Double-well ultracold-fermions computational microscopy: Wave-function anatomy of attractive-pairing and Wigner-molecule entanglement and natural orbitals

TL;DR

This paper uses exact computational methods to analyze the wave-function structure, entanglement, and natural orbitals of ultracold fermions in double-well traps, revealing pairing and Wigner molecule formation across different confinement regimes.

Contribution

It provides the first detailed computational microscopy analysis of fermionic wave-function anatomy and entanglement in double-well ultracold atom systems, bridging theory and experiment.

Findings

Demonstrates attractive pairing in fermionic systems.

Shows formation of Wigner molecules in ultracold fermions.

Validates computational results with experimental measurements.

Abstract

"Bottom-up" approaches to the many-body physics of fermions have demonstrated recently precise number and site-resolved preparations with tunability of interparticle interactions in single-well, SW, and double-well, DW, nano-scale confinements created by manipulating ultracold fermionic atoms with optical tweezers. These experiments emulate an analogue-simulator mapping onto the requisite microscopic hamiltonian, approaching realization of Feynman's vision of quantum simulators that "will do exactly the same as nature". Here we report on exact benchmark configuration-interaction computational microscopy solutions of the hamiltonian, uncovering the spectral evolution, wave-function anatomy, and entanglement properties of the interacting fermions in the entire parameter range, including crossover from a SW to a DW confinement and a controllable energy imbalance between the wells. We demonstrate attractive pairing and formation of repulsive, highly-correlated, ultracold Wigner molecules, well-described in the natural orbital representation. The agreement with the measurements affirms the henceforth gained deep insights into ultracold molecules and opens access to the size-dependent evolution of nano-clustered and condensed-matter phases and ultracold-atoms quantum information.