Figure 1

Experimental configuration. (a) Schematic of the toroidal optical dipole trap formed at the intersection of two red-detuned beams: a horizontal “sheet” beam and a vertical Laguerre-Gaussian beam (${\mathrm{LG}}_0^1$) with a ring-shaped intensity maximum. A pulsed pair of Raman beams (large downward arrows) copropagating with the LG trapping beam creates circulation in the condensate. (b) Energy level diagram for the Raman transition: $|F=1,m_F=-1⟩\to |F=1,m_F=0⟩$. One Raman beam carries $\hslash$ orbital angular momentum per photon (${\mathrm{LG}}_0^1$), the other carries none (Gaussian); the condensate is transferred to a quantized ($l=1$) circulating state. (c) False-color absorption image showing the normalized column density of a condensate in the trap, viewed from above. Arrows: Raman beam polarizations and magnetic bias.Reuse & Permissions

Figure 2

(a) Flow survival as a function of chemical potential ${\mu }_0$ for two barrier heights: $\beta /h=650\mathrm{Hz}$ (upper, blue) and $\beta /h=780\mathrm{Hz}$ (lower, red). Presence or absence of flow for a single condensate is shown by closed circles. Open circles are the average of data within the bins (vertical lines), representing the flow survival probability ($P_{\mathrm{flow}}$) of each bin. A critical chemical potential ${\mu }_c$ for stable flow is found from a sigmoidal fit (solid lines) to the data for each $\beta$. Inset: In situ absorption image of a condensate near ${\mu }_c$ (${\mu }_0/h=870\mathrm{Hz}$, $\beta /h=650\mathrm{Hz}$). (b) Values of ${\mu }_c$ at different $\beta$, determined by fits as described in (a). The open circles correspond to the data in (a). The vertical error bars reflect the width of the sigmoidal fit, $\pm 2{\mu }_w$. The horizontal error bars are the 20 Hz uncertainty in calibrating $\beta$. The dotted line is a linear fit to the data, with slope 1.6(2). Insets: Typical TOF absorption images showing the presence (top left) and absence (bottom right) of circulation.Reuse & Permissions

Figure 3

Critical flow velocity $v_c$ above which the circulation becomes unstable, for each of the barrier heights in Fig. 2b. The value of $v_c$ is shown normalized to the effective sound speed at the barrier ($c_{\mathrm{eff}}$) and is plotted as a function of $c_{\mathrm{eff}}$. The horizontal error bars are the estimated uncertainty in $c_{\mathrm{eff}}$. The vertical error bars are the combined experimental uncertainty in $v_c$ and $c_{\mathrm{eff}}$. The measured ratio $v_c/c_{\mathrm{eff}}\approx 0.6$ and is independent of $c_{\mathrm{eff}}$ to within the experimental uncertainty. Vortexlike excitations are expected to occur in this system at and above a velocity $v_F$, where $v_F<c_{\mathrm{eff}}$ [13]. The gray band indicates estimated upper and lower bounds (see text) on $v_F/c_{\mathrm{eff}}$, using Feynman’s approximate expression for $v_F$.Reuse & Permissions