Simulating quantum transport with ultracold atoms and interaction effects

Quantum transport can be simulated with ultracold atoms by employing spin superpositions of fermions interacting with spin-dependent potentials. Here we first extend this scheme to an arbitrary number of spin components so as to allow simulating transport through a multiterminal quantum dot and derive a current formula in terms of a spin rotation matrix and potential phase shifts. We then show that a Fano resonance manifests itself in measuring a linear conductance at zero temperature in the case of two spin components. We also study how a weak interparticle interaction in bulk affects quantum transport in one dimension with the bosonization and renormalization techniques. In particular, we find that the conductance vanishes for an attractive interaction due to a bulk spin gap, while it is enhanced for a repulsive interaction by a power law with lowering the temperature or the chemical potential difference.

Figure 1

Upper panel: Model potential $V_{\uparrow }\left(r\right)$ in Eq. (16) for $\nu =0.5$ (dotted), $\nu =1.0$ (dashed), and $\nu =1.5$ (solid). The horizontal lines indicate resonance energies at which ${\delta }_{\uparrow }^{\ell }\left(\epsilon \right)=\pi /2$ (mod $\pi$) is crossed for $\ell =0$. Lower panel: Zero-temperature linear conductance $G$ in Eq. (14) multiplied by $2\pi$ for $d=1$ with $\vartheta =\pi /2$ as a function of $\nu$. The dotted curve indicates the nonresonant contribution from $\ell =1$.

Figure 2

“Phase diagram” in the plane of $K_c$ and $K_s^{*}$ where the upper (lower) shaded region indicates ${\overline{w}}_{\alpha }$ ($w_{\alpha }$) being relevant, while it is irrelevant elsewhere. ${\overline{u}}_{\alpha }$ is marginal on the horizontal dashed line and irrelevant elsewhere.