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arXiv:0812.1838

Collective excitations and instabilities in multi-layer stacks of dipolar condensates

Daw-Wei Wang, Eugene Demler

Published Dec 10, 2008• 4 citations
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Abstract

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.

DOI
10.48550/arxiv.0812.1838

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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^{39}39K atoms.
Superfluids with a tendency towards periodic crystalline order have both a phonon and roton like spectrum of collective modes. The softening of the roton spectrum provides one route to a supersolid. We show that roton softening occurs in 87Rb spinor condensates once dipolar interactions and spin dynamics are taken into account. By including the effects of a quasi-two-dimensional geometry and rapid Larmor precession, we show a dynamical instability develops in the collective mode spectrum at finite wavevectors. We construct phase diagrams showing a variety of instabilities as a function of the direction of the magnetic field and strength of the quadratic Zeeman shift. Our results provide a possible explanation of current experiments in the Berkeley group Phys. Rev. Lett. 100:170403 (2008).
We study the pair correlations and excitations of a dipolar Bose gas layer. The anisotropy of the dipole-dipole interaction allows us to tune the strength of pair correlations from strong to weak perpendicular and weak to strong parallel to the layer by increasing the perpendicular trap frequency. This change is accompanied by a roton-roton crossover in the spectrum of collective excitations, from a roton caused by the head-to-tail attraction of dipoles to a roton caused by the side-by-side repulsion, while there is no roton excitation for intermediate trap frequencies. We discuss the nature of these two kinds of rotons and the relation to instabilities of dipolar Bose gases. In both regimes of trap frequencies where rotons occur, we observe strong damping of collective excitations by decay into two rotons.
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 develop a theory for a two-component miscible dipolar condensate in a planar trap. Using numerical solutions and a variational theory we solve for the excitation spectrum and identify regimes where density- and spin-roton excitations are favored. We characterize the various instabilities that can emerge in this system over a wide parameter regime and present results for the stability phase diagram. Importantly this allows us to identify the parameter regimes where a novel roton-immiscibility transition can occur, driven by the softening of the spin-roton excitation.
Dipolar Bose-Einstein condensates may present a rotonlike dispersion minimum, which has yet to be observed in experiments. We discuss a simple method to reveal roton excitations based on the response of quasi-two-dimensional dipolar condensates against a weak lattice potential. By employing numerical simulations for realistic scenarios, we analyze the response of the system as a function of both the lattice spacing and the sss-wave scattering length, showing that the roton minimum may be readily revealed in current experiments by the resonant population of Bragg peaks in time-of-flight measurements.
We characterize the role of roton instability in the formation of a supersolid state of an elongated dipolar condensate, following a quench of the contact interactions across the superfluid-supersolid transition, as observed in recent experiments. We perform dynamical simulations by means of the extended Gross-Pitaevskii equation including quantum corrections, for different final values of the $s\text{\ensuremath{-}}\mathrm{wave}$ scattering length. The corresponding excitation spectrum is computed using an effective one-dimensional description, which provides a reasonably accurate prediction for the growth rate of the most unstable mode observed in the simulations. To analyze the behavior of the system, we employ the inverse participation ratio, which conveniently characterizes the different degree of localization in the superfluid and supersolid phases. By means of a suitable effective ansatz for the density, we derive a simple yet effective expression for the formation time of the supersolid. This expression provides valuable insights regarding its scaling behavior with respect to the sss-wave scattering length.