Laser Physics

Superfluid equation of state of dilute composite bosons or how to include 3- and 4-body problems in the many body problem

X. Leyronas, R. Combescot

Published Apr 1, 2009• 0 citations

Abstract

We show how the 3 and 4-body problems emerge in the BEC limit of the BEC-BCS crossover, where we treat explicitly dimers as made of two fermions. We give the argument leading, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density n up to the Lee-Huang-Yang order, proportional to n 3/2, the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length a M , the composite nature of the dimers appearing only in the next order term proportional to n 2.

DOI: 10.1134/s1054660x09040112

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Laser Physics

Superfluid equation of state of dilute composite bosons or how to include 3- and 4-body problems in the many body problem

X. Leyronas, R. Combescot

Published Apr 1, 2009• 0 citations

Publisher

Abstract

DOI: 10.1134/s1054660x09040112

Related papers

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n

. We derive first the mean-field contribution, which has the expected standard expression when it is written in terms of the dimer-dimer scattering length

{a}_{M}

. We go next in the expansion to the Lee-Huang-Yang order, proportional to

{n}^{3∕2}

. We find the far less obvious result that it retains also the same expression in terms of

{a}_{M}

as for elementary bosons. The composite nature of the dimers appears only in the next term proportional to

{n}^{2}

(\mathrm{density}){}^{4/3}

. The results found involve the exact atom-dimer

{a}_{\mathrm{AD}}

and dimer-dimer

{a}_{\mathrm{DD}}

scattering lengths and therefore include the three- and four-body problems in the many-body problem. We briefly comment on the importance of the different mean-field corrections for recent experiments.

{a}_{B}

of composite bosons, bound states of fermionic pairs, is given by

{a}_{B}=(2/3)\phantom{\rule{4pt}{0ex}}{a}_{F}

, where

{a}_{F}

is the scattering length of fermions.

{a}_{dd}

at short distances and, second, reduces to composite-boson Bogoliubov physics at long distances. It reproduces the Lee-Yang term, whose numerical value is also fixed by

{a}_{dd}

. We have also examined the next term beyond the Lee-Yang correction in a phenomenological fashion, building on cloud size data and collective mode experiments, although one has to view this phenomenological analysis with some caution since experiments are in a state of flux and are performed close to unitarity.