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arXiv:cond-mat/0610014 · Europhysics Letters (EPL)

Driven collective quantum tunneling of ultracold atoms in engineered optical lattices

Рамаз Хомерики, Stefano Ruffo, Sandro Wimberger

Published Feb 1, 2007• 9 citations
arXivHTMLPDF

Abstract

Collective quantum tunneling of a Bose-Einstein condensate between two parts of an optical lattice separated by an energy barrier is theoretically investigated. We show that by a pulsewise change of the barrier height, it is possible to switch between a tunneling regime and a self-trapped one. This property of the system is explained by effectively reducing the nonlinear dynamics of the system to that of a particle moving in a double square well potential. The analysis is performed for both attractive and repulsive interatomic forces, and emphasizes the experimental relevance of our findings.

DOI
10.1209/0295-5075/77/40005

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Collective quantum tunneling of a Bose-Einstein condensate between two parts of an optical lattice separated by an energy barrier is theoretically investigated. We show that by a pulsewise change of the barrier height, it is possible to switch between a tunneling regime and a self-trapped one. This property of the system is explained by effectively reducing the nonlinear dynamics of the system to that of a particle moving in a double square well potential. The analysis is performed for both attractive and repulsive interatomic forces, and emphasizes the experimental relevance of our findings.
It is well known that increasing the nonlinearity due to repulsive atomic interactions in a double-well Bose-Einstein condensate suppresses quantum tunneling between the two sites. Here we find analogous behavior in the dynamical tunneling of a Bose-Einstein condensate between period-one resonances in a single driven potential well. For small nonlinearities we find unhindered tunneling between the resonances, but with an increasing period as compared to the noninteracting system. For nonlinearities above a critical value we generally observe that the tunneling shuts down. However, for certain regimes of modulation parameters we find that dynamical tunneling reemerges for large enough nonlinearities, an effect not present in spatial double-well tunneling. We develop a two-mode model in good agreement with full numerical simulations over a wide range of parameters, which allows the suppression of tunneling to be attributed to macroscopic quantum self-trapping.
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…
The realization of Bose-Einstein condensation in dilute atomic gases opens an exciting way to quantum mechanics and begins a new area of quantum simulation. As a macroscopic quantum object and a many-body bosonic system, the Bose-Einstein condensates can show numerous exotic quantum effects and have naturally attracted great attention. One of the simplest quantum many-body systems to be realized experimentally and studied theoretically is ultra-cold atoms in a double-well potential. This system can exhibit a great variety of quantum interference phenomena such as tunneling oscillation, self-trapping and the entanglement of macroscopic superpositions. Specifically, the double-well potentials built by optical or magnetic fields are easy to change and the many-body interaction between ultra-cold atoms can be changed by the method of Feshbach resonance, enabling the precise quantum control of the double-well dynamics of the condensates. In the present work, we study the dynamics of a condensate in a trapping potential consisting of an unalterable double-well trap and an additional moving optical lattice. If the lattice space is much smaller than the size of the double-well trap, the system can be simplified into a double-well trapped condensate with a tunable effective mass. Using the mean-field factorization assumption, together with a two-mode approximation, we obtain the analytic expressions for the dependence of the tunneling rate and the self-collision strength on the effective mass. The tunneling rate decays and the collision strength grows up with the increase of the effective mass. As a consequence of their different changes, we conclude that the adjustment of the effective mass of the ultra-cold atoms, rather than the changing of the trap barrier or adjusting of the atomic scattering length, is an alternative approach to controlling the double-well dynamics of the condensate. Via numerical simulations of the mean-field dynamical equations with some realistic parameters, we show that a transition between the quantum coherent tunneling and the self-trapping behaviors is experimentally realizable with the mass-control approach. Specifically, we show that the approach is still valid for the case of negative mass. Moreover, we find that the negative-mass case can be used even to stimulate the double-well dynamics of the condensate with a negative atomic scattering length.
Consider the tunneling of a many-body wavefunction through a potential barrier. Specifically we examine quantum many-body tunneling of ultracold bosons in one dimensional optical lattice potentials. Such systems are described by the Bose-Hubbard model, and serve as an ideal testbed for the observation of quantum phenomena on macroscopic length scales. Bright solitons, self-sustaining nonlinear waves, are confined by a thin potential barrier. By decreasing the size of the barrier or by tuning the nonlinearity, we find that the bound states can be transformed into quasi-bound ones as the soliton tunnels collectively out of confinement. The lowly entangled 1D many-body problem can be numerically solved via time-evolving block decimation: a time-adaptive density matrix renormalization group routine. As a sanity check the results can be compared to mean-field theory predictions obtained from numerical analysis of the Nonlinear Schrodinger equation. The goal behind this effort is to explore the previously intractable physics in regimes where the mean-field theory fails, and to provide a stringent test on the validity of quantum mechanics for complex entangled systems.
Abstract In quantum tunneling a particle with energy E can pass through a high potential barrier V(E) due to the wave character of the particle. Bose\|Einstein condensates can display very strong tunneling depending on the structure of the trap, which may be a double\|well or optical lattices. We employed for the first time to our knowledge the periodic instanton method to investigate tunneling of Bose\|Einstein condensates in optical lattices. Our results show that there are two kinds of tunneling in this system, Landau\|Zener tunneling between extended states of the system and Wannier\|Stark tunneling between localized states of the system, and that the latter is 1000 times faster than the former. We also obtain the total decay rate for a wide range of temperature, including classical thermal activation, thermally assisted tunneling and quantum tunneling. Our results agree with experimental data in references[1, 2].Finally, we propose an experimental protocol to observe this new phenomenon in future experiments. periodic instanton, Wannier\|Stark localization, Landau\|Zener tunneling, Wannier\|Stark tunneling