McMaster University Department of Physics & Astronomy           McMaster University

Overview of Ultra-Cold Atoms

Ultracold atoms are a new area of research which began with the development of the technique of laser cooling (1997 Nobel prize in Physics for Chu, Cohen-Tannoudji and Phillips). Laser cooling allows one to cool atoms down to some millionths of a degree above absolute zero, they can then be held in atom traps made from electromagnetic fields and/or `optical lattices’ made from the interference of two or more laser beams. In this second configuration the atoms are analogous to electrons in a crystal lattice like those found in a metal, but with (at least) three crucial differences:

1) Atoms in traps and lattices are extremely idealized systems with almost no imperfections or impurities and minimal interactions with the environment. They are therefore simple to describe theoretically and maintain their quantum coherence for long times in comparison to the relevant timescales of the dynamics.

2) In atomic systems almost all of the parameters are under our control. For example, the dimension and symmetry of the lattice, the strength and even the sign of the interatomic interactions, can be chosen at will.

3) The measurement schemes are radically different from traditional condensed matter schemes, e.g. single atoms can now be non-destructively imaged, allowing us to track (and address) individual atoms in real time.

Cold atoms can therefore be used to investigate single- and many-particle quantum mechanics in a system that can be stripped down to the bare essentials. A good example is the superfluid to Mott insulator transition (the Mott insulator state is believed by some people to play a role in high-temperature superconductivity), which was observed in atoms in an optical lattice in 2002 [Greiner et al, Nature 415, 39 (2002)]---see figure. At a particular ratio between the lattice depth and the interaction strength the atoms undergo an abrupt change from being in a superfluid state, with the atoms delocalized across the lattice, to suddenly having exactly one atom per site with highly suppressed fluctuations. This is an example of a so-called quantum phase transition between different ground states of a many-particle system, in this case between a coherent state, where each atom is in a superposition of being on many different sites, and a Fock state of exactly one per site.


The superfluid-to-Mott insulator experiment by Greiner et al, Nature 415, 39 (2002). a) In the superfluid state the atoms are free to hop around the lattice. There is thus coherence between sites and upon release and expansion of the atomic cloud an atomic matter-wave interference pattern is observed. b) In the Mott insulator state there is exactly one atom per site (Fock state) with no coherence between wells so that upon release and expansion no interference is observed.


A Bose-Einstein condensate (BEC) is a quantum-coherent state of matter in which every atom is in the same quantum state. From an AMO perspective a BEC is to atoms what a laser is to photons. Lasers were pure research in the 1950s and1960s but nowadays they are found in a tremendous range of technology from communications (e.g. the light in optical fibres) to medicine to CD players and supermarket checkouts. Coherent matter-wave optics based on BECs (where all the atomic de Broglie waves are in phase) is just starting out, but is rapidly becoming a very active research area. One reason for all the excitement is that the wavelength of atoms can be orders of magnitude smaller than that of light and so an interferometer based on atoms has the potential to be much more sensitive. Another very important difference is that atoms interact quite differently with their environment than photons. For example, atoms couple directly to the gravitational field and so can be a sensitive measure of gravity. It may come as a surprise to learn that, although gravity has been intensively studied on large length scales, the situation at short length scales, below about a millimeter, is comparatively unknown. Atomic interferometers hold out the possibility of making exquisitely sensitive measurements of the gravitational field at very small distances from an object. Such measurements might have far-reaching consequences since string theory, the current most fundamental but as yet untested theory of `everything’, predicts extra dimensions which can soak up gravitons and thus weaken gravity on small scales [see Lisa Randall, Warped Passages: Unraveling The Mysteries Of The Universe's Hidden Dimensions (Ecco, New York, 2005)].