## Bose-Einstein condensation

In this lecture, I explain how a Bose-Einstein condensate (BEC) of ultracold atoms is created in the lab. During the first three lectures basic atom-light interaction properties are derived. Lectures 4 to 5 explain laser cooling and trapping. Lecture 6 introduces evaporative cooling and Bose-Einstein condensation. In lecture 7 the experimental characterization of some BEC properties are explained. Finally I give an overview of some of our current research projects.

This lecture was taught in autumn 2014 to 2016 in the physics master's programme of the University of Amsterdam. It was accompanied by a lecture on the theory of BEC by Gora Shlyapnikov.

Full lecture as powerpoint presention: BEC_Lecture_UvA_FS_2016.pptx (190MB).

Full lecture with notes as pdf: BEC_Lecture_UvA_FS_2016_with_Notes.pdf (41MB).

Full lecture as pdf: BEC_Lecture_UvA_FS_2016_without_Notes.pdf (55MB).

Mathematica demonstration and figures: BEC_Lecture_UvA_FS_2015.nb (2MB), Rapid_adiabatic_passage.nb (0.6MB).

LaTeX source of equations: BEC_Lecture_UvA_FS_2014.zip (15kB).

Detailed calculations for lecture 3 & 4 (pdf)

**Lecture 1**

Ultracold quantum gases:

What? Why? How?

Labtour

**Lecture 2**

Atom-laser interaction

Bloch sphere

**Lecture 3**

Dressed state picture

Optical Bloch equations

Detecting an ultracold gas

**Lecture 4**

Light forces

Molasses cooling

Sisyphus cooling

**Lecture 5**

Atomic beam oven

Zeeman slower

Magneto-optical trap

Technology for laser cooling

**Lecture 6**

Optical dipole trap

Magnetic trap

Trap technology

Evaporative cooling

Characterizing a BEC

**Lecture 7**

Characterizing a BEC

Our research:

- Laser cooling to BEC

- Towards RbSr molecules

## Quantum simulation

In this lecture, I explain how ultracold quantum gases can be used to study quantum physics in the spirit of quantum simulation. It was taught in spring 2015 in the physics master's programme of the University of Amsterdam. It was accompanied by a lecture on the theory of Fermi quantum gases by Gora Shlyapnikov.

To obtain a download link to the >600 slides powerpoint presentation used during this lecture simply write a short email to schreck at strontiumBEC.com.

**Introduction: Quantum simulation**

**Part 1: Simulation of crystalline solids**

Lattices: dispersion relation, Brillouin zone, Bloch states, Wannier states, Bloch oscillations, experimental realization

Derivation of Hubbard Hamiltonian, discussion of approximations

Superfluid to Mott-Insulator phase transition: phase diagram obtained by Gutzwiller Ansatz

Experimental observation: momentum distributions, measurement of gap, precise comparison with numerical solution

Observation of Mott shells by absorption imaging

Quantum gas microscopy: observation of superfluid to Mott-insulator phase transition

**Part 2: Magnetism**

Origin of magnetism in solid state, types of exchange interaction

Observation of super-exchange interaction

Quantum dynamics of spin impurity observed with quantum gas microscope

Quantum simulation of antiferromagnetic spin chains

Changing the tunnel matrix element by shaking

Quantum simulation of frustrated classical magnetism in triangular optical lattice

**Part 3: Artificial gauge fields**

Artificial gauge fields by rotation, detection of vortices

The quantum Hall effect

Artificial gauge fields and Berry phase

BEC in a uniform light-induced vector potential

Synthetic magnetic fields for ultracold neutral atoms

Optical lattice with magnetic flux

The Harper-Hofstadter Hamiltonian and the Hofstadter butterfly

Realizing the Harper-Hofstadter Hamiltonian

Spin-orbit coupling

**Part 4: Fermi gases**

Creation and detection

Interaction tuning: Feshbach resonances

BEC-BCS crossover: what is it? Measuring the pairing gap

The unitary Fermi gas: equation of state, second sound

Polarons

## Atom lasers

FOMO summer school 2016 lecture on atom lasers.

Powerpoint presention: 20160908_Arcachon_FOMO_School_atom_lasers_FS.pptx (59MB).

PDF: 20160908_Arcachon_FOMO_School_atom_lasers_FS.pdf (7MB).

## Introduction to quantum mechanics, part 3

This lecture is aligned with Griffiths' chapters 5 to 7 and taught in the 2nd year of the bachelor during 10 hours. To obtain a download link to the 330 slides powerpoint presentation used during this lecture simply write a short email to schreck at strontiumBEC.com.