Superfluid transport dynamics in a capacitive atomtronic circuit

We simulate transport in an atomtronic circuit of a Bose-Einstein condensate that flows from a source region into a drain through a gate channel. The time-dependent Gross-Pitaevskii equation (GPE) solution matches the data of a recent experiment. The atomtronic circuit is found to be similar to a variable-resistance RLC circuit, which is critically damped at early times and shows $\mathit{LC}$ oscillations later. The GPE also predicts atom loss from the drain. Studies of the dependence of condensate transport upon gate parameters suggest the utility of the GPE for investigation of atomtronic circuits.

Figure 1

The potential in the horizontal ($xy$) plane consists of the mask potential and the $xy$ part of the (harmonic) sheet potential. The mask potential is zero inside hard-walled circular wells [with centers $(x_k,y_k)$ and radii $r_k$ where $k=1,2]$ and is equal to $V_d$ outside; inside the channel the mask potential is harmonic along the $y$ direction plus a constant step.

Figure 2

Atom number imbalance (with error bars) between source and drain wells versus time from Ref. [4] for different channel transverse trapping frequencies, ${\omega }_y/2\pi$: 112 Hz (gray *'s, bottom curve); 121 Hz (green circles, middle curve); and 129 Hz (blue triangles, top curve). For all cases the channel length was $L_c=26\mu \mathrm{m}$ and the well depths where $V_0/k=83\mathrm{nK}$ where $k$ is the Boltzmann constant. The red solid curves show the GP simulation. The number of condensate atoms was taken to be $N=480000$. The middle and top curves have been vertically offset by 0.5 and 1.0, respectively, for clarity.

Figure 3

(a) Number imbalance, $\mathrm{\Delta }N\left(t\right)$, for a dumbbell potential with channel length $L_c=20\mu \mathrm{m}$, Thomas-Fermi width of $w_{\mathrm{TF}}\approx 22\mu \mathrm{m}$ (or transverse frequency ${\omega }_y/2\pi =63$ Hz), well depth of $V_d/k=97\mathrm{nK}$, and $N=436000$ atoms. The bottom (red) curve is the GP solution. The top (blue) curve shows the fraction of initial number of atoms remaining in the dumbbell area versus time. (b) Dumbbell optical density snapshots at four times during filling of the drain well. (c) Enlargement of the dumbbell optical density at $t=15\mathrm{ms}$. Atoms that flow straight along the dumbbell axis can collide with atoms that bounce off the drain wall at angle $\theta$.

Figure 4

(a) Exponential decay time, $\tau (L_c,w_{\mathrm{TF}})$, vs. the length of the channel $L_c$ and the Thomas-Fermi width of the channel, $w_{TF}$. (b) Conductance $G=1/R$ vs one-dimensional channel density, $n_{1D}$, with a linear fit.

Figure 5

(a) Model RLC circuit with variable resistance. (b) Number imbalance, $\mathrm{\Delta }N\left(t\right)$, from the Gross-Pitaevskii (GP) equation and fitted result (see text) for a dumbbell potential with channel length $L_c=20\mu \mathrm{m}$ and and Thomas-Fermi width of $w_{\mathrm{TF}}\approx 22\mu \mathrm{m}$. (c) The time-dependent resistance, $R\left(t\right)$, derived from the fitted number imbalance.

Figure 6

Classical model for a collision of atoms that bounce off the wall with those that come straight through. Two particles each having mass $m$ and speed $v$ collide at an angle $\theta$.

Figure 7

Collision as observed in the CM frame. The particle speeds before and after the perfectly elastic collision are the same but the velocity directions have rotated by an angle ${\theta }_f$ after the collision.

Figure 8

Collision as observed in the CM frame. The particle speeds before and after the perfectly elastic collision are the same but the velocity directions have rotated by an angle ${\theta }_f$ after the collision.