physicsweb.org/article/world/15/4/7
As Wolfgang Paulis famous exclusion principle states, identical fermions cannot occupy the same quantum state at the same time. But to observe this fundamental difference, gases of bosons or fermions have to be chilled to ultra-low temperatures, where individual quantum states have a high chance of being occupied. At these low temperatures, bosons will eagerly fall into a single quantum state to form a Bose-Einstein condensate, whereas fermions tend to fill energy states from the lowest up, with one particle per quantum state figure 1 . At high temperatures, in contrast, bosons and fermions spread out over many states with, on average, much less than one atom per state. Another difference is that fermions do not undergo a sudden phase transition in the ultra-low temperature regime. Instead, the quantum behaviour emerges gradually as the fermion gas is cooled below the Fermi temperature T F E F / k B , where E F is the Fermi energy - the energy of the highest filled state - and k B is Boltzmanns constant. T F , which is typically less than 1 K for atomic gases, marks the crossover from the classical to the quantum regime. The odd quantum behaviour of fermions permeates all of physics, and is responsible for phenomena ranging from atomic structure to the stability of neutron stars. But unlike other Fermi systems found in nature, a Fermi gas of atoms occurs in a new, ultracold, low-density regime where interparticle interactions are weak. Cooling fermionic atoms The main experimental challenge in creating a fermionic gas is to chill the atoms to ultra-low temperatures. Given the fact that physicists have been able to cool bosons to microkelvin temperatures since 1995, when Bose-Einstein condensates were first created, one might think that experiments to cool fermions would have followed soon afterwards. However, cooling a gas of fermionic atoms is difficult because of their strange collision properties. In general, collisions play a crucial role in the physics of quantum gases. Elastic collisions, for example, keep the gas in thermal equilibrium as it cools. These collisions also affect many of the properties of both Bose-Einstein condensates and Fermi gases by determining the interparticle interactions. However, differences in the collisional behaviour of bosonic and fermionic atoms arise at temperatures well above those that are required for the gas as a whole to behave quantum mechanically. Typically, atoms in an ultracold gas will only collide if they approach each other head-on in what is known as an s-wave collision, where there is no relative angular momentum between the two atoms. But due to the Pauli exclusion principle, these s-wave collisions are forbidden for fermions that are in the same internal quantum state - ie that have the same spin-state. This lack of collisions makes it impossible to cool such a fermionic atomic gas efficiently. However, fermionic atoms that are in different internal states can collide through s-wave collisions see box . This means that it is, after all, possible to cool fermions to near absolute zero, as my colleague Brian DeMarco and I showed in 1999, when we created the worlds first quantum-degenerate Fermi gas of atoms.
Quantum degeneracy Using these novel experimental techniques, physicists have been able to cool Fermi gases of atoms into the quantum-degenerate regime below the Fermi temperature, T F . But because the effects of quantum statistics become stronger as a gas is cooled further into this regime, the ultimate cooling limit is an important issue. Experiments at JILA using potassium-40 in two spin-states, and at Rice and the ENS in Paris using lithium-6, have so far cooled atoms to about 20 of T F . We do not yet know why potassium-40 atoms cannot be cooled any further, although the quantum nature of fermions as well as technical challenges could both play a role. In the experiments on lithium at Rice and the ENS, however, sympathetic cooling is limited by the formation of lithium-7 Bose-Einstein condensates. The effectively attractive interactions between lithium-7 atoms make the condensate collapse, causing atoms to leave the trap. The fermions can therefore no longer cool by being in contact with the boson gas. The quantum behaviour of an atomic Fermi gas was first revealed in thermodynamic measurements. At JILA we study the atomic Fermi gas by analysing absorption images of the expanded gas. As the gas expands, fast atoms travel further from the centre of the gas than slow-moving atoms. An optical image of the gas therefore reveals the momentum distribution of the atoms: those atoms with low momentum remain near the centre of the cloud, while atoms with high momentum appear at the edges.
We have used this technique to show how a Fermi gas of potassium-40 atoms enters the quantum regime. When the gas is cooled below T F , the number of particles with low momenta ie near the centre of the image falls below the value expected from classical physics. Only one fermion is allowed to occupy each quantum state, which means that the low-energy states are quickly filled and the other fermions must therefore fill states of higher and higher energy. Indeed, experiments reveal that the mean energy per particle rises well above the classical value figure 2a . Hulet and co-workers at Rice, as well researchers at the ENS, have carried out similar experiments to show the differences in size between a Fermi gas lithium-6 and a Bose gas lithium-7. In the quantum regime, the mean energy per fermion rises above the value expected from classical physics or in a Bose gas. The fermion atoms have more kinetic energy, which means that the trapped Fermi gas spreads over a larger volume than the Bose gas figure 2b . This quantum phenomenon, called Fermi pressure, is seen in astrophysics and is responsible for stabilizing white-dwarf and neutron stars against their gravitational potential. Interactions in a Fermi gas of atoms Physicists studying Bose-Einstein condensation soon realized that interactions between the atoms play a key role in determining properties such as the size and even the stability of the condensates. Indeed, the differences between condensates made from rubidium, sodium or lithium atoms depend simply on the strength of the interparticle interactions at ultra-low temperatures and whether these interactions are attractive or repulsive. In our work at JILA, for example, we have used potassium-40 atoms in two spin-states to create a two-component interacting Fermi gas, in which we have observed the effect of a strange phenomenon known as Pauli blocking. Occurring in all Fermi systems, Pauli blocking is a consequence of the fact that identical fermions can never occupy the same quantum state. A fermionic atom can therefore only change energy - in a collision, for example - if the final energy state is unoccupied. But in the quantum regime, it is highly likely that low-energy states are already occupied. Pauli blocking therefore tends to suppress any process in which atoms change energy states.
We have observed Pauli blocking by measuring collective excitations of the trapped gas figure 3 . These excitations, which are essentially sound waves, involve small relative motions between the two different gases in our samples. They provide valuable information about how the atoms in a Fermi gas collide. Indeed, collective excitations have proved to be a very valuable way of studying other quantum fluids. They have been widely used to characterize Bose-Einstein condensates - for example to investigate interactions, to probe finite temperature effects, and even to detect superfluidity and vortices. In an atomic Fermi gas, Pauli blocking of collisions is revealed by changes to the damping time for collective excitations. What is particularly interesting about Pauli blocking is that it is a quantum-mechanical effect in which collisions are affected by atoms that are far away from one another. Fermi gases - the future Even though the study of Fermi gases of atoms is still in its infancy, it is clear that this new field complements research into Bose-Einstein condensation. While experiments on Fermi gases h...
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