Quantized conductance through the quantum evaporation of bosonic atoms

We analyze theoretically the quantization of conductance occurring with cold bosonic atoms trapped in two reservoirs connected by a constriction with an attractive gate potential. We focus on temperatures slightly above the condensation threshold in the reservoirs. We show that a conductance step occurs, coinciding with the appearance of a condensate in the constriction. Conductance relies on a collective process involving the quantum condensation of an atom into an elementary excitation and the subsequent quantum evaporation of an atom, in contrast with ballistic fermion transport. The value of the bosonic conductance plateau is strongly enhanced compared to fermions and explicitly depends on temperature. We highlight the role of the repulsive interactions between the bosons in preventing them from collapsing into the constriction. We also point out the differences between the bosonic and fermionic thermoelectric effects in the quantized conductance regime.

Figure 1

Two reservoirs (L, R) can exchange particles through a smoothly tapered constriction inside which the spatially dependent and attractive gate potential $E_G$ is varied.

Figure 2

Linear condensate density at the center of the constriction as a function of the gate potential. The exact numerical result (thick red line) interpolates in between the Gaussian approximation (dashed blue), valid for $|E_{G0}|\gtrsim \hslash {\omega }_0$, and the Thomas-Fermi result (dotted green), holding for large $|E_{G0}|$.

Figure 3

(a) Transport function of an isotropic harmonic constriction for fermions (thin dashed line) and for bosons (full solid curve). (b) and (c): Derivatives $\partial f^F{/\partial \mu |}_T$ and $\partial f^B{/\partial \mu |}_T$ of the Fermi $\left(T/T_F=0.1\right)$ and Bose $\left(T/T_B=1.2\right)$ distributions.

Figure 4

Quantized conductance for (a) ultracold fermions $\left(T/T_F=0.1\right)$ and (b) cold bosons $\left(T/T_B=1.2\right)$. In both cases, $\hslash {\omega }_0/k_{\mathrm{B}}{T}_D=4$. For fermions, the thick solid line is the exact solution $G\left(E_{G0}\right)$ and the thin dashed curve is the single-transport-channel prediction of Eq. (3). The results have been vertically rescaled by the step heights $1/(z^{-1}\pm 1)$.

Figure 5

Atom number difference $\delta N\left(t\right)/N$ (thick solid line), its isothermal approximation ${\delta N\left(t\right)/N|}_T$ (thin solid line), and temperature difference $\delta T\left(t\right)/T$ (dashed line), following an atom number mismatch $\delta N_0$, for (a) fermions and (b) bosons, obtained by solving Eq. (4) numerically with the parameters of Fig. 4. The value of $E_G$ is chosen at the conductance step for bosons, and at the first conductance step for fermions. All plotted quantities should be multiplied by $\delta N_0/N$.