Spin vs. position conjugation in quantum simulations with atoms: application to quantum chemistry

TL;DR

The work demonstrates a spin–position conjugation that allows bosonic atoms to emulate fermionic bonding in chemistry within optical-tweezer lattices, enabling analogue quantum simulations of mono- and divalent bonds for up to four particles with minimal total spin. By analyzing Hong-Ou-Mandel interference for both Bose-Einstein and Fermi-Dirac statistics and extending to three- and four-particle systems, it shows that symmetric and antisymmetric representations become equivalent under permutation symmetry, permitting bosons to reproduce fermionic spatial distributions. The study develops MO-LCAO-based joint density formulations to quantify antibunching as a signature of covalent-like bonding and introduces a Quantum Lego framework for preparing and tracking degenerate ground states as a mesoscopic qubit. This approach provides a practical, scalable path to simulate electronic charge distributions and bonding dynamics with neutral atoms, offering insights into reaction pathways and potential quantum-information applications in molecular settings.

Abstract

The permutation symmetry is a fundamental attribute of the collective wavefunction of indistinguishable particles. It makes a difference for the behavior of collective systems having different quantum statistics but existing in the same environment. Here we show that for some specific quantum conjugation between the spin and spatial degrees of freedom the indistinguishable particles can behave similarly for either quantum statistics. In particular, a mesoscopically scaled collection of atomic qubits, mediated by optical tweezers, can model the behavior of a valent electronic shell compounded with nuclear centers in molecules. This makes possible quantum simulations of mono and divalent bonds in quantum chemistry by manipulation of up to four bosonic atoms confined with optical microtraps.

Figures (6)

• Figure 1: Diagram visualization of transformations (\ref{['2.9']}) (left) and (\ref{['2.21']}) (right), both leading to bunching of either photons, prepared in a symmetric polarization-entangled state and mixed by a beamsplitter (BS), or electrons, incoming in a singlet spin-entangled state and scattered by potential barrier (PB), see text. The inward single arrows and outward double arrows indicate the wave-vectors, for either photons or electrons, respectively before and after scattering. The orthogonal arrows indicate their vector and spin polarizations.
• Figure 2: One-dimensional visualization of a double well microtrap potential, see text.
• Figure 3: The considered site configurations for systems of three and four particles, see text.
• Figure 4: (a) The probability density function for a single particle, calculated for a system of three particles and triangle site configuration shown in Fig. \ref{['fig3']}. Here $a=2\delta x$ and $h=2.5\delta x$, where $\delta x$ is position uncertainty of the original site state. (b)-(d) The conditional probability densities for a particle position if one particle is located at the points indicated by cross markers in the plots. The probability distributions are plotted in the $(x,y)$-plane transverse to direction of the trapping light beams with the grid unit equated to $\delta x$.
• Figure 5: Same as in Fig. \ref{['fig4']} but for configuration of four particles, shown in Fig. \ref{['fig3']}, with $a=2\delta x$ and $b=2.5\delta x$.