Atomic Josephson vortices

We show that Josephson vortices in a quasi-one-dimensional atomic Bose Josephson junction can be controllably manipulated by imposing a difference of chemical potentials on the atomic Bose-Einstein condensate waveguides forming the junction. This effect, which has its origin in the Berry phase structure of a vortex, turns out to be very robust in the whole range of the parameters where such vortices can exist. We also propose that a Josephson vortex can be created by the phase imprinting technique and can be identified by a specific tangential feature in the interference picture produced by expanding clouds released from the waveguides.

Figure 1

Motion of the JV along the junction (left) generated by change of relative chemical potential $\eta$ (right) from numerical simulations of the system (15), (16). Left figure: the atomic density in a single waveguide is represented by intensity of white color; the JV path in $x\text{−}t$ coordinates corresponds to the dark color (the density depletion in the JV center) relative to the white color of the background. Here $\nu =0.1$, and the dissipative term from Ref. 5 is given by the value of the kinetic parameter $\tilde{\sigma }=2$. The units of $x$ and $t$ are the coherence length $l_c$ and the coherence time $t_0$, respectively.

Figure 2

Evolution of the relative phase after the imprinting as follows from Eqs. (15), (16). Small dissipative term discussed in Ref. 5 with $\tilde{\sigma }=6$ has been added; $\nu =0.1$. The units of $x$ and $t$ are the coherence length $l_c$ and the coherence time $t_0$, respectively.

Figure 3

Interference patterns of two expanded overlapping BEC clouds released from the waveguides as given by direct numerical integration of Eq. (37). Waveguides initially contained: (a) uniform BECs, (b) two DS aligned at $x=0$, (c) JV solution located at $x=0$. The image (d) is the relative intensity between (b) and (c); $\nu =0.01$, $t=100$, $d=2^{-3∕2}$, $z_0=3$. The unit of $x$ and $y$ is the coherence length $l_c$.