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Bulletin of the American Physical Society

Dynamics of Macroscopic Quantum Tunneling from Superfluid to Mott Insulating Regimes

Diego A. Alcala, Marie A. McLain, Lincoln D. Carr

Published Mar 2, 2020• 0 citations
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Quantum Phases and Correlations Drive the Dynamics of Macroscopic Quantum Tunneling Escape in Quantum Simulators

Diego A. Alcala, Marie A. McLain, Lincoln D. Carr

Quantum tunneling remains unexplored in many regimes of many-body quantum physics, including the effect of quantum phase transitions on tunneling dynamics. In general, the quantum phase is a statement about the ground state and has no relation to far-from-equilibrium dynamics. Although tunneling is a highly dynamical process involving many excited states, we find that the quantum phase of the Bose-Hubbard model determines phase-dependent tunneling outcomes for the quantum tunneling escape, or quasi-bound problem. Superfluid and Mott insulator correlations lead to a new quantum tunneling rate, the quantum fluctuation rate. This rate shows surprising and highly dynamical features, such as oscillatory interference between trapped and escaped atoms and a completely different macroscopic quantum tunneling behavior for superfluid and Mott insulator phases. In the superfluid phase we find that escape dynamics are wave-like and coherent, leading to interference patterns in the density with a rapid decay process which is non-exponential. Quantum entropy production peaks when about half the atoms have escaped. In the Mott phase, despite stronger repulsive interactions, tunneling is significantly slowed by the presence of a Mott gap, creating an effective extra barrier to overcome. Only one atom can tunnel at a time, yet the decay process is nearly linear, completely defying the single-particle exponential model. Moreover, quantum entropy peaks when only about one quarter of the atoms have escaped. These and many other such effects go beyond the usual notions of single-particle quantum tunneling, quantum statistical effects on tunneling, and well-known semi-classical approaches from WKB to instanton theory. These results thus open up a new regime of exploration of far-from-equilibrium dynamics for quantum simulators and quantum dynamics.

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Quantum Phases Drive the Dynamics of Macroscopic Quantum Tunneling Escape in Quantum Simulators

Diego A. Alcala, Marie A. McLain, Lincoln D. Carr

Mott tunneling dynamics are entirely distinct from the superfluid ones and ground state properties of quantum phases can predict highly non-equilibrium behavior. We consider quasi-bound state dynamics or tunneling escape in the Bose-Hubbard model from a behind a finite barrier, which can be realized in quantum simulators. In the superfluid regime we find that escape dynamics are wave-like and coherent, leading to interference patterns in the density with a non-exponential but still rapid decay process. Quantum entropy production peaks when about half the atoms have escaped. In contrast, in the Mott insulator regime we find the dynamics are atom-like and incoherent, with no interference fringes. Quantum entropy production peaks at double the value of the superfluid case and when only about one quarter of the atoms have escaped. Despite stronger repulsive interactions, tunneling is significantly slowed by the presence of a Mott gap, creating an effective extra barrier to overcome, and the decay process is nearly linear. Moreover, we introduce a new quantum tunneling rate, the fluctuation rate, which shows oscillatory interference between the trapped and the escaped atoms on short time scales beyond the constant waiting time known for single-particle tunneling before exponential decay ensues. The fluctuation rate is overall positive for the superfluid and initially negative for the Mott insulator, only turning positive in the latter case when about half the atoms have escaped. Finally, off-diagonal correlators show entirely different structure for the two quantum phases. In the superfluid case, the barrier height and interaction strength can be used to tune from pulsed to continuous-wave positive correlation emissions in the escape region. In the Mott insulator, negative correlations between the trap and the escape region emphasize emission one atom at a time.

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

Marie A. McLain

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…

•Jan 1, 2018•0 citations

Macroscopic quantum tunneling of a bose condensate

Henk T. C. Stoof

arXiv:cond-mat/9601150•Journal of Statistical Physics•Jun 1, 1997•108 citations
Quantum tunneling remains unexplored in many regimes of many-body quantum physics, including the effect of quantum phase transitions on tunneling dynamics. In general, the quantum phase is a statement about the ground state and has no relation to far-from-equilibrium dynamics. Although tunneling is a highly dynamical process involving many excited states, we find that the quantum phase of the Bose-Hubbard model determines phase-dependent tunneling outcomes for the quantum tunneling escape, or quasi-bound problem. Superfluid and Mott insulator correlations lead to a new quantum tunneling rate, the quantum fluctuation rate. This rate shows surprising and highly dynamical features, such as oscillatory interference between trapped and escaped atoms and a completely different macroscopic quantum tunneling behavior for superfluid and Mott insulator phases. In the superfluid phase we find that escape dynamics are wave-like and coherent, leading to interference patterns in the density with a rapid decay process which is non-exponential. Quantum entropy production peaks when about half the atoms have escaped. In the Mott phase, despite stronger repulsive interactions, tunneling is significantly slowed by the presence of a Mott gap, creating an effective extra barrier to overcome. Only one atom can tunnel at a time, yet the decay process is nearly linear, completely defying the single-particle exponential model. Moreover, quantum entropy peaks when only about one quarter of the atoms have escaped. These and many other such effects go beyond the usual notions of single-particle quantum tunneling, quantum statistical effects on tunneling, and well-known semi-classical approaches from WKB to instanton theory. These results thus open up a new regime of exploration of far-from-equilibrium dynamics for quantum simulators and quantum dynamics.
Mott tunneling dynamics are entirely distinct from the superfluid ones and ground state properties of quantum phases can predict highly non-equilibrium behavior. We consider quasi-bound state dynamics or tunneling escape in the Bose-Hubbard model from a behind a finite barrier, which can be realized in quantum simulators. In the superfluid regime we find that escape dynamics are wave-like and coherent, leading to interference patterns in the density with a non-exponential but still rapid decay process. Quantum entropy production peaks when about half the atoms have escaped. In contrast, in the Mott insulator regime we find the dynamics are atom-like and incoherent, with no interference fringes. Quantum entropy production peaks at double the value of the superfluid case and when only about one quarter of the atoms have escaped. Despite stronger repulsive interactions, tunneling is significantly slowed by the presence of a Mott gap, creating an effective extra barrier to overcome, and the decay process is nearly linear. Moreover, we introduce a new quantum tunneling rate, the fluctuation rate, which shows oscillatory interference between the trapped and the escaped atoms on short time scales beyond the constant waiting time known for single-particle tunneling before exponential decay ensues. The fluctuation rate is overall positive for the superfluid and initially negative for the Mott insulator, only turning positive in the latter case when about half the atoms have escaped. Finally, off-diagonal correlators show entirely different structure for the two quantum phases. In the superfluid case, the barrier height and interaction strength can be used to tune from pulsed to continuous-wave positive correlation emissions in the escape region. In the Mott insulator, negative correlations between the trap and the escape region emphasize emission one atom at a time.
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…