Do mixtures of bosonic and fermionic atoms adiabatically heat up in optical lattices?

Physical Review Letters

Volumn 100, Issue 14, 2008, Pages

  Cramer, M ^a   Ospelkaus, S ^b,c   Ospelkaus, C ^b,d   Bongs, K ^b   Sengstock, K ^b   Eisert, J ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF HAMBURG   (Germany)

^c UNIVERSITY OF COLORADO   (United States)

^d NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ATOMS; FERMIONS; MIXTURES;

FERMIONIC ATOMS; HARTREE-FOCK-BOGOLIUBOV-POPOV APPROXIMATION; OPTICAL LATTICES;

BOSONS;

EID: 42149148029     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.100.140409     Document Type: Article

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37. The ultralow temperature approximation for the energy E/(NBkBTc0)=5η/7+10.6η1/2t7/2 used in Ref. to obtain the entropy is somewhat misleading in its predictions. Comparing it to the local-density HFBP result shows that for the considered parameter and temperature regime the expression E/(NBkBTc0)=3ζ(4)t4/ζ(3)+η(1-t3)2/5(5+16t3)/7 is more appropriate; see also Ref.. Here, η=ζ(3)1/3152/5(NB1/6aBB/aho)2/5/2, t=T/Tc0, and Tc0 is the critical temperature in the absence of interactions. In Fig. 2 we depict the entropy obtained from the above expression (green dashed line) and the one used in Ref. (green solid line). For the parameters in Ref. we have also compared both expressions to the local-density HFBP result (both former expressions are approximations to the latter) and found the same fundamental difference. Interestingly, this refined study shows that instead of the claimed adiabatic heating, cooling should occur for typical initial temperatures. This is also substantiated by the observation of the spatial shell structures in Ref., which would not be visible in the case of heating.