Laser Cooling and Trapping of Atoms and Molecules

Course manual 2025/2026

Course content

This course introduces the physical principles and modern techniques of laser cooling and trapping, a cornerstone of atomic, molecular, and optical physics with key applications in precision spectroscopy, quantum technologies, and ultracold matter. We begin with the light–matter interaction for atoms (interaction Hamiltonian, rotating-wave approximation, density-matrix and optical Bloch equation methods, and angular-momentum tools such as Wigner 3j-symbols) and use these to derive optical forces on two-level systems, distinguishing scattering and dipole forces for atoms at rest and in motion.

Building on this foundation, we cover beam slowing (including Zeeman slowers), optical molasses and magneto-optical traps, and the central limits and mechanisms of cooling (Doppler and recoil limits, sub-Doppler/Sisyphus cooling). We then extend the discussion from atoms to molecules, emphasizing the additional challenges posed by multi-level structure, dark states, and type-I vs type-II transitions, and comparing trapping strategies for atomic and molecular MOTs. Further topics include magnetic and optical dipole traps, optical lattices, collisions and evaporative cooling, and state-of-the-art approaches for neutral particles.

Finally, the course introduces trapping and cooling of charged particles in Paul and Penning traps, including motional ground-state cooling and quantum-logic techniques. Weekly tutorials and numerical homework develop practical skills via simulations (rate equations, optical Bloch equations, force calculations, and Monte Carlo modeling) that mirror analysis workflows used in current research experiments.

Content:

1. Light-matter interactions, atoms (interaction Hamiltonian, rotating-wave approximation, density matrix, Wigner 3j-symbols)
2. Force on two-level atoms (scattering vs dipole forces, atoms at rest vs moving atoms)
3. Atomic/molecular beam slowing (Zeeman slower, dark states, type-I vs type-II transitions)
4. Optical molasses and magneto-optical traps (atomic MOTs, introduction to molecules, molecular MOTs)
5. Sub-Doppler cooling (Doppler limit, recoil limit, Sisyphus cooling)
6. Magnetic and optical traps, lattices for neutral atoms/molecules, state-of-the-art technologies (collisions and evaporative cooling)
7. Ion traps (Paul vs Penning trap, motional ground-state cooling, quantum-logic techniques)

The lecture will be complemented by tutorials featuring a variety of exercises aimed at reinforcing and applying the concepts covered in class. Additionally, a Mathematica notebook will be provided to support numerical exploration of key topics, such as solving rate equations and optical Bloch equations to calculate forces, as well as conducting Monte Carlo simulations for laser cooling and trapping.

Study materials

Literature

• Laser Cooling and Trapping, Harold J. Metcalf & Peter Straten, 1999.

• Introduction to Quantum Optics, Gilbert Grynberg, Alain Aspect & Claude Fabre, 2010.

Syllabus

• Will be provided on Canvas.

Practical training material

• Lecture notes, exercises and assignments  will be provided on Canvas.

Software

• Mathematica (if you wish, also Matlab, Python, ...)

Objectives

• Understanding the origin of optical forces for laser cooling and trapping.
• Understanding the confinement of neutral and charged particles (dipole traps, MOTs, magnetic traps, ion traps).
• Analyzing and evaluating the differences/challenges when applying various techniques to atoms vs molecules.

Teaching methods

• Lecture
• Self-study
• Laptop seminar

• Lectures: Provide the structured foundation—key concepts, physical intuition, and the main theoretical tools—so students can understand and derive the central results.

• Laptop seminars: Deepen and apply the material by solving problems and running simulations (e.g., OBEs/rate equations, forces, trajectories); students gain hands-on skills to model and simulate realistic, research-style experiments and interpret results.

Learning activities

Attendance

Additional requirements for this course:

Students are strongly recommended to attend all lectures and exercise sessions. 

Assessment

Mini-tests during the tutorial sessions (constitute 20% of the final grade).

Assignments

There will be homework assignments every week, which also involve numerical exercises.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Additional information

Bring your laptop to the TA sessions.

Contact information

Coordinator

• dr. M. Beyer