Ultra-cold Matter Research 

   We are in the process of constructing an apparatus based on an "atom chip" for studying ultra-cold matter -- sub-microKelvin quantum degenerate gases. The apparatus will be used for ultra-cold matter interferometry research and to explore new condensed matter and many-body physics systems. Here are some links to our research:

Animated data of the formation of an 87Rb BEC
(data courtesy of the Thywissen Lab, U. of Toronto).

Basic Introduction to Ultra-cold Matter

   We work with atomic gases at ultra-low temperatures (10-1000 nK). At these extremely low temperatures, the physics of the gas is no longer classical and can only be described by the laws of quantum mechanics. When a system is made of identical indistinguishable particles, quantum mechanics predicts that the particles will obey two mutually exclusive sets of rules called quantum statistics. Particles with integer spin obey Bose-Einstein statistics and are called bosons. Particles with half-integer spin obey Fermi-Dirac statistics and are called fermions. The effects of quantum statistics are only observable typically at ultra-cold temperatures.


   All particles with integer spin, such as photons, gluons, and some atoms, are bosons. Identical bosons tend to clump together in the same quantum state. In the language of quantum mechanics, the total wave function of identical bosons must be symetric under exchange of any of its particles.

   When bosons are cooled to ultra-low temperatures, they all tend to congregate in the ground state, or lowest energy level, of the system which they constitute. Bosons tend to do this even when the average energy of the particles is several times the energy spacing between levels -- nevertheless, the system must be very cold. This ultra-cold clumping phenomena is called Bose-Einstein condensation (BEC). When a system of particles condenses to BEC, it is a very abrupt phenomena that happens at a specific critical temperature, Tc. While the existence of a BEC was predicted by Einstein in 1921, it was observed for the first time at JILA (Boulder, Colorado, USA) in 1995 by Carl Wieman and Eric Cornell in a dilute gas of bosonic rubidium atoms (rubidium-87).

One can see the transition to BEC by looking at images of the atomic cloud. A sharp peak in the density appears at the BEC phase transition:

[Data for images courtesy of the Thywissent lab, University of Toronto]

A BEC in atoms is similar to a laser with photons. In both cases multiple bosons (aotms or photons) occupy a same quantum state.


   Particles with half-integer spin, such as electrons, quarks, protons, neutrons, and some atoms (the ones that are not bosons), are fermions. Identical fermions tend to avoid each other and obey the Pauli exclusion principle: Identical fermions cannot occupy the same quantum state. According to quantum mechanics, the total wave function of identical fermions must be anti-symetric under exchange of any of its particles.

   When fermions are cooled, the system loses energy, but the particles cannot all occupy the lowest energy level due to the Pauli exclusion principle. Instead, the paticles fill up the energy level ladder up to an energy determined by the number of particles. This energy is called the Fermi energy, EF, and also sets the temperature (Fermi temperature, TF) at which Fermi-degeneracy becomes appears. When the system is close to filling up the energy ladder, the particles are said to form a degenerate Fermi gas (DFG). The following cartoon illustrates the transition from a thermal gas to a DFG:

   The transition from a thermal gas to a DFG is not abrupt, but rather a smooth continuous process, and does not display any strong qualitative feature such as the bimodal distribution of a BEC. On July 14, 2005, we observed a gas of Fermi-degenerate potassium-40 atoms for the first in our lab, and the first ever to do so in a chip micro-magnetic trap. The following images show a K-40 gas above and below the Fermi temperature -- the red circle indicates the position of the Fermi energy, EF:

[Data for images courtesy of the Thywissen lab, University of Toronto]

   Once the K-40 atoms have been cooled to below the Fermi temperature, further cooling does not significantly reduce the atomic cloud size with respect to the "Fermi radius" associated with Fermi energy.

Web page updated: January 12, 2007.