INDISCERNIBILITY
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Recently, Bose-Einstein condensates have been prepared in the laboratory. By means of lasers and magnetic traps, atoms are cooled to the critical temperature. When the critical temperature is reached, the atoms undergo a quantum mechanical phase transition and form a coherent cloud of particles all occupying the same quantum state.They can then serve as sources of coherent atomic beams – so-called atom lasers (because they are a sort of analogue of usual photon lasers). The purely quantum nature of this device is demonstrated by the fact that, if two condensates are released and allowed to expand, they display a high-contrast interference pattern in their overlap region, just as photons or individual atoms do in the double-slit experiment (see Figure 3).

 

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Quantum statistics is the key tool to address several physical problems. By applying the Fermi-Dirac statistics to the electron gas model one can satisfactorily account for:

•  the electronic contribution to specific heat of metals

•  the contact potential (i.e. the fact that if two metals are connected electrically, a potential difference is observed)

•  the thermionic emission responsible for the emission of electrons from the heated filament of a vacuum tube.

Well known bosonic models, governed by the Bose-Einstein statistics are:

•  the photon gas (explaining blackbody radiation and laser)

•  the phonon gas (explaining specific heat of crystalline solids).

When a gas of bosonic atoms is cooled below a critical temperature, a large fraction of the atoms condenses in the lowest quantum state (for fermions this possibility is prevented by the Pauli's exclusion principle). This phenomenon was first predicted by Albert Einstein in 1925 and is called Bose-Einstein condensation. Bose-Einstein condensates exhibit impressive large-scale quantum effects. A concrete example is provided by superfluid helium. When the temperature of liquid helium is reduced to 2.18 K, a dramatic change in its properties is observed. Heat conductivity increases and viscosity drops by a factor of about one million. Notice that this phenomenon does not occur with He 3 (the isotope of helium that has atomic weight 3), since in this case the individual atoms are fermions (see also experimental evidence).

Interference experiment with two components of an atomic Bose-Einstein condensate. The measurement is repeated at different temperatures : before the phase transition (figure (a): no interference pattern); when a fraction of the atoms is in the condensate state (figure (b)), and when the atoms are fully condensed (figure (c): contrasted interference fringes)
FIGURE 3

A number of interesting philosophical puzzles arise from the indiscernibility principle, related to old and hard problems about identity, the existence of individuals, etc. Insofar as quantum particles are concerned, fermions are usually granted a higher status of materiality and individuality than bosons (which are supposed to ‘mediate' the interactions between fermions in quantum field theory). However, the grounds for such a distinction are put into question by supersymmetric theories.