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arXiv:0908.1009 · Physical Review A

Phonon instability and self-organized structures in multilayer stacks of confined dipolar Bose-Einstein condensates in optical lattices

Patrick Köberle, Günter Wunner

Published Dec 1, 2009• 19 citations

Abstract

In calculations to date [D.-W. Wang and E. Demler, e-print arXiv:0812.1838; M. Klawunn and L. Santos, Phys. Rev. A 80, 013611 (2009)] of multilayer stacks of dipolar condensates, created in one-dimensional optical lattices, the condensates have been assumed to be two dimensional. In a real experiment, however, the condensates do not extend to infinity in the oblate direction, but have to be confined by a trap potential, too. By three-dimensional numerical simulations of this realistic experimental situation we find a crucial dependence of the phonon instability boundary on the number of layers. Moreover, near the boundary of the phonon instability, a variety of structured ground-state wave functions emerges, which may indicate the onset of a roton instability [S. Ronen, D. C. E. Bortolotti, and J. L. Bohn, Phys. Rev. Lett. 98, 030406 (2007); R. M. Wilson, S. Ronen, J. L. Bohn, and H. Pu, Phys. Rev. Lett. 100, 245302 (2008)]. We also consider the effect of a variable number of atoms per layer on the appearance of the phonon instability.

DOI: 10.1103/physreva.80.063601

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In calculations to date [D.-W. Wang and E. Demler, e-print arXiv:0812.1838; M. Klawunn and L. Santos, Phys. Rev. A 80, 013611 (2009)] of multilayer stacks of dipolar condensates, created in one-dimensional optical lattices, the condensates have been assumed to be two dimensional. In a real experiment, however, the condensates do not extend to infinity in the oblate direction, but have to be confined by a trap potential, too. By three-dimensional numerical simulations of this realistic experimental situation we find a crucial dependence of the phonon instability boundary on the number of layers. Moreover, near the boundary of the phonon instability, a variety of structured ground-state wave functions emerges, which may indicate the onset of a roton instability [S. Ronen, D. C. E. Bortolotti, and J. L. Bohn, Phys. Rev. Lett. 98, 030406 (2007); R. M. Wilson, S. Ronen, J. L. Bohn, and H. Pu, Phys. Rev. Lett. 100, 245302 (2008)]. We also consider the effect of a variable number of atoms per layer on the appearance of the phonon instability.

We propose a two-dimensional model for a multilayer stack of dipolar Bose-Einstein condensates formed by a strong optical lattice. We derive effective intra- and interlayer dipole-dipole interaction potentials and provide simple analytical approximations for a given number of lattice sites at arbitrary polarization. We find that the interlayer dipole-dipole interaction changes the transverse aspect ratio of the ground state in the central layers depending on its polarization and the number of lattice sites. The changing aspect ratio should be observable in time-of-flight images. Furthermore, we show that the interlayer dipole-dipole interaction reduces the excitation energy of local perturbations affecting the development of a roton minimum.

The self-trapping phenomenon of Bose-Einstein condensates (BECs) in optical lattices is studied by numerically solving the Gross-Pitaevskii equation. Our numerical results reproduce the self-trapping that was observed in a recent experiment [Anker et al., Phys. Rev. Lett. 94, 020403 (2005)]. However, we do not find that the appearance of the steep edges on the boundaries of the wave packet is the critical signal of the self-trapping. More importantly, we discover that the self-trapping breaks down at long evolution times; that is, the self-trapping in optical lattices is only temporary and has a lifetime. This temporariness is caused by the tunneling of atoms at the edge of the BEC wave packet towards outside wells. Our analysis shows that the phenomena observed numerically can all be understood by regarding the optical lattice as a train of double-well potentials.

We analyze theoretically the collective mode dispersion in multi-layer stacks of two dimensional dipolar condensates and find a strong enhancement of the roton instability. We discuss the interplay between the dynamical instability and roton softening for moving condensates. We use our results to analyze the decoherence rate of Bloch oscillations for systems in which the s-wave scattering length is tuned close to zero using Feshbach resonance. Our results are in qualitative agreement with recent experiments of Fattori {\it et al.} on

^{39}

K atoms.

We propose a realistic experimental setup for creating quasi-two-dimensional (2D) bright solitons in dipolar Bose-Einstein condensates (BECs), the existence of which was proposed by Tikhonenkov et al. [Phys. Rev. Lett. 100, 090406 (2008)]. A challenging feature of the expected solitons is their strong inherent anisotropy due to the necessary in-plane orientation of the local moments in the dipolar gas. This may be the first chance of making multidimensional matter-wave solitons, as well as solitons featuring the anistropy due to their intrinsic dynamics. Our analysis is based on the extended Gross-Pitaevskii equation, which includes three-body losses and noise in the scattering length, induced by fluctuations of currents inducing the necessary magnetic fields, which are factors crucial to the adequate description of experimental conditions. By means of systematic three-dimensional (3D) simulations, we find a ramping scenario for the change of the scattering length and trap frequencies which results in the creation of robust solitons, that readily withstand the concomitant excitation of the condensate.

We predict the effect of the roton instability for a two-dimensional weakly interacting gas of tilted dipoles in a single homogeneous quantum layer. Being typical for strongly correlated systems, the roton phenomena appear to occur in a weakly interacting gas. It is important that in contrast to a system of normal to the layer dipoles, breaking of the rotational symmetry for a system of tilted dipoles leads to the convergence of the condensate depletion even up to the threshold of the roton instability, with mean-field approach being valid. Predicted effects can be observed in a wide class of dipolar systems. We suggest observing predicted phenomena for systems of ultracold atoms and polar molecules in optical lattices, and estimate optimal experimental parameters.