Spontaneous formation of a doubly quantized vortex in the anomalous component of a trapped Bose gas

We study the behavior of an unusual doubly quantized vortex in a harmonically trapped Bose gas at nonzero temperatures by using the time-dependent Hartree-Fock-Bogoliubov equations. This structure, which exhibits nontrivial features, generates spontaneously in the anomalous fraction when phases corresponding to the singly charged vortex are imposed in the condensed and the anomalous components of the gas. Our numerical calculations show that at low temperature, condensed atoms tend to fill the core of the anomalous vortex. We demonstrate that the decay of this vortex is attributed to dissipation induced by the anomalous fluctuations. Excitation frequency and the radius core of the anomalous vortex are also investigated.

Figure 1

Condensed density (blue dotted lines) and anomalous vortex (red dashed lines) vs the radial distance for $N_c/N=60\%$ and for $\beta =1.05$ (left panel). Two-dimensional (2D) densities, integrated along the $z$ direction for the condensed atoms (red/dark blue) and anomalous vortex (green/yellow) (right panel).

Figure 2

Time evolution of the nucleation process of a doubly quantized vortex in the anomalous component at $N_c/N=55\%$. Axial images for interaction strength $a{n}_z$ = 5.6.

Figure 3

Radii of vortex cores as a function of the reduced temperature. Parameters are the same as in Fig. 1.

Figure 4

Frequency of the anomalous vortex as a function of the reduced temperature. Parameters are the same as in Fig. 1. Solid line, $\beta$ = 1.05; red dashed lines, $\beta$ = 1 (HFB-Popov approximation). Here we have followed the method outlined in [29, 33, 39] to calculate the reduced temperature.

Figure 5

Vortex frequency as a function of the anomalous fraction. Parameters are the same as in Fig. 1.