# Teaching

## Quantum computing and Quantum simulation with atoms

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)