Dynamical Instability of a Doubly Quantized Vortex in a Bose-Einstein Condensate

Doubly quantized vortices were topologically imprinted in $|F=1⟩{}^{23}\mathrm{N}\mathrm{a}$ condensates, and their time evolution was observed using a tomographic imaging technique. The decay into two singly quantized vortices was characterized and attributed to dynamical instability. The time scale of the splitting process was found to be longer at higher atom density.

Figure 1

(a) Wire pattern on the atom chip. A magnetic trap is formed by a current $I_C$ flowing through the center wire in conjunction with an external uniform magnetic field $B_x$. The axial confinement along the $z$ direction is generated by currents $I_L$ and $I_R$ in the end cap wires. Each current is controlled independently. A $2\mu \mathrm{m}$ thick Au film was deposited by evaporation on a thermally oxidized Si substrate and wires were patterned by photolithography and wet etching. The width of the center wire and the end cap wires were $50\mu \mathrm{m}$ and $100\mu \mathrm{m}$, respectively. (b) Imprinting of a vortex in a Bose-Einstein condensate. By inverting the $z$ direction magnetic field $B_z$, a doubly quantized vortex was imprinted in $|F=1⟩$ condensates, using topological phases as in Ref. 19. The direction of $I_L$ and $I_R$ were also reversed to maintain the axial confinement. The dashed lines indicate the selective probing region for tomographic imaging as described in the text.

Figure 2

Decay of a doubly quantized vortex. Axial absorption images of condensates after 15 ms of ballistic expansion with a variable hold time after imprinting a doubly quantized vortex. A doubly quantized vortex decayed into two singly quantized vortices. For this data, the interaction strength was $a{n}_z\approx 7.5$ (see text for definition). The field of view in each image is $320\mu \mathrm{m}\times 320\mu \mathrm{m}$.

Figure 3

Density dependence of the decay process. The time scale for the decay process of doubly quantized vortex states was measured by observing the vortex cores and classifying them as one vortex (open circles) or two vortices (solid circles). Data were collected with three axial trap frequencies $f_z=2.7$, 3.7, and 12.1 Hz and the interaction strength $a{n}_z$ was controlled by changing the atom number by rf induced evaporation before imprinting. Typical absorption images for (a) fast decay at low density ($a{n}_z=1.5$) and (b) slow decay at high density ($a{n}_z=10.1$). The field of view in the absorption images is $300\mu \mathrm{m}\times 300\mu \mathrm{m}$. (c) The separation of two visible cores vs the hold time for $2<a{n}_z<3$ (solid triangles) and $6<a{n}_z<8$ (open triangles). The solid and dashed lines indicate the diameter of one vortex core and of the condensate, respectively.

Figure 4

Examples for the dynamic evolution after imprinting a doubly quantized vortex: (a) Surface excitation. Regular density modulation of the surface was observed after 51 ms hold time for $a{n}_z=1.8$. (b) Same as (a) with a contour line. (c) Crossing of vortex lines. 55 ms hold time and $a{n}_z=8.4$. (d) Same as (c) with guidelines for vortex lines. The field of view is $270\mu \mathrm{m}\times 270\mu \mathrm{m}$.