Michael Kohl, University of Bonn
In these lectures we are going to review the physics of ultracold fermionic atoms in optical lattices. We start from the basic principles of non-interacting Fermions in a band structure. Subsequently, we will move on to interacting systems and discuss the Mott insulator and anti-ferromagnetic order. The discussion of preparation and detection techniques of complex quantum states and current experiments completes the lectures.
Mikhail Lukin and Giulia Semeghini, Harvard University
Programmable quantum simulations and quantum information processing based on Rydberg atom arrays
We will discuss the recent advances involving programmable, coherent manipulation of quantum many-body systems using neutral atom arrays excited into Rydberg states, allowing the control over 200 qubits in two dimensions. These systems can be used for realization and probing of exotic quantum phases of matter and exploration of their non-equilibrium dynamics. Recent advances involving the realization and probing of quantum spin liquid states - the exotic topological states of matter have thus far evaded direct experimental detection and the observation of quantum speedup for solving optimization problems will be described. In addition, the realization of novel quantum processing architecture based on dynamically reconfigurable entanglement and the steps towards quantum error correction will be discussed. Finally, we will discuss prospects for using these techniques for realization of large-scale quantum simulators and processors.
Masahito Ueda, The University of Tokyo
Non-Hermitian Physics
Beyond-hermitian physics has recently attracted a great deal of attention due to remarkable advances in experimental techniques and theoretical methods in AMO, condensed matter and nonequilibrium statistical physics. Complete knowledge about quantum jumps allows a description of quantum dynamics at the single-trajectory level. A subclass thereof without quantum jumps can be described by a non-hermitian Hamiltonian. Here, symmetry, topology and many-body effects are fundamentally altered. Importantly, transposition and complex conjugation, which are equivalent in hermitian physics, become inequivalent, leading to proliferation of new topological phases and symmetry classes. In random matrix theory, transposition symmetry leads to two new universality classes of level-spacing statistics other than the Ginibre ensemble. In many-body physics, non-hermiticity leads to the dynamical sign reversal of magnetism in dissipative Hubbard models, violation of the g-theorem in the Kondo problem, and quantum phase transitions without gap closing. In the lecture, I will provide an overview on the fundamentals and new frontiers about beyond-Hermitian quantum physics.
Ref. Y. Ashida, Z. Gong, and M. Ueda, Adv. Phys. 69, 249 (2021)
Baptiste Boyer, Université de Sherbrooke
Encoding quantum information in states of light: bosonic codes in circuit QED
The main approach to quantum computing is to encode logical information in ensembles of physical two-level systems such as superconducting qubits or trapped ions. Another promising strategy is rather to encode the information in a harmonic oscillator using a bosonic code. Because of the simplicity of these physical systems, harmonic oscillators are often longer-lived than physical qubits, and have simpler error models. Moreover, their large Hilbert space (formally infinite) allows to redundantly encode the information using a small amount of hardware.In these lectures, I will introduce these bosonic codes and some related topics. I will discuss the main codes that are studied today, how to prepare the code words, how to perform logical operations and how to visualize them.
Masahito Ueda, The University of Tokyo
Quantum Thermalization
Ultracold atomic physics has offered a fresh view about why isolated quantum systems thermalize without thermal reservoirs. This question dates back to von Neumann’s original attempt to derive the second law of thermodynamics from quantum mechanics. Quantum thermalization also has a close link with quantum information because thermalization proceeds in Hilbert space rather than phase space via quantum entanglement. Moreover, recent advances in quantum gas microscopy has enabled one to observe single-shot measurement of a quantum many-body wavefunction at the level of single atoms. In this regime, measurement backaction cannot be ignored and we are led to reconsider the foundation of statistical mechanics to incorporate measurement backaction and ponder whether thermalization occurs at the level of single quantum trajectories. This question is relevant to quantum computation. In the lecture, I will give a brief introduction of quantum thermalization and review some of the recent experiments in ultracold atoms.
Wolfgang Ketterle, Massachusetts Institute of Technology
Wednesday, July 13
Superfluidity, Bogoliubov excitations and the superfluid-to-Mott-insulator transition in optical lattices
In this lecture, we start out with the weakly interacting Bose gas and its excitation spectrum. We discuss the limiting cases of bosons in weak and strong lattices, and then describe the quantum phase transition between those two limits.
Friday, July 15
Spin physics of ultracold atoms in optical lattices
Starting from the Bose-Hubbard model, we derive spin Hamiltonians where spin-spin interactions arise due to superexchange. Heisenberg spin models, where only neighboring spins interact, are the paradigmatic model for many interesting phenomena. Using lithium-7 atoms and Feshbach resonances to tune the interactions, one can create spin ½ Heisenberg models with adjustable anisotropy, including the special XX-model which can be exactly solved by mapping it to non-interacting fermions. Spin transport changes from ballistic to diffusive depending on the anisotropy. For transverse spin patterns, a superexchange induced effective magnetic field causes dephasing. Spin helices can be exact eigenstates for special values of their winding angle and are called phantom helix states since they contribute momentum, but no energy.
Tanya Zelevinsky, Columbia University
Cold molecules for fundamental physics and chemistry
Techniques for controlling quantum states of atoms have led to extremely precise metrology, studies of degenerate gases, and new quantum information technologies. Extending such techniques to molecules further enriches the understanding of fundamental physics, basic chemical processes, and many-body science. Samples of ultracold molecules can be created by binding laser-cooled atoms, or by direct cooling. We cover very basic properties of molecules and discuss applications of cold molecules in fundamental physics and chemistry.
Tuesday Industry Panel
Philippe Bouyer, MuQuans
Jim Shaffer, QVIL
Will Lunden, Vector Atomic
Georg Raithel and David Anderson, Rydberg Technologies
Moderator: John Donohue, Institute for Quantum Computing
Wednesday Industry Panel
Tom Noel, ColdQuanta
Justin Ging and Krish Kotru, Atom Computing
Tony Ransford, Quantinuum
Harry Levine, Amazon AWS Quantum
Moderator: John Donohue, Institute for Quantum Computing
