Courses Catalogue

Syllabus of the course: Advanced Atomic and Molecular Physics

In this web page we provide the syllabus of the course Advanced Atomic and Molecular Physics, offered by the Department of Physics.
The list of the courses offered during the current accademic year is available here.
The list of all courses offered by the Department of Physics is available here.

InstructorWolf von Klitzing
ProgramMonday, 14:00-16:00, Room 4
Wednesday,9:00-11:00,Room 4
Web page
Goal of the course

The Nobel Laureate A.A. Michelson once remarked "An eminent physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals." This is as true as ever, only that the decimal place has moved in some cases to the 18th digit. Atom-interferometric measurements of gravity can now be measured to a precision capable of detecting the gravitational pull of a person standing next to the experiment. Todays atomic clocks and atom-interferometric devices are amongst the most precise measurements of mankind – and thus carry the promise of great scientific break through.

In this course I will give an overview over precision quantum experiments with ultra-cold atoms. The course will address some of the theoretical basis but focus on the state-of-the-art experiments. However, one of the main aims of this course is to convey the fascination of fundamental experiments – to quote Michelson, who was once asked why he tried so hard to measure light with ever greater precision, gave some half-hearted talk, then smiled and said: “But the real reason is because it is such good fun.”

SyllabusThe following sections represent about one week each. Since this is the first time, that I teach this course, the list is somewhat tentative and will be adapted following the input of the students.
  • Introduction
    In the first lecture, I will put precision experiments into context. What can be measured? How? Why does it matter? I will then give an overview over the physics of this course as well as showcasing the surprising physics of ultra-cold atoms and its enormous potential for precision experiments. I will give examples of ultra-cold atoms in astronomy and compare it to the lowest temperatures achievable on earth, which can be orders of magnitude smaller than the anything in nature. We will then turn towards precision measurements. Michelson once said that "An eminent physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals." We will look at matter-wave interferometry as a tool, which provides access to the sixth or even eighteenth decimal. Atom and ion clocks produce the most precise measurement to date. Modern atom clocks now reach an absolute precision of 1016. We will discuss how such precision can be reached and what exciting new experiments can be done with this (relativistic geodesy for example). We will also briefly discuss the principles involved in gravity detection and show some of the leading experiments (in space and on earth). We will also consider one of the most promising atom-sources for precision experiment: BEC and atom lasers, which are very interesting in themselves as curious example of non-local matter.

  • Background
    We will recall some of the basics of atom physics as relevant to ultra-cold atom physics, e.g. atomic transitions and scattering rates, atomic beam splitters.

  • Matter-Wave interferometry (I)
    We will study their principles of operation, such as the coherent matter-wave beam splitters. We will discuss the operational elements and principles of the different types of atom interferometers: Michelson, Sagnac, Mach-Zehnder etc. Finally, we will discuss some of the fundamental limited of interferometers, such as projection and sampling noise

  • Quantum Gasses
    Here, we will discuss the following questions: What happens, when one cools a gas of non-interacting bosons? What happens to the particle distribution? At the lowest temperatures, we reach Bose-Einstein Condensation. How is it formed? What is required? We will also briefly discuss Fermi statistics and its effect on thermal atoms Interaction has a profound effect on condensed atoms. The interaction energies can become much larger than the confinement. We will derive the shape of a BEC due to the interactions.

  • Cooling (I)
    This section is concerned with the experimental techniques required to reach the ultra-cold temperatures, at which the thermal gas starts to exhibit quantum phenomena. The magneto-optical trap (MOT) is the first step in any quantum gas experiment. Here light is used to cool atoms down to about 100μK above the absolute zero temperature. In combination with magnetic fields the atoms can then be compressed into a small volume. We will briefly mention the need for evaporative cooling.

  • Trapping
    A dissipative trap like the MOT is always intimately linked to the environment and as such can never reach very low temperatures. Therefore, a conservative potential is required, which can serve as the perfect thermos-flask. We will discuss dipole traps, magnetic trap, and rf-dressed traps as examples just such traps. I will round this up with time-averaged traps.

  • Cooling (II)
    The second chapter on cooling will focus on how to realize evaporative cooling in conservative potentials. We will discuss dipole and two different magnetic traps. We will discuss an interesting case of cooling without collisions nor change in entropy: Delta kick cooling. Having the tools of cooling in our hands, we will look at the question How do many thermal atoms join to form a BECs? We will look at the mechanisms and dynamics of Bose-Einstein condensation.

  • Atom Lasers
    The atoms in a condensate are de-localized. They behave more like classical waves (matter-waves) than like individual atoms. So, how about matter-wave optics? Indeed, one can perform optics with matter-wave. There are magnetic lenses and mirrors and even coherent atom beam splitters. In this section we will discuss optical elements for matter-waves, and then turn to atom-lasers. We will discuss various types of atoms lasers, including the strong coupling regime, with which our laboratory has produced the most powerful atom laser in the world.

  • Matter-Wave interferometry (II)
    Having seen coherent matter-waves and its optics, including beam splitters, we will now look at interferometry with BECs. We will compare thermal interferometers to their BEC counterparts. Finally, we will turn to the question of the ultimate sensitivity of atom-interferometers.

  • Summary and Conclusions
    We will wrap up with a summary of the more interesting points of the course.

  • Presentation of course papers
    During the entire duration of the course, the students will be encouraged to read one paper of current scientific literature and present it during the lecture.


1. C. J. Pethick and H. Smith Bose-Einstein condensation in dilute gases (2nd Edition) Cambridge Univ. Press (2008)
2. P.R. Berman Atom interferometry Academic Press (1996)
3. Harold J Metcalf and Peter Van der Straten Laser cooling and trapping Springer (1999)

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