Quantum simulations with cold atoms

Ultracold atoms have become extremely well controlled systems, whose parameters can be settled precisely and independently. Such high level of control and the detection possibilities have opened the way to a large variety of applications. Among them, the concept of quantum simulation, envisioned by Richard Feynman, has been extensively investigated in the cold atom domain in the last decades. The idea is to use a well-controlled quantum system (here ultracold atomic quantum gases) to reproduce the behavior of another quantum system, which cannot be directly calculated, even with the computer capacities available nowadays.

One of the main assets of ultracold atomic clouds for quantum simulation is that they constitute systems with a large number of atoms that can be isolated from their environment. Additionally, even though ultracold atomic clouds are dilute gases, interatomic interactions play a major role, leading to collective effects within the clouds. Ultracold quantum gases are therefore particularly well suited to simulate many-body effects, encountered for instance in condensed matter physics. In addition, dynamics is accessible thanks to the large time scales associated to the low energy scales of ultracold atoms.

A striking example of the link between cold atoms and condensed matter physics is the possibility to trap atoms in optical lattices, i.e. spatially periodic trapping potentials, which present analogies with the crystal structure of solids. Such a system offers the possibility to control in an independent way all the parameters of the Hubbard Hamiltonian (Fermi or Bose-Hubbard Hamiltonian, depending on the fermionic or bosonic nature of the trapped atoms), which governs its behavior. In this context, the experiment that pioneered quantum simulations with cold atoms was the demonstration of the superfluid-Mott insulator transition in 2002 in the group of Immanuel Bloch (Germany).

Since then many experiments have been performed with cold atoms to simulate fundamental problems encountered in other domains, in condensed matter physics but also in nuclear physics, astrophysics or gravitational physics. Many experimental and theoretical achievements have been realized on e.g. quantum magnetism, topological phases, engineering unconventional Hamiltonians using temporal driving, quantum transport, low-dimensional systems, strongly interacting fermions, mixtures, long-range interactions, to name a few. Over the years, the subject of quantum simulations with ultracold atoms have become a field in itself, with many groups involved and dedicated conferences.

Even though some of the achievements mentioned above have been presented at other sessions of the Cold-Atoms PreDoc School, we think that a school dedicated to quantum simulations with ultracold atoms is timely, regarding the recent scientific advances and the strong interest worldwide. Among the numerous subjects presented above, we chose to focus in the 2021 school on the following aspects, non-equilibrium dynamics, quantum magnetism, temporal driving and topology, quantum transport, that are important research directions in the field.