In physics, a Tonks–Girardeau gas is a Bose–Einstein condensate in which the repulsive interactions between bosonic particles confined to one dimension dominate the physics of the system. It is named after physicists Marvin D. Girardeau and Lewi Tonks.
Consider a row of bosons all confined to a one-dimensional line. They cannot pass each other and therefore cannot exchange places. The resulting motion has been compared to a traffic jam: the motion of each boson would be strongly correlated with that of its two neighbours.
Because the particles cannot exchange places, one might expect their behaviour to be fermionic, but it turns out that their behaviour differs from that of fermions in several important ways: the particles can all occupy the same momentum state which corresponds to neither Bose-Einstein nor Fermi–Dirac statistics.
The fermionic exchange rule implies more than the exclusion of two particles from the same point: in addition, the momentum of two identical fermions can never be the same, wherever they are located. Mathematically, there is an exact one-to-one mapping of impenetrable bosons (in a one-dimensional system) onto a system of fermions that do not interact at all.
In the case of a Tonks–Girardeau gas (TG), so many properties of this one-dimensional string of bosons would be sufficiently fermion-like that the situation is often referred to as the 'fermionization' of bosons.
Until 2004, there were no known examples of TGs. However, in a paper in the 20 May 2004 edition of Nature, physicist Belén Paredes and coworkers present a technique of creating such a gas using an optical lattice.
The optical lattice is formed by six intersecting laser beams, which generate an interference pattern. The beams are arranged as standing waves along three orthogonal directions. This results in an array of optical dipole traps where atoms are stored in the intensity maxima of the interference pattern.
The researchers first loaded ultracold rubidium atoms into one-dimensional tubes formed by a two-dimensional lattice (the third standing wave is off for the moment). This lattice is very strong, so that the atoms do not have enough energy to tunnel between neighbouring tubes. On the other hand, the density is still too low for the transition to the TG regime. For that, the third axis of the lattice is used. It is set to a lower intensity than the other two axes, so that tunneling in this direction stays possible. For increasing intensity of the third lattice, atoms in the same lattice well are more and more tightly trapped, which increases the collisional energy. When the collisional energy becomes much bigger than the tunneling energy, the atoms can still tunnel into empty lattice wells, but not into or across occupied ones.
* BCS theory
* Tonks–Girardeau gas of ultracold atoms in an optical lattice, Nature 429, 277-281
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