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arXiv:2002.09373 · Physical Review Research

Quantum simulation of two-dimensional quantum chemistry in optical lattices

Javier Argüello-Luengo, Alejandro González-Tudela, Tao Shi, Peter Zoller, J. Ignacio Cirac

Published Oct 16, 2020• 16 citations
arXivHTMLPDF

Abstract

The authors propose to explore the electronic states of chemistry models using fermionic cold atoms trapped in an optical lattice as a simulator. They show that different schemes can be used to induce an effective repulsion among these simulated electrons, and numerically benchmark the effect of discretization for simple molecules.
DOI
10.1103/physrevresearch.2.042013

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•May 12, 2020•1 citation
Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work [J. Arg\"uello-Luengo et al., Nature (London) 574, 215 (2019)], ultracold fermionic atoms have been proposed for this purpose by showing us how to simulate in an analog way the quantum chemistry Hamiltonian projected in a lattice basis set. Here, we continue exploring this path and go beyond these results in several ways. First, we numerically benchmark the working conditions of the analog simulator and find less demanding experimental setups where chemistry-like behavior in three dimensions can still be observed. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite-size effects and provide a way to mitigate them. Finally, we benchmark the simulator characterizing the behavior of two-electron atoms (He) and molecules (HeH+{\mathrm{HeH}}^{+}HeH+) beyond the example considered in the original work.
Here, we propose a platform based on ultracold fermionic molecules trapped in optical lattices to simulate nonadiabatic effects, as they appear in certain molecular dynamical problems. 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.
A quantum simulator is a well-controlled quantum system which can be used to simulate another quantum system. Quantum degenerate gases confined by optical standing waves(optical lattices) have been considered to simulate condensed matter systems. We focus on two issues in this problem. The first one is the realization of interesting quantum phases by engineering Hamiltonians with the cold atoms toolbox. Secondly, the systems we studied are often intractable to analytical methods, which makes it a crucial issue to solve them with numerical methods. For the first issue we find several interesting phases can be studied with cold atoms in optical lattices. We show that a ppp-wave superfluid is stablized through a dissipation blockade mechanism. This mechanism also induces a new insulator formed by ppp-wave Feshbach molecules. We find that the anisotropic nature of interaction between polar molecules or dipolar atoms can be used to realize two charge density waves with different patterns and a supersolid phase which has not been found conclusively in the condensed matter system. Finally, we propose to realize a long sought spin liquid phase with hard-core bosons subject to a spin-dependent lattice and Raman induced hoppings. For the second issue we choose to numerically study these systems with the so-called tensor network algorithm which is a variational method based on the matrix(tensor) product states product states which are designed to approximate generic wave functions from their entanglement properties. In general the tensor network algorithm has advantages that it is applicable beyond one dimension, and can be used to study physical properties in the thermodynamic limit directly. We apply this method to map out the phase diagrams of the above systems. Furthermore, we show that it is capable of capturing the phase diagram of a frustrated magnetism model, the Heisenberg model on a checkerboard lattice. The great controllability and isolation from the environment of a cold atom system offer a playground to study interesting physics in strongly correlated systems. Several proposed control schemes in this thesis have been demonstrated in experiments. By providing detailed evidence from numerical simulations, this work addresses practical routes to novel quantum phases.
Most experiments with ultracold atoms in optical lattices have contact interactions and therefore operate at high densities of around one atom per site to observe the effect of strong interactions.Strong ranged interactions can be generated via Rydberg dressing, which opens up the path to exploring the physics of few interacting particles.Rather than the unit cells of a crystal, the sites of the optical lattice can now be interpreted as discretized space.This allows the study of completely new types of problems in a familiar architecture.We investigate the possibility of realizing problems akin to those found in quantum chemistry, although with a different scaling law in the interactions.Through numerical simulation, we show that simple pseudoatoms and pseudomolecules could be prepared with high fidelity in state-of-the-art experiments.
Abstract. We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize the majority of phases in the periodic table of topological insulators.
In this thesis, I present the experimental realisation of the two-dimensional Hubbard model with ultracold fermionic Potassium-40 atoms in optical lattices. By tuning the dimensionality, kinetic and interaction in the optical lattices, we perform an analogue quantum simulation to explore the phase diagram of the Hubbard model. \n \nThe first key result is the experimental observation of particle-hole symmetry, namely a phase mapping between repulsive and attractive interactions. We compare a density-ordered, Mott-insulating phase with repulsive interaction to a spin-ordered, preformed pair phase and found excellent agreement with the theoretical prediction. The precise control and excellent detection capability of our quantum gas apparatus allow us to validate the particle-hole symmetry, and utilise it to explore quantum phases with a novel approach. \n \nNext, we investigate the spin-ordering on the repulsive side. By implementing a novel scheme based on coherent manipulation of spin correlations, we probe the anti-ferromagnetic ordering in the low-temperature phase diagram. The momentum-resolved spin correlations permit the reconstruction of spatial correlators without site-resolved imaging fidelity. \n \nFinally, we probe the attractive side of the phase diagram with a focus in pairing phenomenon, in which we draw a close analogy with BCS-BEC crossovers present in high-temperature superconducting cuprates and trapped ultracold Fermi gases. From the pair correlation function derived from thermodynamics observables, we observe the competition between the effective Pauli repulsion in fermionic systems and the on-site attraction we implemented.