Resistive Flow in a Weakly Interacting Bose-Einstein Condensate

We report the direct observation of resistive flow through a weak link in a weakly interacting atomic Bose-Einstein condensate. Two weak links separate our ring-shaped superfluid atomtronic circuit into two distinct regions, a source and a drain. Motion of these weak links allows for creation of controlled flow between the source and the drain. At a critical value of the weak link velocity, we observe a transition from superfluid flow to superfluid plus resistive flow. Working in the hydrodynamic limit, we observe a conductivity that is 4 orders of magnitude larger than previously reported conductivities for a Bose-Einstein condensate with a tunnel junction. Good agreement with zero-temperature Gross-Pitaevskii simulations and a phenomenological model based on phase slips indicate that the creation of excitations plays an important role in the resulting conductivity. Our measurements of resistive flow elucidate the microscopic origin of the dissipation and pave the way for more complex atomtronic devices.

Figure 1

The experimental setup. (a) Two repulsive potentials at $\pm \theta$ form two weak links and separate two regions, i.e., a source and a drain. Both weak links are set into motion with equal and opposite speed $v_{\mathrm{WL}}$, inducing a flow of atoms from the source into the drain. The regions are characterized by the number of atoms $N_{S,D}$ and the chemical potential ${\mu }_{S,D}$. (b) In situ absorption images of the atomic density after a variable time $t$. For this speed ($v_{\mathrm{WL}}=13\mu \mathrm{m}/\mathrm{s}$), we observe no change in the density far from the barriers. (c) On the other hand, a barrier speed of $v_{\mathrm{WL}}=880\mu \mathrm{m}/\mathrm{s}$ results in a density difference, which corresponds to a chemical potential difference that allows for resistive flow. In (b),(c) the strength of the weak link is $U_{\mathrm{WL}}/{\mu }_0=0.53(6)$, where ${\mu }_0$ is the chemical potential before applying the weak links. The field of view in (b) and (c) is $72\mu \mathrm{m}\times 72\mu \mathrm{m}$.

Figure 2

Time evolution of the chemical potential difference $\mathrm{\Delta }\mu$ as function of time for different weak link speeds $v_{\mathrm{WL}}$. For this data, the strength of the weak link is $U_{\mathrm{WL}}/{\mu }_0=0.53(6)$, where ${\mu }_0/h=3\mathrm{kHz}$. The red circles represent the experimental data. The black dash-dotted line shows the superflow model, which does not accurately predict the increase in $\mathrm{\Delta }\mu$ (lower row). In contrast, the data show good agreement with the resistive flow model (blue dashed line). The GPE calculation (red line) shows qualitative agreement.

Figure 3

Final chemical potential difference for different weak link speeds and strengths. $\mathrm{\Delta }{\mu }_F$ is measured after a sweep angle of approximately 90°. Shown are the experimental data (red circles), the flow model incorporating resistance (blue dashed line) and the superflow model (black dash-dotted line). The results of the GPE calculation (red line) are compared to the experimental data in the middle panel. The middle panel corresponds to the potential strength presented in Figs. 1 and 2.

Figure 4

Conductance (upper panel) and maximum superfluid current (lower panel) for different weak link strengths. These values (filled circles) are obtained from fits of the data shown in Fig. 3, using Eq. (1). For the highest weak link strengths (open circles), this model fails to describe the data well. We fit the values shown with the estimates of the conductance and the superfluid current obtained from the phase-slip picture (solid red line).