Tuning the structural and dynamical properties of a dipolar Bose–Einstein condensate: ripples and instability islands

Abstract

It is now well established that the stability of aligned dipolar Bose gases can be tuned by varying the aspect ratio of the external harmonic confinement. This paper extends this idea and demonstrates that a Gaussian barrier along the strong confinement direction can be employed to tune both the structural properties and the dynamical stability of an oblate dipolar Bose gas aligned along the strong confinement direction. In particular, our theoretical mean-field analysis predicts the existence of instability islands immersed in otherwise stable regions of the phase diagram. Dynamical studies indicate that these instability islands, which can be probed experimentally with present-day technology, are associated with the going soft of a Bogoliubov-de Gennes excitation frequency with radial breathing mode character. Furthermore, we find dynamically stable ground state densities with ripple-like oscillations along the radial direction. These structured ground states exist in the vicinity of a dynamical radial roton-like instability.PACS numbers:

Fortran and C programs for the time-dependent dipolar Gross–Pitaevskii equation in an anisotropic trap

“…(18) and (19) are shown in Table 3. These results for energy E and chemical potential µ are compared with those calculated by Asad-uz-Zaman et al [16,29]. The present calculation is performed in the Cartesian x, y, z coordinates and the dipolar term is evaluated by FT to momentum space.…”

“…In this subsection we describe the numerical codes for solving the dipolar GP equations (29) and (41) in 1D, Eqs. (46) and (55) in 2D, and Eq.…”

Roton excitations in a trapped dipolar Bose-Einstein condensate

“…We note that the effect of a barrier-type perturbation in the z direction was considered in Ref. [23], and found to enrich the stability properties compared to the harmonically trapped case. Also Lu et al [38] examined the properties of a condensate in a box potential, and predict the formation of spatial density oscillations in the condensate due to the sharp edges of the potential.…”

“…While robust numerical techniques for calculating the quasiparticles of a fully trapped dipolar BEC have been developed (e.g., see [20]), there has been no comprehensive study of rotons for the trapped system. However, some aspects of the lowest energy rotons in the trapped system have emerged in studies of condensate structure and stability [21][22][23][24][25][26]. Recent work [27] presented an approximate description of the trapped rotons by requantizing a local density treatment of the excitation spectrum, enabling an analytic prediction for the roton spectrum and wave functions.…”

A general theory of flattened dipolar condensates

“…For example, experiments have confirmed that flattened dipolar BECs, with dipoles polarized normal to the trap plane, are stable against an attractive short-ranged contact interaction [7,8]. Theoretical predictions for this regime include the emergence of novel density oscillating condensate ground states [9][10][11][12], enhanced density fluctuations [13][14][15], roton-like excitations [9,[16][17][18][19][20][21], and modified collective and superfluid properties [22]. Additionally, for a negative DDI (e.g.…”