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arXiv:1206.2770 · Physical Review A

Roton spectroscopy in a harmonically trapped dipolar Bose-Einstein condensate

P. B. Blakie, D. Baillie, R. N. Bisset

Published Aug 15, 2012• 77 citations
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Abstract

We study a harmonically trapped Bose-Einstein condensate with dipole-dipole interactions in a regime where a roton spectrum emerges. We show that the roton spectrum is clearly revealed in the static and dynamic structure factors which can be measured using Bragg spectroscopy. We develop and validate a theory based on the local-density approximation for the dynamic structure factor.

DOI
10.1103/physreva.86.021604

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We study a harmonically trapped Bose-Einstein condensate with dipole-dipole interactions in a regime where a roton spectrum emerges. We show that the roton spectrum is clearly revealed in the static and dynamic structure factors which can be measured using Bragg spectroscopy. We develop and validate a theory based on the local-density approximation for the dynamic structure factor.
We measure the excitation spectrum of a stable dipolar Bose-Einstein condensate over a wide momentum range via Bragg spectroscopy. We precisely control the relative strength ε_{dd} of the dipolar to the contact interactions and observe that the spectrum increasingly deviates from the linear phononic behavior for increasing ε_{dd}. Reaching the dipolar-dominated regime ε_{dd}>1, we observe the emergence of a roton minimum in the spectrum and its softening towards instability. We characterize how the excitation energy and the strength of the density-density correlations at the roton momentum vary with ε_{dd}. Our findings are in excellent agreement with numerical calculations based on mean-field Bogoliubov theory. When including beyond-mean-field corrections, in the form of a Lee-Huang-Yang potential, we observe a quantitative deviation from the experiment, questioning the validity of such a description in the roton regime.
Motivated by the recent experimental achievements in using the Bragg spectroscopy to measure the excitation spectrum of an ultra-cold atomic system with long-range interactions, we investigate the dynamic structure factor of a cigar-shaped dipolar Bose condensate trapped in a one-dimensional optical lattices. Our results show that the Bogoliubov bands of the system, particularly the lowest one, can be significantly influenced when one tunes the dipole orientation. Consequently, the calculated static structure factor of an optically trapped dipolar Bose gas shows marked difference from the non-dipolar one. Moreover, we show that the effects of dipole-dipole interaction on the dynamic structure factor is also strongly affected by the strength of the optical confinement.
We consider the quasiparticle excitations of a trapped dipolar Bose-Einstein condensate. By mapping these excitations onto linear and angular momentum we show that the roton modes are clearly revealed as discrete fingers in parameter space, whereas the other modes form a smooth surface. We examine the properties of the roton modes and characterize how they change with the dipole interaction strength. We demonstrate how the application of a perturbing potential can be used to engineer angular rotons, i.e., allowing us to controllably select modes of nonzero projection of angular momentum to become the lowest energy rotons.
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 consider the noncondensate density and density fluctuations of a trapped dipolar Bose-Einstein condensate, focusing on the regime where a rotonlike excitation spectrum develops. Our results show that a characteristic peak in the noncondensate density occurs at trap center due to the rotons. In this regime we also find that the anomalous density becomes positive and peaked, giving rise to enhanced density fluctuations. We calculate the noncondensate density in momentum space and show that a small momentum halo is associated with the roton excitations.
We observe signatures of radial and angular roton excitations around a droplet crystallization transition in dipolar Bose-Einstein condensates. In situ measurements are used to characterize the density fluctuations near this transition. The static structure factor is extracted and used to identify the radial and angular roton excitations by their characteristic symmetries. These fluctuations peak as a function of the interaction strength indicating the crystallization transition of the system. We compare our observations to a theoretically calculated excitation spectrum allowing us to connect the crystallization mechanism with the softening of the angular roton modes.