Lecture: Quantum computing and Quantum simulation with atoms

SoSe 2023

This course covers applications of ultracold neutral atoms for quantum technologies, with the main focus on quantum simulation and quantum computation. Atoms provide many opportunities for the realization of high-fidelity qubits across different energy scales, ranging from the microwave to the optical domain. Laser cooling techniques allow us to efficiently cool the atoms to extremely low temperatures, so that atoms can be trapped in optical potentials generated with laser beams. The high degree of control that has been achieved, for instance, led to the development of the world’s best clocks. In this course we will introduce fundamental concepts and experimental techniques needed to prepare, manipulate and detect cold neutral atoms in optical arrays. We will discuss how interactions between atoms can be engineered to realize few-qubit gates to build a universal quantum computer. Moreover, the interaction between and the dynamics of many particles in optical arrays naturally enable analog quantum simulations of complex many-body systems, ranging from condensed matter to statistical physics and high-energy physics.

4h Lecture + 2h Tutorials, 9 ECTS points (LMU system)

Teaching assistants

Simon Karch
Renhao Tao

Time & Place

Monday 2-4pm, H030 in Schellingstr. 4
Tuesday 2-4pm, N020, kleiner Physikhörsaal

Prerequisites

Basic knowledge in atomic physics and quantum mechanics.

Content

I. Rydberg atom arrays
1. Fundamentals

Dipole-dipole interactions between atoms
Rydberg atoms
Two-photon excitation and Rydberg blockade
Lindblad master equation & composite quantum systems
Rydberg dressing

2. Quantum simulation & Quantum computation

Spin models and topology in the SSH model
Artificial magnetic fields
Digital quantum computation fundamentals
Rydberg-blockaded phase gate, parity oscillations
Geometric phase, spin-1/2 particle in magnetic field

II. Initialization & detection

Trapping and cooling of neutral atoms
Doppler cooling and doppler limit
Magneto-optical trap and (Raman) sideband cooling

III. Ultracold atoms in optical lattices

Optical lattices
Bose-Hubbard model
Fermi-Hubbard model
Artificial gauge fields and topology

Two-qubit gates using controlled collisions

Literature:

A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nature Physics 16, 132-142 (2020)
T. F. Gallagher, Rydberg Atoms, Cambridge University Press
M. Saffman et al., Quantum information with Rydberg atoms, Rev. Mod. Phys. 82, 2313 (2010)
Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems, M. Lewenstein, A. Sanpera, V. Ahufinger, OUP Oxford
F. Marquardt and A. Püttmann, Introduction to dissipation and decoherence in quantum systems, arXiv:0809.4403
N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands for ultracold atoms, Rev. Mod. Phys. 91, 015005 (2019)