Condensate fraction of asymmetric three-component Fermi gas

doi:10.1088/1674-1056/23/2/020308

Abstract In this paper, we investigate the condensate fraction (CF) of fermionic pairs in the BCS–BEC crossover for three-component Fermi gas with both asymmetric interactions and unequal chemical potentials in two-dimensional free space. By using the functional-path-integral method, we have analytically derived the number densities and bound-state energy, from which the off-diagonal long-range order is analyzed in terms of the asymptotic behavior of the two-body density matrix. The explicit formula of CF is obtained as a function of the bound-state energy and population imbalance. It is demonstrated that the CF spectrum with respect to the bound-state energy can be used to characterize the quantum phase transition between the two kinds of Sarma phases as well as the transition from three-component to two-component superfluid. Moreover we obtain the same analytic formula of CF in the BCS superfluid phase as that of homogeneous Fermi gas with equal chemical potentials.

Keywords: condensate fraction BCS–BEC crossover Sarma phases

Received: 06 March 2013
Revised: 16 July 2013
Accepted manuscript online:

PACS:	03.75.Hh	(Static properties of condensates; thermodynamical, statistical, and structural properties)
	03.75.Ss	(Degenerate Fermi gases)
	05.30.Fk	(Fermion systems and electron gas)
	74.20.Fg	(BCS theory and its development)

Fund: Project supported by the Graduate Outstanding Innovation Item of Shanxi Province, China (Grant No. 20123005) and the National Natural Science Foundation of China (Grant Nos. 11075099 and 11275118).

Corresponding Authors: Liang Jiu-Qing
E-mail: jqliang@sxu.edu.cn

About author: 03.75.Hh; 03.75.Ss; 05.30.Fk; 74.20.Fg

Cite this article:

Du Jia-Jia (杜佳佳), Liang Jun-Jun (梁军军), Liang Jiu-Qing (梁九卿) Condensate fraction of asymmetric three-component Fermi gas 2014 Chin. Phys. B 23 020308

[1]	Jochim S, Bartenstein M, Altmeyer A, Hendl G, Riedl S, Chin C, Denschlag J H and Grimm R 2003 Science 302 2101
[2]	Greiner M, Regal C A and Jin D S 2003 Nature 426 537
[3]	Zwierlein M W, Abo-Shaeer J, Schirotzek A, Schunck C and Ketterle W 2004 Nature 435 1047
[4]	Zwierlein M W, Stan C A, Schunck C H, Raupach S M F, Gupta S, Hadzibabic Z and Ketterle W 2003 Phys. Rev. Lett. 91 250401
[5]	Zwierlein M W, Schirotzek A, Schunck C H and Ketterle W 2006 Science 311 492
[6]	Kinast J, Hemmer S L, Gehm M E, Turlapov A and Thomas J E 2004 Phys. Rev. Lett. 92 150402
[7]	Bloch I, Dalibard J and Zwerger W 2008 Rev. Mod. Phys. 80 885
[8]	Falco G M and Stoof H T C 2004 Phys. Rev. Lett. 92 130401
[9]	Hu H, Minguzzi A, Liu X J and Tosi M P 2004 Phys. Rev. Lett. 93 190403
[10]	Zhai H 2009 Phys. Rev. A (Rapid Communication) 80 051605
[11]	Cui X L and Zhai H 2010 Phys. Rev. A (Rapid Communication) 81 041602
[12]	Zhou Y, Ma X D and Huang G X 2006 Chin. Phys. Lett. 23 2662
[13]	Zhang W Y and Wang C T 2010 Chin. Phys. Lett. 27 040304
[14]	Huang B B and Wan S L 2009 Chin. Phys. Lett. 26 070304
[15]	Wang Y S, Yan P G, Li B and Liu X S 2012 Chin. Phys. B 21 010309
[16]	Ma Z Q and Yang C N 2009 Chin. Phys. Lett. 26 120505
[17]	Hao Y J 2011 Chin. Phys. B 20 060307
[18]	Chao G and Zhen H Y 2012 Phys. Rev. A 86 043609
[19]	He L Y and Zhuang P F 2008 Phys. Rev. A 78 033613
[20]	Conduit G J, Conlon P H and Simons B D 2008 Phys. Rev. A 77 053617
[21]	Marini M, Pistolesi F and Strinati G C 1998 Eur. Phys. J. B 1 151
[22]	Du J J, Chen C and Liang J J 2009 Phys. Rev. A 80 023601
[23]	Parish M M 2011 Phys. Rev. A 83 051603
[24]	Salasnich L 2007 Phys. Rev. A 76 015601
[25]	Iskin M and Sa de Melo C A R 2006 Phys. Rev. Lett. 97 100404
[26]	Iskin M and Sa de Melo C A R 2007 Phys. Rev. A 76 013601
[27]	Liu W V and Wilczek F 2003 Phys. Rev. Lett. 90 047002
[28]	Hu H and Liu X J 2006 Phys. Rev. A 73 051603
[29]	Pao C H, Wu S T and Yip S K 2006 Phys. Rev. B 73 132506
[30]	Su W C 2006 Phys. Rev. A 74 063627
[31]	He L Y, Jin M and Zhuang P F 2006 Phys. Rev. A 74 033604
[32]	Ozawa T and Baym G 2010 Phys. Rev. A 82 063615
[33]	Cherng R W, Refael G and Demler E 2007 Phys. Rev. Lett. 99 130406
[34]	Salasnich L 2011 Phys. Rev. A 83 033630
[35]	Salasnich L e-print arXiv: 1108 0076
[36]	Du J J, Liang J J and Liang J Q 2012 Phys. Rev. A 85 033610
[37]	Salasnich L, Manini N and Parola A 2005 Phys. Rev. A 72 023621
[38]	Ortiz G and Dukelsky J 2005 Phys. Rev. A 72 043611
[39]	Astrakharchik G E, Boronat J, Casulleras J and Giorgini S 2005 Phys. Rev. Lett. 95 230405
[40]	Regal C A, Greiner M and Jin D S 2004 Phys. Rev. Lett. 92 040403
[41]	Sarma G 1963 J. Phys. Chem. Solids 24 1029
[42]	Fulde P and Ferrell R A 1964 Phys. Rev. 135 A550
[43]	Larkin A J and Ovchinnikov Y N 1964 Zh. Eksp. Teor. Fiz. 47 1136 [1963 Sov. Phys. JEPT 20 762]
[44]	Zwierlein M W, Stan C A, Schunck C H, Raupach S M F, Kerman A J and Ketterle W 2004 Phys. Rev. Lett. 92 120403
[45]	Zwierlein M W, Schunck C H, Stan C A, Raupach S M F and Ketterle W 2005 Phys. Rev. Lett. 94 180401
[46]	Vivas H e-print arXiv: 0504 600
[47]	Yang C Y 1962 Rev. Mod. Phys. 34 694
[48]	Campbell C E, Clark J W and Panat P V 1997 Condensed Matter Theories (New York: Nova Science) Vol. 12, p. 131

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Condensate fraction of asymmetric three-component Fermi gas

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