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arXiv:1301.1991 · Physical Review A

Stability spectroscopy of rotons in a dipolar Bose gas

John Corson, Ryan Wilson, John L. Bohn

Published May 1, 2013• 19 citations
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Abstract

We study the stability of a quasi-one-dimensional dipolar Bose-Einstein condensate that is perturbed by a weak lattice potential along its axis. Our numerical simulations demonstrate that systems exhibiting a roton-maxon structure destabilize readily when the lattice wavelength equals either half the roton wavelength or a low roton subharmonic. We apply perturbation theory to the Gross-Pitaevskii and Bogoliubov--de Gennes equations to illustrate the mechanisms behind the instability threshold. The features of our stability diagram may be used as a direct measurement of the roton wavelength for quasi-one-dimensional geometries.

DOI
10.1103/physreva.87.051605

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We study the stability of a quasi-one-dimensional dipolar Bose-Einstein condensate that is perturbed by a weak lattice potential along its axis. Our numerical simulations demonstrate that systems exhibiting a roton-maxon structure destabilize readily when the lattice wavelength equals either half the roton wavelength or a low roton subharmonic. We apply perturbation theory to the Gross-Pitaevskii and Bogoliubov--de Gennes equations to illustrate the mechanisms behind the instability threshold. The features of our stability diagram may be used as a direct measurement of the roton wavelength for quasi-one-dimensional geometries.
We examine the stability of quasi-two-dimensional dipolar Bose-Einstein condensates in the presence of weak optical lattices of various geometries. We find that when the condensate possesses a roton-maxon quasiparticle dispersion, the conditions for stability exhibit a strong dependence both on the lattice geometry and the polarization tilt. This results in rich structures in the system's stability diagram akin to spectroscopic signatures. We show how these structures originate from the mode matching of rotons to the perturbing lattice. In the case of a one-dimensional lattice, some of the features emerge only when the polarization axis is tilted into the plane of the condensate. Our results suggest that the stability diagram may be used as a novel means to spectroscopically measure rotons in dipolar condensates.
The work of this thesis concerns the properties of a Bose gas of polarised dipoles that have long-range and anisotropic interactions. Our work is divided into two parts. First, the stability of a dipolar Bose gas at finite temperature (both above and below the critical Bose-Einstein condensation (BEC) temperature Tc). Second, the fluctuations of a dipolar BEC at zero and small finite temperature (T ≪ Tc) in a regime where rotonic excitations emerge. \n \nPart I: Stability of a Trapped Finite Temperature Dipolar Bose Gas: Above Tc we implement a semiclassical Hartree-Fock theory and characterise the dependence of the stability boundary on temperature, trap geometry and the strength of the dipole-dipole interaction and contact interaction. We find that stability is greatly enhanced above Tc and that trap geometry continues to play a key role. Furthermore, we find that for oblate traps a novel double instability feature emerges. \nTo extend our stability analysis to the low temperature regime, T < Tc, we develop a beyond semiclassical Hartree theory. We use this to characterise the stability boundary as a function of geometry. Interestingly, we find large beyond semiclassical effects above Tc for prolate trapping geometries. We characterise thermal effects on biconcave condensate states. \n \nPart II: Rotons and Fluctuations in a Trapped Dipolar Condensate: To study density fluctuations we implement a numerical scheme to solve the Gross-Pitaevskii equation and the Bogoliubov de Gennes equations. We find that the phonon and roton gases spatially separate and we characterise the role of the anomalous density on the density fluctuations of the thermally activated rotons. We develop a numerical scheme that calculates number fluctuations within cells of various shapes and sizes, and find a strong peak in the fluctuations when the cell size is around half the roton wavelength, which should be detectable by current experiments. By tailoring the cell shape we predict that experiments should be able to detect the effects of individual roton modes. \nFor the study of zero temperature fluctuations we deploy the Gross-Pitaevskii and Bogoliubov de Gennes equations to calculate the dynamic and static structure factors for a highly oblate BEC. We find a clear signature of the roton gas dispersion relation within the structure factors. This signature should be detectible in current experiments using Bragg spectroscopy.
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 immiscibility-miscibility transition (IMT) of a two-component Bose-Einstein condensate (BEC) with dipole-dipole interactions. In particular, we consider the quasi-two-dimensional geometry, where a strong trapping potential admits only zero-point motion in the trap direction, while the atoms are more free to move in the transverse directions. We employ the Bogoliubov treatment of the two-component system to identify both the well-known long-wavelength IMT in addition to a rotonlike IMT, where the transition occurs at finite-wave number and is reminiscent of the roton softening in the single-component dipolar BEC. Additionally, we verify the existence of the roton IMT in the fully trapped, finite systems by direct numerical simulation of the two-component coupled nonlocal Gross-Pitaevskii equations.