Quantum simulator of dynamics beyond Born-Oppenheimer using ultra-cold fermionic molecules in optical lattices

Cold atomic systems in optical lattices have been one of the leading platforms to simulate quantum many-body physics over the past two decades. Their combination of exceptional control  and detection techniques has enabled the study of relevant many-body phenomena in condensed matter or lattice high-energy physics problems [1,2]. Recently, a new avenue has opened in optical lattice setups with proposals to simulate few-body problems similar to those appearing in quantum chemistry, but with different interaction scalings and dimensionalities [3]. 

Here, we propose a platform based on ultra-cold fermionic molecules trapped in optical lattices to simulate nonadiabatic effects, as they appear in certain molecular dynamical problems [4]. The idea consists of a judicious choice of two rotational states as the simulated electronic or nuclear degrees of freedom, in which their dipolar interactions induce the required attractive or repulsive interactions between them. We benchmark our proposal by studying the scattering of an electron or a proton against a hydrogen atom, showing the effect of electronic exchange and inelastic ionization as the mass ratio between the simulated nuclei and electrons –a tunable experimental parameter in our simulator– becomes comparable. These benchmarks illustrate how the simulator can qualitatively emulate phenomena like those appearing in molecular dynamical problems even if the simulated interaction occurs in two-dimensions with a dipolar scaling. Beyond the molecular implementation proposed here, our proposal can be readily extrapolated to other atomic platforms, e.g., based on fermionic Rydberg atoms.

[1] Gross, C., Bloch, I. (2017). Quantum simulations with ultracold atoms in optical lattices. Science, 357(6355), 995 (2017)

[2] A. Di Meglio, et al., Quantum computing for high-energy physics: State of the art and challenges, PRX Quantum 5, 037001 (2024)

[3]  J. Argüello-Luengo, A. González-Tudela, T. Shi, P. Zoller, J. I. Cirac, Analogue quantum chemistry simulation, Nature 574, 215 (2019)

[4] J. Argüello-Luengo, A. González-Tudela, J. I. Cirac, Optical Lattice Quantum Simulator of Dynamics beyond Born-Oppenheimer, Phys. Rev. Lett. 135 (13), 133402 (2025)