Loss and revival of phase coherence in a Bose–Einstein condensate moving through an optical lattice

Abstract

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 to 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.

Role of transverse excitations in the instability of Bose-Einstein condensates moving in optical lattices

“…For each p, the order parameter p0 ͑r , z͒ and its energy E p are calculated by solving the stationary GP equation by means of iterative methods. Then the Bogoliubov equations (12) and (13) are transformed into matrix equations by projecting the functions u and v on the Bessel-Fourier basis ͉l , n͘ϵJ 0 ͑␣ 0n r / r max ͒exp͑i2q B lz͒, where ␣ 0n are zeros of the Bessel functions J 0 ͑r͒ and r max is the radius of the computational box [18,19]. The resulting equations are not diagonal over the Fourier index l, and involve the numerical diagonalization of a 2 ϫ N r ϫ N z rank matrix.…”

“…4 where we plot the real and imaginary parts of the eigenfrequencies obtained by solving Eqs. (12) and (13) in the case p / q B = 0.55. Finally, as one can see in the last two frames of Fig.…”

“…If one considers not too large displacements the evolution of the condensate wave function can be safely described by a state of well defined quasimomentum (before instabilities occur) [12]. Using the formalism of Secs.…”

“…Experimentally the dissipative dynamics of BECs moving through optical lattices has been investigated both in the weak [1,2] and tight-binding regimes [3,4], and a number of papers have recently been published in connection with these and similar experiments [5][6][7][8][9][10][11][12][13].…”

Density Modulations Associated with the Dynamical Instability in the Bose–Hubbard Model

“…Analyses based on the Gross-Pitaevskii (GP) equation have elucidated that the density modulation is formed as a result of the complicated mode mixing in momentum space. 21,22 On the other hand, Mun et al 11 experimentally determined the phase boundary of dynamical instability in a wide range of interactions using a BEC in a 3D moving optical lattice. Here, * E-mail address: asaoka@olive.apph.tohoku.ac.jp the system is described using the Bose-Hubbard (BH) model at low fillings and far from that observed in the experiment by Fallani et al It was demonstrated that the measured results are in good agreement with the stability phase diagram of the BH model obtained by the dynamical Gutzwiller approximation.…”