Quantencomputing und Quantensimulationen mit Atomen
Quantum computing and quantum simulation with atoms

This module 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.

After successful completion of the module the students are able to:

1. Explain the working principle of different laser cooling techniques
2. Understand and describe the properties of optical potentials generated with laser beams
3. Understand the realization and limitations of single-qubit and two-qubit gates in atom arrays
4. Explain basic quantum algorithms
5. Understand the rich properties of the phase diagram of Fermi-/Bose-Hubbard models
6. Describe different experimental techniques to study many-body systems
7. Discuss different model systems that can be realized with cold atoms for quantum simulation

No preconditions in addition to the requirements for the Master’s program in Quantum Science and Technology.

The module consists of lectures (4 SWS) and tutorial classes (2 SWS). The main teaching material will typically be presented on the blackboard, or a tablet computer and projector, supplemented by computer presentation slides to show important research results. Weekly problem sets are offered to comprehend the lecture content better and improve their familiarity with them. The solutions to the problem sets are discussed in the weekly exercise classes.

Blackboard / tablet computer, computer presentation slides

Exploring the Quantum, Atoms, Cavities and Photons by S. Haroche and J.-M. Raimond

Quantum Computation & Quantum Information by M. A. Nielsen, I. J. Chuang

A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nature Physics 16, 132-142 (2020)

Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems, M. Lewenstein, A. Sanpera, V. Ahufinger, OUP Oxford

I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases,
 Rev. Mod. Phys. 80, 885 (2008)

N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands für ultracold atoms, Rev. Mod. Phys. 91, 015005 (2019)

There will be a written exam of 120 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

• Describe the realization of a two-qubit gate in an atom array
• Discuss the experimental verification of a successful generation of a Bell-state
• Derive an expression for the AC-Stark shift
• Explain the phase diagram of the single-component Bose Hubbard model
• Explain the technique of Floquet engineering for the realization of artificial magnetic fields