摘要By the density-functional calculation we investigate the ground-state properties of Bose-Fermi mixture confined in one-dimensional harmonic traps. The homogeneous mixture of bosons and polarized fermions with contact interaction can be exactly solved by the Bethe-ansatz method. After giving the exact formula of ground state energy density, we employ the local-density approximation to determine the density distribution of each component. It is shown that with the increase in interaction, the total density distribution evolves to Fermi-like distribution and the system exhibits phase separation between two components when the interaction is strong enough but finite. While in the infinite interaction limit both bosons and fermions display the completely same Fermi-like distributions and phase separation disappears.
Abstract:By the density-functional calculation we investigate the ground-state properties of Bose-Fermi mixture confined in one-dimensional harmonic traps. The homogeneous mixture of bosons and polarized fermions with contact interaction can be exactly solved by the Bethe-ansatz method. After giving the exact formula of ground state energy density, we employ the local-density approximation to determine the density distribution of each component. It is shown that with the increase in interaction, the total density distribution evolves to Fermi-like distribution and the system exhibits phase separation between two components when the interaction is strong enough but finite. While in the infinite interaction limit both bosons and fermions display the completely same Fermi-like distributions and phase separation disappears.
HAO Ya-Jiang
. Ground State Density Distribution of Bose-Fermi Mixture in a One-Dimensional Harmonic Trap[J]. 中国物理快报, 2011, 28(1): 10302-010302.
HAO Ya-Jiang
. Ground State Density Distribution of Bose-Fermi Mixture in a One-Dimensional Harmonic Trap. Chin. Phys. Lett., 2011, 28(1): 10302-010302.
[1] Stöferle T, Moritz H, Schori C, Köhl M and Esslinger T 2004 Phys. Rev. Lett. 92 130403
[2] Paredes B, Widera A, Murg V, Mandel Q, Fölling S, Cirac I, Shlyapnikov G V, Hänsch T W and Bloch I 2004 Nature 429 277
[3] Kinoshita T, Wenger T and Weiss D S 2004 Science 305 1125
[4] Ho T L and Shenoy V B 1996 Phys. Rev. Lett. 77 3276
[5] Ao P and Chui S T 1998 Phys. Rev. A 58 4836
[6] Pu H and Bigelow N P 1998 Phys. Rev. Lett. 80 1130
[7] Cazalilla M A and Ho A F 2003 Phys. Rev. Lett. 91 150403
[8] Zhou L, Qian J, Pu H, Zhang W and Ling H Y 2008 Phys. Rev. A 78 053612
[9] Molmer K 1998 Phys. Rev. Lett. 80 1804
Lewenstein M, Santos L, Baranov M A and Fehrmann H 2004 Phys. Rev. Lett. 92 050401
Mathey L, Wang D W, Hofstetter W, Lukin M D and Demler E 2004 Phys. Rev. Lett. 93 120404
Guan X W, Batchelor M T and Lee J Y 2008 Phys. Rev. A 78 023621
Frahm H and Palacios G 2005 Phys. Rev. A 72 061604(R)
[10] Imambekov A and Demler E 2006 Phys. Rev. A 73 021602(R)
Imambekov A and Demler E 2006 Ann. Phys. (N. Y.) 321 2390
[11] Schreck F, Khaykovich L, Corwin K L, Ferrari G, Bourdel T, Cubizolles J and Salomon C 2001 Phys. Rev. Lett. 87 080403
Hadzibabic Z, Stan C A, Dieckmann K, Gupta S, Zwierlein M W, Gorlitz A and Ketterle W 2002 Phys. Rev. Lett. 88 160401
[12] Thalhammer G, Barontini G, De Sarlo L, Catani J, Minardi F and Inguscio M 2008 Phys. Rev. Lett. 100 210402
Papp S B, Pino J M and Wieman C E 2008 Phys. Rev. Lett. 101 040402
[13] Pilch K, Lange A D, Prantner A, Kerner G, Ferlaino F, Naegerl H C and Grimm R 2009 Phys. Rev. A 79 042718
[14] Olshanii M 1998 Phys. Rev. Lett. 81 938
[15] Petrov D S, Shlyapnikov G V and Walraven J T M 2000 Phys. Rev. Lett. 85 3745
[16] Chen S and Egger R 2003 Phys. Rev. A 68 063605
[17] Guan L, Chen S, Wang Y and Ma Z Q 2009 Phys. Rev. Lett. 102 160402
[18] Li Y Q, Gu S J, Ying Z J and Eckern U 2003 Europhys. Lett. 61 368
[19] Fuchs J N, Gangardt D M, Keilmann T and Shlyapnikov G V 2005 Phys. Rev. Lett. 95 150402
Batchelor M T, Bortz M, Guan X W and Oelkers N 2006 J. Stat. Mech. P03016
[20] Guan X W, Batchelor M T and Takahashi M 2007 Phys. Rev. A 76 043617
Oelkers N, Batchelor M T, Bortz M and Guan X W 2006 J. Phys. A 39 1073
[21] Hao Y, Zhang Y, Liang J Q and Chen S 2006 Phys. Rev. A 73 063617
[22] Deuretzbacher F, Bongs K, Sengstock K and Pfannkuche D 2007 Phys. Rev. A 75 013614
Yin X, Hao Y, Chen S and Zhang Y 2008 Phys. Rev. A 78 013604
[23] Hao Y, Zhang Y, Guan X W and Chen S 2009 Phys. Rev. A 79 033607
[24] Zöllner S, Meyer H D and Schmelcher P 2008 Phys. Rev. A 78 013629
[25] Hao Y and Chen S 2009 Eur. Phys. J. D 51 261
[26] You Y Z 2010 Chin. Phys. Lett. 27 080305
[27] Kolomeisky E B, Newman T J, Straley J P and Qi X 2000 Phys. Rev. Lett. 85 1146
[28] Dunjko V, Lorent V and Olshanii M 2001 Phys. Rev. Lett. 86 5413
[29] Öhberg P and Santos L 2002 Phys. Rev. Lett. 89 240402
[30] Kim Y E and Zubarev A L 2003 Phys. Rev. A 67 015602
Brand J 2004 J. Phys. B 37 S287
[31] Astrakharchik G E, Blume D, Giorgini S and Pitaevskii1 L P 2004 Phys. Rev. Lett. 93 050402
[32] Y E Kim and Zubarev A L 2004 Phys. Rev. A 70 033612
Magyar R J and Burke K 2004 Phys. Rev. A 70 032508
[33] Gao X, Polini M, Asgari R and Tosi M P 2006 Phys. Rev. A 73 033609
[34] Hu H, Liu X J and Drummond P D 2007 Phys. Rev. Lett. 98 070403
[35] Girardeau M D 1960 J. Math. Phys. (N. Y.) 1 516
Girardeau M D 1965 Phys. Rev. 139 B500
[36] Hao Y and Chen S 2009 Phys. Rev. A 80 043608
[37] Lieb E H and Liniger W 1963 Phys. Rev. 130 1605
[38] Batchelor M T, Bortz M, Guan X W and Oelkers N 2005 Phys. Rev. A 72 061603(R)
Guan X W, Batchelor M T and Lee J Y 2008 Phys. Rev. A 78 023621
[39] Lai C K and Yang C N 1971 Phys. Rev. A 3 393
[40] Yin X, Chen S and Zhang Y 2009 Phys. Rev. A 79 053604
[41] Lieb E H, Seiringer R and Yngvason J 2003 Phys. Rev. Lett. 91 150401
[42] Dalfovo F and Stringari S 1996 Phys. Rev. A 53 2477