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Physics World

When is a boson not a boson?

D. ter Haar

Published Sep 1, 1995• 0 citations
Publisher

Abstract

I have read with interest recent articles about quantum gases in Physics World (July pp37–41, August p2l). I would, however, like to issue a word of warning before the Orwellian chant “even number of fermions bosons, odd number of fermions fermion” becomes too ingrained in the physics folklore.
DOI
10.1088/2058-7058/8/9/14

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The laser cooling mechanisms described in Chapter 4 operate irrespective of the statistics of the atom, and they can therefore be used to cool Fermi species. The statistics of a neutral atom is determined by the number of neutrons in the nucleus, which must be odd for a fermionic atom. Since alkali atoms have odd atomic number Z , their fermionic isotopes have even mass number A . Such isotopes are relatively less abundant than those with odd A since they have both an unpaired neutron and an unpaired proton, which increases their energy by virtue of the odd–even effect. In early experiments, 40 K and 6 Li atoms were cooled to about one-quarter of the Fermi temperature. More recently, fermionic alkali atoms have been cooled to temperatures well below one-tenth of their Fermi temperature, and in addition a degenerate gas of the fermionic species 173 Yb (with I = 5/2) has been prepared. In the classical limit, at low densities and/or high temperatures, clouds of fermions and bosons behave alike. The factor governing the importance of quantum degeneracy is the phase-space density ϖ introduced in Eq. (2.24), and in the classical limit ϖ ≪ 1. When ϖ becomes comparable with unity, gases become degenerate: bosons condense in the lowest single-particle state, while fermions tend towards a state with a filled Fermi sea. As one would expect on dimensional grounds, the degeneracy temperature for fermions – the Fermi temperature T F – is given by the same expression as the Bose–Einstein transition temperature for bosons, apart from a numerical factor of order unity.
After reading John Bush’s article “The new wave of pilot-wave theory” (Physics Today, August 2015, page 47), I want to remind readers of the limitations of the analogy. The oil-drop experiments provide a tangible partial analogue of the pilot-wave picture, but one that is restricted to single-particle phenomena. Such experiments cannot reproduce the types of phenomena that depend on entanglement; only in the case of a single particle does the wavefunction have the same mathematical form—a scalar function over space—as the waves in the oil.Once two particles are involved, the fact that the wavefunction is defined over the configuration space of the system rather than over physical space becomes crucial, and the partial analogy to the oil drops fails. In other words, the analogy does not extend to what most people consider the most interesting aspects of quantum mechanics.© 2016 American Institute of Physics.
We investigate the physics of a medium-size quantum particle' gases, of the order of hundreds or thousands of fermions/bosons (far below the thermodynamic limit N → 1024N \, \rightarrow \, 10^{24}N→1024). Appeal to microcanonical ensemble becomes then unavoidable. The so-called statistical complexity is our protagonist. Interesting facts are uncovered, both for fermions and bosons, yielded by statistical quantifiers.