Vortex precession dynamics in general radially symmetric potential traps in two-dimensional atomic Bose-Einstein condensates

Abstract

We consider the motion of individual two-dimensional vortices in general radially symmetric potentials in Bose-Einstein condensates. We find that although in the special case of the parabolic trap there is a logarithmic correction in the dependence of the precession frequency ω on the chemical potential µ, this is no longer true for a general potential V (r) ∝ r p . Our calculations suggest that for p > 2, the precession frequency scales with µ as ω ∼ µ −2/p . This theoretical prediction is corroborated by numerical computations, both at the level of spectral (Bogolyubov-de Gennes) stability analysis by identifying the relevant precession mode dependence on µ, but also through direct numerical computations of the vortex evolution in the large µ, so-called Thomas-Fermi, limit. Additionally, the dependence of the precession frequency on the radius of an initially displaced from the center vortex is examined and the corresponding predictions are tested against numerical results.

On some configurations of oppositely charged trapped vortices in the plane

“…However, the ground state of the system, i.e., the background over which the vortices are located decreases in its density as one moves radially outwards, due to the presence of the parabolically confining external potential. As has been extensively examined since early on [23] (see also the recent discussion of [36]), this has an implication of radially increasing the precession frequency according to…”

“…Near the center of the trap it is reasonable to assume that vortices have a nearly constant precession frequency ω pr . This has been described, e.g., recently in [36]. The second term captures the inter-vortex interactions of the j-th vortex with all the other vortices (summed over k).…”

“…Vortical patterns not only in two but also in higher dimensions (e.g., filaments in the form of lines and rings in 3d) were also produced by means of dynamical instabilities such as the extensively studied transverse instability [3,20,38]. The topic of one [36] and few vortices (possibly of different signs [58,26,50,28]) remains under active experimental investigation still to this day.…”

Controlled engineering of a vortex-bright soliton dynamics using a constant driving force

“…2(d). It is worth noting that the decrease of the period as the force or the precessional amplitude increases is a very common feature of vortex dynamics [38].…”

Dynamics of the Creation of a Rotating Bose–Einstein Condensation by Two Photon Raman Transition Using a Laguerre–Gaussian Laser Pulse

“…Creation of vortex states in atomic Bose-Einstein condensates (BECs) has been the subject of quite intensive research, with particular focus on superfluid properties [1][2][3] and quantum turbulence [4][5][6][7][8][9][10]. A number of theoretical and experimental studies have considered the properties of vortex states in single and multicomponent BECs [11][12][13][14][15][16], their stability [17][18][19][20][21][22][23][24] and collective excitations [25][26][27][28][29], thus opening up an avenue of opportunities to explore and develop quantum state engineering in a macroscopic system [21,30,31]. Owing to the highly controllable state-of-the-art BEC experiments, the presence of a vortex in BECs can be detected and their dynamics can be monitored with good spatial and temporal resolution [31][32][33][34][35][36].…”