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Journal of Computational Methods in Sciences and Engineering

Condensation of fermion composite particles

M. M. Mestechkin

Published Jun 9, 2011• 0 citations
Publisher

Abstract

The possibility of condensation of electron pairs has been established by Yang and Coleman. Recent observations of Bose–Einstein condensate (BEC) of alkali atoms, containing odd number of electrons, require some explanation, which also must be based
DOI
10.3233/jcm-2011-0370

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As we all know, single microscopic particles such as electrons or atoms do not behave according to the familiar classical (Newtonian) physics which describes the everyday world, but rather according to the prescriptions of quantum mechanics, the outcome is often bizarre and counterintuitive. When a macroscopic number of such particles (say ∼ 10) is assembled under conditions where the effects of quantum mechanics are important, the results can be even more spectacular; they include macroscopic phenomena such as superfluidity and superconductivity, which are completely impossible to explain in classical terms. Most, though not all of these exotic phenomena, are a result of a phenomenon which I shall refer to generically as “quantum condensation,” in which a macroscopic number of particles or pairs of particles—a nonzero fraction of all particles present—occupy a single quantum state; this phenomenon is traditionally referred to as Bose-Einstein condensation (BEC) when it occurs in a system of bosons such as liquid He, and as Cooper pairing when it occurs, for pairs of particles, in a system of fermions such as the electrons in a superconducting metal. As a result of quantum condensation, the characteristically quantum-mechanical behavior which we are used to seeing at the level of single electrons is as it were amplified by the cooperation of condensed particles and can manifest itself at the macroscopic level. The present essay is intended as a general introduction to the subject of quantum condensation and its consequences, as manifested in a variety of physical systems. I will try to review the fundamental physical ideas, usually without de-
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We study the zero-temperature grand potential of a three-dimensional superfluid made of ultracold fermionic alkali-metal atoms in the BCS-BEC crossover. In particular, we analyze the zero-point energy of both fermionic single-particle excitations and bosonic collective excitations. The bosonic elementary excitations, which are crucial to obtain a reliable equation of state in the Bose-Einstein condensate regime, are obtained with a low-momentum expansion up to the forth order of the quadratic (Gaussian) action of the fluctuating pairing field. By performing a cutoff regularization and renormalization of Gaussian fluctuations, we find that the scattering length aB{a}_{B}aB​ of composite bosons, bound states of fermionic pairs, is given by aB=(2/3)aF{a}_{B}=(2/3)\phantom{\rule{4pt}{0ex}}{a}_{F}aB​=(2/3)aF​, where aF{a}_{F}aF​ is the scattering length of fermions.