A Fermi gas is a collection of non-interacting fermions. It is the quantum mechanical version of an ideal gas, for the case of fermionic particles. Electrons in metals and semiconductors and neutrons in a neutron star can be approximately considered Fermi gases. The energy distribution of the fermions in a Fermi gas in thermal equilibrium is determined by their density, the temperature and the set of available energy states, via Fermi-Dirac statistics. By the Pauli principle, no quantum state can be occupied by more than one fermion, so the total energy of the Fermi gas at zero temperature is larger than the product of the number of particles and the single-particle ground state energy. For this reason, the pressure of a Fermi gas is nonzero even at zero temperature, in contrast to that of a classical ideal gas. This so-called degeneracy pressure stabilizes a neutron star (a Fermi gas of neutrons) or a White Dwarf star (a Fermi gas of electrons) against the inward pull of gravity.
It is possible to define a Fermi temperature below which the gas can be considered degenerate. This temperature depends on the mass of the fermions and the energy density of states. For metals, the electron gas's Fermi temperature is generally many thousands of kelvins, so they can be considered degenerate. The maximum energy of the fermions at zero temperature is called the Fermi energy. The Fermi energy surface in momentum space is known as the Fermi surface.
Since interactions are neglected by definition, the problem of treating the equilibrium properties and dynamical behaviour of a Fermi gas reduces to the study of the behaviour of single independent particles. As such, it is still relatively tractable and forms the starting point for more advanced theories (such as Fermi liquid theory or perturbation theory in the interaction) which take into account interactions to some degree of accuracy.
A system of identical Fermions is called a “Fermigas.” If the temperature is low enough, the Fermigas is “degenerate,” which means the low-lying states are filled up to a well-defined maximum energy, as shown in the diagram.
Following groundbreaking low-temperature experiments with a gas of Bose atoms, which resulted in a form of matter called a Bose-Einstein Condensate (BEC) [See Matters of State], other researchers cooled fermionic atoms, looking for a degenerate Fermigas, but this proved much more difficult.
In a degenerate Fermigas, however, the low-energy states are already filled, so if two atoms collide, there are no lower-energy states available for the atoms to go to after the collision and they must stay in the original ones.
Once the Fermigas had reached the quantum regime, we obtained information about it by turning the magnetic trap off, allowing the gas to expand and measuring the shadow of the gas cast by a laser.
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.
The lack of collisions in a single-component Fermigas of atoms could be exploited for precision measurements of these atoms, while recent experiments on two-component Fermi gases have begun to study the interplay of interactions and quantum statistics in determining behaviour.
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