Critical Energy Dissipation in a Binary Superfluid Gas by a Moving Magnetic Obstacle

We study the critical energy dissipation in an atomic superfluid gas with two symmetric spin components by an oscillating magnetic obstacle. Above a certain critical oscillation frequency, spin-wave excitations are generated by the magnetic obstacle, demonstrating the spin superfluid behavior of the system. When the obstacle is strong enough to cause density perturbations via local saturation of spin polarization, half-quantum vortices (HQVs) are created for higher oscillation frequencies, which reveals the characteristic evolution of critical dissipative dynamics from spin-wave emission to HQV shedding. Critical HQV shedding is further investigated using a pulsed linear motion of the obstacle, and we identify two critical velocities to create HQVs with different core magnetization.

Figure 1

Oscillating magnetic obstacle in a symmetric binary superfluid. (a) Schematic of the experiment. A focused near-resonant Gaussian laser beam, which provides a repulsive (attractive) potential for the spin–$\uparrow (\downarrow )$ component, undergoes sinusoidal oscillations along a linear path at the central region of the trapped sample. (b) Spin and mass density variations, $\mathrm{\Delta }{n}_s$ and $\mathrm{\Delta }n$, as functions of the obstacle strength $V_0$. For $V_0>V_c$, the spin polarization is saturated due to the density depletion of the spin–$\uparrow$ component. Insets: the representative density profiles of the spin–$\uparrow$ (yellow solid) and spin–$\downarrow$ (green dashed) components for weak (left) and strong obstacles (right).

Figure 2

Generation of spin excitations in a spinor BEC by an oscillating magnetic obstacle. Magnetization ($M_z$) images of the condensate stirred with an obstacle of $V_0/V_c\approx 0.9$ [(a)–(d)] and $\approx 2.2$ [(e)–(h)] for various oscillation frequencies $f$. The images were obtained after a 19-ms time of flight. Fully magnetized pointlike domains in (g) and (h) indicate HQVs with ferromagnetic cores. (i)–(l) Images of the spin–$\uparrow$ component for the same stirring conditions in (e)–(h), taken after Stern-Gerlach spin separation. The HQVs are distinguishable as density-depleted holes in (k) and (l).

Figure 3

Critical energy dissipation in the binary superfluid. Magnetization variance ${\sigma }_M$ as a function of the oscillation frequency $f$ for the weak (red circles) and strong (blue squares) obstacles. At the top axis, $v_{\max }$ denotes the maximum speed of the oscillating obstacle. ${\sigma }_M$ was measured from the area of $157\times 106\mu {\mathrm{m}}^2$ at the central region of the condensate. Each data point is the mean value of five to seven measurements of the same experiment, and its error bar represents their standard deviation. Inset: an expanded view on the boxed region at low $f$.

Figure 4

Critical HQV shedding. (a) Magnetization images of the condensate after a linear sweep of the strong obstacle for various obstacles’ moving velocity $v$. (b) Occurrence probabilities for spin–$\downarrow$-core HQV (red squares), spin–$\uparrow$-core HQV (blue triangles), and either of them (black circles) as functions of $v$. The probabilities for each $v$ were obtained from 14 to 18 measurements of the same experiment. The solid lines denote a guide for the eyes to each data set based on the sigmoid functions. (c) Examples of the magnetization images for $v=1.4\mathrm{mm}/\mathrm{s}$. Only spin–$\uparrow$-core HQVs appear. The two images on the right side are the images of the spin–$\uparrow$ component for the same stirring condition.