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arXiv:cond-mat/0207172 · Physical Review Letters

Dynamical Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates

Augusto Smerzi, Andrea Trombettoni, P. G. Kevrekidis, A. R. Bishop

Published Oct 3, 2002• 326 citations
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Abstract

We predict a dynamical classical superfluid-insulator transition in a Bose-Einstein condensate trapped in an optical and a magnetic potential. In the tight-binding limit, this system realizes an array of weakly coupled condensates driven by an external harmonic field. For small displacements of the parabolic trap about the equilibrium position, the condensates coherently oscillate in the array. For large displacements, the condensates remain localized on the side of the harmonic trap with a randomization of the relative phases. The superfluid-insulator transition is due to a discrete modulational instability, occurring when the condensate center of mass velocity is larger than a critical value.

DOI
10.1103/physrevlett.89.170402

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We report the experimental observation of the disruption of the superfluid atomic current flowing through an array of weakly linked Bose–Einstein condensates. The condensates are trapped in an optical lattice superimposed on a harmonic magnetic potential. The dynamical response of the system to a change of the magnetic potential minimum along the optical lattice axis goes from a coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap ('classical' insulator regime). The localization occurs when the initial displacement is larger than a critical value or, equivalently, when the velocity of the wavepacket's centre of mass is larger than a critical velocity dependent on the rate of tunnelling between adjacent sites.
We predict a dynamical classical superfluid–insulator transition in a Bose–Einstein condensate (BEC) trapped in combined optical and axially symmetrical harmonic potentials initiated by the periodic modulation of the radial trapping potential. The transition is marked by a loss of phase coherence in the BEC and a subsequent destruction of the interference pattern upon free expansion. For a weak modulation of the radial potential the phase coherence is maintained. For a stronger modulation and a longer holding time in the modulated trap, the phase coherence is destroyed thus signalling a classical superfluid–insulator transition. The results are illustrated by a complete numerical solution of the axially symmetrical mean-field Gross–Pitaevskii equation for a repulsive BEC. Suggestions for future experimentation are made.
We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.
We create Bose-Einstein condensates of 87Rb in a static magnetic trap with a superimposed blue-detuned 1D optical lattice. By displacing the magnetic trap center we are able to control the condensate evolution. We observe a change in the frequency of the center-of-mass oscillation in the harmonic trapping potential, in analogy with an increase in effective mass. For fluid velocities greater than a local speed of sound, we observe the onset of dissipative processes up to full removal of the superfluid component. A parallel simulation study visualizes the dynamics of the Bose-Einstein condensate and accounts for the main features of the observed behavior.
We investigate the phase coherence of a trapped Bose–Einstein condensate that undergoes a dynamical superfluid–insulator transition in the presence of a one-dimensional optical lattice. We study the evolution of the condensate after a sudden displacement of the harmonic trapping potential by solving the Gross–Pitaevskii equation, and comparing the results with the prediction of two effective 1D models. We show that, owing to the 3D nature of the system, the breakdown of the superfluid current above a critical displacement is not associated with a sharp transition, but there exists a range of displacements for which the condensate can recover a certain degree of coherence. We also discuss the implications on the interference pattern after the ballistic expansion as measured in recent experiments at LENS.
We consider a system formed by an array of Bose–Einstein condensates trapped in a harmonic potential with a superimposed periodic optical potential. Starting from the boson field Hamiltonian, appropriate to describe a dilute gas of bosonic atoms, we reformulate the system dynamics within the Bose–Hubbard model scenario. Then we analyse the effective dynamics of the system when the optical-potential depth is suddenly varied according to a procedure applied in many of the recent experiments on superfluid–Mott transition in Bose–Einstein condensates. Initially the condensate array generated in a weak optical potential is assumed to be in the superfluid ground state which is well described in terms of coherent states. At a given time, the optical-potential depth is suddenly increased and, after a waiting time, it is quickly decreased so that the initial depth is restored. We compute the system-state evolution and show that the potential jump brings on an excitation of the system, incorporated in the final condensate wavefunctions, whose effects are analysed in terms of two-site correlation functions and of on-site population oscillations. Also we show how too long a waiting time can destroy completely the coherence of the final state, making it unobservable.