity we present a theoretical framework for two-body tunneling based on the rigged Hilbert space formulation. In this approach, bound, resonant, and scattering states are included on an equal footing and we argue that the coupling of all these components is vital for a correct description of the relevant threshold phenomena. In particular, we study the tunneling mechanism for two-body systems in one-dimensional traps and different interaction regimes. We find a strong dominance of sequential tunneling of single particles for repulsive and weakly attractive systems, while there is a signature of correlated pair tunneling in the calculated many-particle flux for strongly attractive interparticle interaction.
A scheme to control the many-boson tunneling process from a trap through a potential barrier to open space is devised and demonstrated. The number of ejected particles and their velocities can be controlled by two parameters, the threshold of the potential and the interparticle interaction. Employing a recently developed efficient many-body method, results for two, three, and one hundred interacting bosons in one spatial dimension can be computed numerically exactly, solving thereby an intricate problem of general interest. It is shown that the control scheme devised for the many-boson tunneling process performs very well for the dynamics of the momentum density, the correlations, and the coherence, as well as for the number of particles remaining in the trap. To interpret the many-body tunneling process, a transparent model assembling the many-body process from single-particle emission processes is derived. Analysis of the energetics of available decay channels together with the numerical results rules out the situation of two (or more) bosons tunneling together to open space. The present investigation generalizes the findings reported by us [Proc. Natl. Acad. Sci. USA 109, 13521 (2012)] for many-boson tunneling to open space in the absence of a threshold.
We investigate the mechanism in the tunneling dynamics of open ultracold few-boson systems by numerically solving the time-dependent few-boson Schrödinger equation exactly. By starting from a weakly repulsive, initially coherent two-boson system we demonstrate that the decay dynamics incorporate fragmentation. The wavefunction of the tunneling state exhibits a pronounced dynamically-stable pattern which we explain by an analytical model. By studying more bosons and stronger interactions we arrive to the conclusion that the decay by tunneling is not a coherent process and exhibits a wealth of phenomena depending on the interaction between the particles.
We study the full-fledged microscopic dynamics of two interacting, ultracold bosons in a one-dimensional double-well potential, through the numerically exact diagonalization of the many-body Hamiltonian. With the particles initially prepared in the left well, we increase the width of the right well in subsequent trap realizations and witness how the tunneling oscillations evolve into particle loss. In this closed system, we analyze the spectral signatures of single- and two-particle tunneling for the entire range of repulsive interactions. We conclude that for comparable widths of the two wells, pairwise tunneling of the bosons may be realized for specific system parameters. In contrast, the decay process (corresponding to a broad right well) is dominated by uncorrelated single-particle decay.
Abstract. We study the effects of the environment at zero temperature on tunneling in an open system described by a static double-well potential. We show that the evolution of the system in an initial Schrödinger cat state, can be summarized in terms of three main physical phenomena, namely decoherence, quantum tunneling and noise-induced activation. Using large-scale numerical simulations, we obtain a detailed picture of the main stages of the evolution and of the relevant dynamical processes. The tunneling of a particle through a potential barrier is a fundamental effect in quantum mechanics. Macroscopic quantum tunneling can be associated with the tunneling of a many-body wavefunction through a potential barrier, and therefore provides a more stringent test of the validity of quantum mechanics than one particle case. One place where the study of macroscopic quantum tunneling is experimentally accesible is in the tunneling of a Bose-Einstein condensate (BEC) out of an optical trap. These systems have a controllable number of atoms and hence straddle the boundary between microscopic and macroscopic, and hence between quantum and classical systems. Proposals to perform interference experiments using confined atoms
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…