Counter-rotating vortices in miscible two-component Bose-Einstein condensates

Abstract

Counter-rotating vortices in miscible two-component Bose-Einstein condensates, in which superflows counter-rotate between the two components around the overlapped vortex cores, are studied theoretically in a pancake-shaped potential. In a linear stability analysis with the Bogoliubov-de Gennes model, we show that counter-rotating vortices are dynamically unstable against splitting into multiple vortices. The instability shows characteristic behaviors as a result of counter-superflow instability, which causes relaxation of relative flows between the two components in binary condensates. The characteristic behaviors are completely different from those of multiquantum vortices in single-component Bose-Einstein condensates; the number of vortices generated by the instability can become larger than the initial winding number of the counter-rotating vortex. We also investigate the nonlinear dynamics of the instability by numerically solving the Gross-Pitaevskii equations. The nonlinear dynamics drastically changes when the winding number of counter-rotating vortices becomes larger, which lead to nucleation of vortex pairs outside of the vortex core. The instability eventually develops into turbulence after the relaxation of the relative rotation between the two components.

Analytical study of parameter regions of dynamical instability for two-component Bose-Einstein condensates with coaxial quantized vortices

“…However, the results are not inconsistent because the coupling constant g in Ref. [10] is much larger than that in our perturbative method. …”

“…[10], which were obtained by numerically solving the differential equations. However, the results are not inconsistent because the coupling constant g in Ref.…”

“…Previous works on this matter numerically solve the differential equations (see Refs. [9][10][11]). The inter-component interaction and mutual influence between multiple vortices make the dynamical behavior of this system diverse and nontrivial.…”

Kármán vortex street in a two-component Bose–Einstein condensate

“…In order to study the vortex shedding from obstacle, we consider a two-component BEC composed of 23 Na and 87 Rb atoms. Here, in order to simplify the problem without loss of generality, the interaction parameters can be taken as g 11 =g 22 =1.0 and g 12 =g 21 =0.5 to satisfy the condition g g g 11 22 12 2 > and g 0 jj > ¢ , so that the two components are miscible and stable [38,39]. This situation can be easily realized in the experiments and it will be discussed later in detail.…”

“…In the two-component BEC, a variety of dynamical properties have been observed and reported [24][25][26][27][28][29], and the tunable inter-component interaction has been realized experimentally by using the Feshbach resonance technology [30,31]. Especially, the quantized vortices have been created and studied [32][33][34][35][36][37][38][39]. For instance, a vortex dipole can not only penetrate the interface between the two components, but also disappear or disintegrate at the interface, depending on its velocity and the interaction parameters [40].…”