Double-Well Ultracold-Fermions Computational Microscopy: Wave-Function Anatomy of Attractive-Pairing and Wigner-Molecule Entanglement and Natural Orbitals

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 analoguesimulator mapping onto the requisite microscopic hamiltonian, approaching realization of Feynmans' 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.Key words: ultracold atoms, double-well nano-confinement, Wigner molecule, configuration interaction, entanglement, strong correlated matter *Corresponding Author: uzi.landman@physics.gatech.edu arXiv:1508.02308v3 2 Ingress to the origins of complex physical phenomena often requires experiments whereby theories are tested or suggested through artificial manipulations of physical circumstances. During the past decade, a cornucopia of new tools have emerged resulting from the discovery and advancement of methods for the preparation and trapping of ultracold atomic gases, controlled tuning of the interparticle interactions (via magnetic manipulation of the Feshbach resonance), and the creation of synthetic gauge fields through atom-light interactions in optical lattices of varied geometries and topologies 1,2 . The remarkable pristine nature of these systems, and the exquisite level of control that can be exercised over them, brought forth a realization of Richard Feynman's vision 3 for the construction of physical quantum simulators, capable of an exact simulation, of systems or situations that are computationally or analytically intractable. Indeed, in the past several years we witnessed a surge of realizations of such exact simulations addressing diverse fields (see reviews in refs.1 and 2), including in particular the behavior of strongly interacting fermions where computations are precluded because of the "fermion sign problem." 4 . These systems range from high-Tc superconductivity 1,2 , collosal magnetoresistance 5 and quantum Hall effects 2 to atomic frequency resonators 6 , interferometry 7,8 , matter wave gyroscopes 9 and the development of scalable quantum computers with neutral atoms 10,11 .Progress aiming at a "bottom-up" app...

Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg andt–Jmodels

“…The external confining potential (in H(i)) that models a DW is based on a two-center-oscillator (TCO) model [12,26] exhibiting a variable smooth neck along the x-direction. Along the x direction, this TCO model allows for an independent variation of both the separation d and of the barrier height V b between the two wells; see figure 3.…”

“…To date the theoretical studies of magnetism of a few ultracold atoms have mainly addressed [17][18][19][20][21][22] strictly one-dimensional systems trapped within a SW (see, however, [19,20] for DW configurations), where the fermionization theory [23][24][25] (applicable to 1D systems in the limit of infinite strength of the contact interaction) can assist in inventing analytic forms for the correlated many-body wave functions. However, the recently demonstrated ability to create needle-shaped double well (DW) traps [15], and the anticipated nearfuture further development of small arrays of such needle-like quasi-1D traps in a parallel arrangement (PA, see schematics in figure 1), whose corresponding physics incorporates certain two-dimensional (2D) aspects [26], enjoin the development of additional conceptual and computational theoretical methodologies.…”

“…In this paper, using large-scale configuration-interaction (CI) calculations as means for exact diagonalization of the microscopic Hamiltonian, we report that for N=4 (even number) strongly interacting ultracold fermions in a DW trap with parallel arrangement (DWPA [26]; see figures 1(II), (III)) the many-body problem can be reduced to that of a 2D rectangular AFM Heisenberg ring. The associated mapping between the many-body wave function and the spin eigenfunctions [31] for N=3 and N=4 electrons confined in single and double semiconductor quantum dots has been predicted in previous studies [11,12] to occur through the formation of quantum molecular structures in the regime of strong long-range Coulombic repulsion.…”

“…The SPD and CPD in (h), (i) correspond to the S=0, S z =0 CI excited state (orange curve in the associated spectrum (e)). g here is the 1D contact-interaction strength along the y direction [26]. All three CPDs display the distributions of the two down spins when the fixed spin-up fermion (see the black arrow) is placed at = -( r 0, 0.8 like + He 2 , NO, and -F 2 .…”

“…The emergence of the simple, as well as the resonating Heisenberg clusters, is a consequence of the spatial localization of the strongly interacting, highly correlated fermionic atoms and the formation [26] of quantum 1D and 2D molecule-like structures, referred to as ultracold Wigner molecules (UCWMs). The name of Wigner is used here in the context of ultracold atoms in order to emphasize the universal aspects that are present in the few-fermion molecular structures irrespective of the nature of the repelling two-body interaction, i.e., contact versus long-range Coulomb.…”