A passive atomtronics filter for Fermi gases

TL;DR

The paper addresses designing a passive, spin-selective component filter for a two-component Fermi gas in atomtronic circuits. It introduces density–potential functional theory (DPFT) as an orbital-free framework to compute ground-state densities of two-component fermions with repulsive contact interactions in two dimensions, and proposes a barbell trapping potential that connects two ring traps to fix the interface orientation. The authors show, first for few-body systems and then under experimentally realistic conditions, that increasing the repulsion drives a clear phase separation into one spin component per ring, with a sharp or smooth transition depending on the interaction model (bare vs dressed). They demonstrate robustness of the filter against parameter variations and trap imperfections, and illustrate that DPFT can guide the design of atomtronic devices for mesoscopic fermionic gases, including large-N regimes aligning with Cai_2022. The work also discusses broader implications and potential extensions to quantum batteries, heat engines, and integration with interferometers or spin-orbit gates.

Abstract

We design an atomtronic filter device that spatially separates the components of a two-component Fermi gas with repulsive contact interactions in a two-dimensional geometry. With the aid of density--potential functional theory (DPFT), which can accurately simulate Fermi gases in realistic settings, we propose and characterize a barbell-shaped trapping potential, where a bridge-shaped potential connects two ring-shaped potentials. In the strongly repulsive regime, each of the ring traps eventually stores one of the fermion species. Our simulations are a guide to designing component filters for initially mixed, weakly repulsive spin components. We demonstrate that the functioning of this barbell design is robust against variations in experimental settings, for example, across particle numbers, for small deformations of the trap geometry, or if interatomic interactions differ from the bare contact repulsion. Our investigation marks the first step in establishing DPFT as a comprehensive simulation framework for fermionic atomtronics.

Figures (8)

• Figure 1: Illustration of the phase transition of a two-component Fermi gas in the ring-shaped potential $V_R$ of \ref{['eq:Gaussian']}, with default parameters from Table \ref{['tab:default']}, driven by the repulsive contact interaction strength $c$. First separations (into ten domains) are visible at ${c \approx 6.2}$, and the number of domains reduces step-wise until the two components are segregated into one domain each at ${c_{\mathrm{split}} \approx 6.31}$. Due to the rotational symmetry of the system, the domain interfaces can be oriented in any direction (cf. black dashed lines). The observation of the metastable configuration at ${c = 6.3}$, with energy ${E=-1422.037\,\mathcal{E}}$ (the ground-state energy is ${E=-1422.687\,\mathcal{E}}$), heralds the transition into the symmetric split as $c$ exceeds $c_{\mathrm{split}}$. We use harmonic oscillator units.
• Figure 2: By connecting two Gaussian rings \ref{['eq:Gaussian']} with a Gaussian bridge \ref{['eq:Bridge']}, we realize the barbell-shaped potential \ref{['eq:Barbell']} as the fundamental structure for atomtronic component filtering. The black dashed line shows the contour at ${V_0/2}$. We use harmonic oscillator units.
• Figure 3: Transition of a two-component Fermi gas in a barbell-shaped potential from a mixed phase into a filtered, split phase. (a) The sweep of repulsion $c$ from 6.0 to 10.0 (see Table \ref{['tab:default']} for the other parameters) reveals the increasing spatial separation between the Fermi gas components, which respect the mirror symmetry of the trapping potential. (b) The phase transition is accompanied by a redistribution between the kinetic energy of both components and the interaction energy, while the potential energies and the total energy show comparably little variation, because the density redistributions occur preferably at small slopes of the external potential, i.e., at the bottom of the trap. (c) The trade-off between kinetic and interaction energy can be visualized with the polarization \ref{['eq:Polarization']}, which anti-correlates with the interaction energy; we rescale quantities $Q$ for presentational purposes according to ${\overline{Q} = Q/\max \abs{Q}}$. With this normalization, we also find the gradients $-\overline{\partial_c \mathcal{P}}$ and $\overline{\partial_c E_{\mathrm{int}}}$ closely correlated. We use harmonic oscillator units.
• Figure 4: Exploration of the parameter space of the barbell potential \ref{['eq:Barbell']}. Each panel shows polarization $\mathcal{P}$, interaction energy $E_{\mathrm{int}}$ ($\overline{Q}$ denotes ${Q/\max \abs{Q}}$), and their derivatives $\partial_x$ as one of the parameters (here denoted as $x$) from Table \ref{['tab:default']} is varied: bridge length $d$ (a), bridge width $\Delta_B$ (b), ring radius $R$ (c), ring width $\Delta_R$ (d), and depth $V_0$ of the potential energy (e). We find correlation patterns between $\mathcal{P}$ and $E_{\mathrm{int}}$ that are consistent with those in Fig. \ref{['fig:Standard']} and, importantly, persist as all parameters are varied individually. The vertical black dashed lines mark the parameters of the special cases shown in Fig. \ref{['fig:Others']} below. We use harmonic oscillator units.
• Figure 5: Partially mixed density profiles in various parameter regimes of the barbell potential, cf. the black dashed lines in Fig. \ref{['fig:OthersPol']}. The changes relative to Table \ref{['tab:default']} are given in the boxes. We use harmonic oscillator units.