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arXiv:1810.08347 · Physical Review A

Excitations of a vortex line in an elongated dipolar condensate

Au-Chen Lee, D. Baillie, R. N. Bisset, P. B. Blakie

Published Dec 17, 2018• 15 citations
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Abstract

We characterize the properties of a vortex line in an elongated dipolar Bose--Einstein condensate. Increasing the strength of the dipole-dipole interactions (DDIs) relative to the short-ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.

DOI
10.1103/physreva.98.063620

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We characterize the properties of a vortex line in an elongated dipolar Bose--Einstein condensate. Increasing the strength of the dipole-dipole interactions (DDIs) relative to the short-ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.
We theoretically consider the properties of a dipolar Bose-Einstein condensate with a vortex. Our theory includes the influence of the leading order quantum fluctuation corrections which allows the condensate to stabilize into a droplet state in the regime of dominant dipole interactions. We develop numerical techniques to accurately and efficiently calculate the stationary vortex states and the quasi-particle excitations. These methods are carefully benchmarked where possible. We make a brief study of self-bound vortex droplets, considering their basic properties, and presenting a phase diagram for where they exist. We also compare our calculations to results which appeared from another group during our research. We show that their results suffer from serious numerical issues and are unreliable. We focus on studying the properties of a vortex line in an elongated dipolar Bose-Einstein condensate confined by a prolate trap. Increasing the strength of the dipole-dipole interactions relative to the short ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response, and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.
We study the stability of singly and doubly quantized vortex states of harmonically trapped dipolar Bose-Einstein condensates (BECs) by calculating the low-lying excitations of these condensates. We map the dynamical stability of these vortices as functions of the dipole-dipole interaction strength and trap geometry by finding where their excitations have purely real energy eigenvalues. In contrast to BECs with purely contact interactions, we find that dipolar BECs in singly quantized vortex states go unstable to modes with an increasing number of angular and radial nodes for more oblate trap aspect ratios, corresponding to local collapse that occurs on a characteristic length scale. Additionally, we find that dipolar BECs in doubly quantized vortex states are unstable to decay into a different topological state (with two singly quantized vortices) for all interaction strengths when the trap geometry is sufficiently prolate to make the dipoles attractive, and in windows of interaction strength when the trap geometry is sufficiently oblate to make the dipoles repulsive.
We investigate the formation of vortices in quasi-two-dimensional dipolar Bose-Einstein condensates (BECs) through the interplay between two-body contact and long-ranged dipole-dipole interactions (DDIs), as both interactions can be tuned from repulsive to attractive. By solving the associated Gross-Pitaevskii equation for a rotating system, our initial approach concentrates on stabilizing a collapsing condensate with attractive sss-wave two-body interactions by employing sufficiently large repulsive DDIs. Subsequently, the same procedure was applied after reversing the signs of both interactions to evaluate the sensitivity of vortex formation to such an interchange of interactions. As a reference to guide our investigation, valid for generic dipolar atomic species, we have assumed a condensate with the strong dipolar dysprosium isotope, 164Dy^{164}\mathrm{Dy}164Dy. The correlation of the results with other dipolar BEC systems was exemplified by considering rotating BECs with two other isotopes, namely 168Er^{168}\mathrm{Er}168Er and 52Cr^{52}\mathrm{Cr}52Cr. For a purely dipolar condensate (no contact interactions) under fixed rotation, we show how the number of visible vortices increases as the DDI becomes more repulsive, accomplished by tuning the orientation of the dipoles through a characteristic angle parameter.
Quantized vortices have been observed in a variety of superfluid systems, from 4He^{4}\mathrm{He}4He to condensates of alkali-metal bosons and ultracold Fermi gases along the BEC-BCS crossover. In this article we study the stability of singly quantized vortex lines in dilute dipolar self-bound droplets. We first discuss the energetic stability region of dipolar vortex excitations within a variational ansatz in the generalized nonlocal Gross-Pitaevskii functional that includes quantum fluctuation corrections. We find a wide region where stationary solutions corresponding to axially symmetric vortex states exist. However, these singly charged vortex states are shown to be unstable, either by splitting the droplet in two fragments or by vortex-line instabilities developed from Kelvin-wave excitations. These observations are the results of large-scale fully three-dimensional simulations in real time. We conclude with some experimental considerations for the observation of such states and suggest possible extensions of this work.
The physics of vortex lines in dipolar condensates is studied. Because of the nonlocality of the dipolar interaction, the 3D character of the vortex plays a more important role in dipolar gases than in typical short-range interacting ones. In particular, the dipolar interaction significantly affects the stability of the transverse modes of the vortex line. Remarkably, in the presence of a periodic potential along the vortexline, the spectrum of transverse modes shows a rotonlike minimum, which eventually destabilizes the straight vortex when the BEC as a whole is still stable, opening the possibility for new scenarios for vortex-line configurations in dipolar gases.
The static and dynamic properties of vortices in dipolar Bose-Einstein condensates (dBECs) can be considerably modified relative to their nondipolar counterparts by the anisotropic and long-ranged nature of the dipole-dipole interaction. Working in a uniform dBEC, we analyze the structure of single vortices and the dynamics of vortex pairs, investigating the deviations from the nondipolar paradigm. For a straight vortex line, we find that the induced dipolar interaction potential is axially anisotropic when the dipole moments have a nonzero projection orthogonal to the vortex line. This results in a corresponding elongation of the vortex core along this projection as well as an anisotropic superfluid phase and enhanced compressibility in the vicinity of the vortex core. Consequently, the trajectories of like-signed vortex pairs are described by a family of elliptical and oval-like curves rather than the familiar circular orbits. Similarly for opposite-signed vortex pairs their translation speeds along the binormal are found to be dipole-interaction dependent. We expect that these findings will shed light on the underlying mechanisms of many-vortex phenomena in dBECs such as quantum turbulence, vortex reconnections, and vortex lattices.