Quantum simulations with ultracold atoms in optical lattices: past, present and future

Abstract

Ultracold atoms in optical lattices have been celebrated as the representative of the quantum simulator, which is a subcategory of a quantum computer that can solve many-body quantum problems. The system is made of ultracold quantum gases and defect-free light crystals, mimicking the behavior of electrons in a solid-state material. It provides unprecedented tunability of experimental parameters, such as the interaction between particles, dimensions, and disorder, and offers direct accessibility of the many-body quantum state through the measurement of correlation functions. It is an ideal experimental platform to realize exotic Hamiltonian like the Haldane model and to study non-equilibrium dynamics because of its high degrees of isolation from environmental noise. In this article, I review a short history of how the field comes up with the idea of a quantum simulator, the state-of-the-art quantum techniques, and future outlooks.