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Journal of Physics B Atomic Molecular and Optical Physics

Atom-pair tunnelling-induced quantum phase transition and scaling behaviour of fidelity susceptibility in the extended boson Josephson-junction model

J. L. Liu, J.-Q. Liang

Published Dec 23, 2010• 7 citations
Publisher

Abstract

In this paper we theoretically investigate the nonlinear tunnelling of two weakly linked Bose–Einstein condensates in a double-well trap in a strong interaction regime with the two-body interaction extended to neighbouring lattice sites. As a consequence the boson Josephson-junction tunnelling depends on the atom–atom interaction and the total atom number as well. A crucial atom-pair tunnelling term, obtained directly from the extension, results in significant energy spectrum corrections and an abrupt change of the ground state viewed as quantum phase transition. An atom-number oscillation state with a tunable relative phase between two Bose–Einstein condensates predicted for the first time is seen to be a degenerate ground state in an interaction region. The quantum phase transitions between degenerate and non-degenerate ground states driven by the atom-pair tunnelling are analysed. We show the scaling behaviours and the critical exponents of fidelity susceptibility, which can classify the universality.

DOI
10.1088/0953-4075/44/2/025101

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•Jan 1, 2018•0 citations
In this paper we theoretically investigate the nonlinear tunnelling of two weakly linked Bose–Einstein condensates in a double-well trap in a strong interaction regime with the two-body interaction extended to neighbouring lattice sites. As a consequence the boson Josephson-junction tunnelling depends on the atom–atom interaction and the total atom number as well. A crucial atom-pair tunnelling term, obtained directly from the extension, results in significant energy spectrum corrections and an abrupt change of the ground state viewed as quantum phase transition. An atom-number oscillation state with a tunable relative phase between two Bose–Einstein condensates predicted for the first time is seen to be a degenerate ground state in an interaction region. The quantum phase transitions between degenerate and non-degenerate ground states driven by the atom-pair tunnelling are analysed. We show the scaling behaviours and the critical exponents of fidelity susceptibility, which can classify the universality.
In this paper, we investigated theoretically the dynamic effect induced by nonlinear tunneling of two weakly linked Bose–Einstein condensates in an extended boson Josephson-junction model, in which the two-body interaction is extended to neighboring lattice sites in strong interaction regime. As a consequence the dynamic properties compared with the usual Josephson-junction model are crucially modified by the atom-pair tunneling, which leads to the macroscopic quantum-states of coherent relative-phase between two condensates seen to be effective Schrödinger cat states. The relative-phase is controllable by system parameters and thus can be used to realize the qubit in quantum computation.
We propose a Hamiltonian of ultracold spinless atom in optical lattices including the two-body interaction of nearest neighbors, which reduces to the Bose-Hubbard model in weak-interaction limit. An atom-pair hopping term appearing in the Hamiltonian explains naturally the recent experimental observation of correlated tunneling in a double-well trap with strong atom-atom interactions and moreover leads to a dynamic process of atom-pair tunneling where strongly interacting atoms can tunnel back and forth as a fragmented pair. Finally a dynamics of oscillations induced by the atom-pair tunneling is found in the strong interaction regime, where the Bose-Hubbard model gives rise to the insulator state with fixed time-averaged value of atom-occupation number only. Quantum phase transitions between two quantum phases characterized by degenerate and nondegenerate ground states are shown to be coinciding with the Landau second-order phase-transition theory. In the system of finite atom number the degeneracy of ground states can be removed by quantum tunneling for the even number of atoms but not for the odd number.
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”.
In this paper, we discuss coherent atomic oscillations between two weakly coupled Bose–Einstein condensates that are energetically different. The weak link is notionally provided by a laser barrier in a (possibly asymmetric) multi-well trap or by Raman coupling between condensates in different hyperfine levels. The resultant boson Josephson junction dynamics is described by a double-well nonlinear Gross–Pitaevskii equation. On the basis of a new set of Jacobian elliptic function solutions, we describe the period of the oscillations as well as associated quantities and predict novel observable consequences of the interplay of the energy difference and initial phase difference between the two condensate populations.
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.
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…