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Quantum criticality emerges when the collective fluctuations of matter undergo a continuous phase transition at zero temperature and has been a research focus in conventional condensed-matter physics over the past several decades. In the quantum critical regime, the exotic and universal properties are expected. These properties are independent of the microscopic details of the system, but depend only on a few general properties of the system, such as its dimensionality and the symmetry of the order parameter. The research of quantum criticality can not only help us to understand quantum phase transitions, but also provide a novel route to new material design and discovery.Ultracold bosonic gases have provided a clean system for studying the quantum critical phenomena. The critical behavior of a weakly interacting three-dimensional (3D) Bose gas should be identical to that of 4He at the superfluid transition, which belongs to the 3D XY universality class. From the normal fluid to the superfluid, the system undergoes a phase transition from completely disorder to long-range order, while in the vicinity of the phase transition point, the system parameters will show some singularity characteristics. In this paper, we observe the critical behavior of 87Rb Bose gas in a quadrupole-Ioffe configuration (QUIC) trap near the phase transition temperature Tc. A novel singularity behavior of the full width at half maximum of momentum distribution (FWHMMD) of atomic gas is discovered in the experiment. Prior to our experiment, we prepare a sample with 7.8105 87Rb atoms in the 5S1/2 |F=2, mF=2 state. Then the sample is held in a QUIC trap for a presetting period of time to control the temperature of atom sample precisely. During the holding time, the sample is heated up due to background gas collisions or fluctuations of the trap potential. In our experiment, the heating rate is deduced to be 0.3480.078 nK/ms from the absorption image. For a bosonic gas in a harmonic trap, critical gas can only cover a finite-size region due to a spatially varying density. We define the finite-size region as a critical region determined by the Ginzburg criterion. Then the FWHMMDs of atomic gas in the critical region are measured for different temperatures near the critical point. To this aim, we first extract the momentum distribution of atomic gas from the absorption image of the atomic clouds released from the QIUC trap after free expansion. Thus momentum distribution of atomic gas in the critical region can be extracted from the absorption image by subtracting the momentum distribution of thermal gas outside the critical region. According to the statistical results of the FWHMMD at different temperatures, we find that the FWHMMD suddenly reduces, thus revealing a very notable singularity behavior when the temperature is very close to the phase transition temperature Tc.
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Keywords:
- critical region /
- critical behavior /
- phase transition temperature /
- full width at half maximum of momentum distribution
[1] Huang K 1987 Statistical Mechanics (New York: John Wiley Sons) pp392-415
[2] Coleman P, Schofield A J 2005 Nature 433 226
[3] Sachdev S 2003 Rev. Mod. Phys. 75 913
[4] Li Z, Zhou R, Zheng G Q {2015 Acta Phys. Sin. 64 217404 (in Chinese) [李政, 周睿, 郑国庆 2015 物理学报 64 217404]
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[6] Gasparini F M, Kimball M O, Mooney K P, Diaz-Avila M 2008 Rev. Mod. Phys. 80 1009
[7] Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[8] Davis K B, Mewes M O, Andrews M R, van Druten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969
[9] Bradley C C, Sacket C A, Tollett J J, Hulet R G 1995 Phys. Rev. Lett. 75 1687
[10] Khl M, Moritz H, Stferle T, Schori C, Esslinger T 2005 J. Low. Temp. Phys. 138 635
[11] Polkovnikov A, Altman E, Demler E 2006 Proc. Natl. Acad. Sci. U.S.A 103 6125
[12] Hadzibabic Z, Kruger P, Cheneau M, Battelier B, Dalibard J 2006 Nature 441 1118
[13] Bezett A, Blakie P B 2009 Phys. Rev. A 79 033611
[14] Donner T, Ritter S, Bourdel T, Ottl A, Khl M, Esslinger T 2007 Science 315 1556
[15] Xiong W, Zhou X J, Yue X G, Chen X Z, Wu B, Xiong H W 2013 Laser Phys. Lett. 10 125502
[16] Sondhi S L, Girvin S M, Carini J P, Shahar D 1997 Rev. Mod. Phys. 69 315
[17] Buckingham M J, Fairbank W M 1961 Progress in Low Temperature Physics (Vol. 3) (Amserdam: North-Holland) pp80-122
[18] Feng M, Zhong Y P, Liu T, Yan L L, Yang W L, Twamley J, Wang H 2015 Nat. Commun. 6 7111
[19] Damle K, Senthil T, Majumdar S N, Sachdev S 1996 Euro. Phys. Lett. 36 7
[20] Giorgini S, Pitaevskii L P, Stringari S 1996 Phys. Rev. A 54 R4633
[21] Pethick C J, Smith H 2008 Bose-Einstein Condensation in Dilute Gases (2nd Ed.) (New York: Cambridge University Press) pp21-28
[22] L B L, Tan X Z, Wang B, Cao L J, Xiong H W 2010 Phys. Rev. A 82 053629
[23] Mewes M O, Andrews M R, van Druten N J, Kurn D M, Durfee D S, Ketterle W 1996 Phys. Rev. Lett. 77 416
[24] Ma S K 2000 Modern Theory of Critical Phenomena (New York: Westview Press) pp16-32
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[1] Huang K 1987 Statistical Mechanics (New York: John Wiley Sons) pp392-415
[2] Coleman P, Schofield A J 2005 Nature 433 226
[3] Sachdev S 2003 Rev. Mod. Phys. 75 913
[4] Li Z, Zhou R, Zheng G Q {2015 Acta Phys. Sin. 64 217404 (in Chinese) [李政, 周睿, 郑国庆 2015 物理学报 64 217404]
[5] Imada M, Fujimori A, Tokura Y 1998 Rev. Mod. Phys. 70 1039
[6] Gasparini F M, Kimball M O, Mooney K P, Diaz-Avila M 2008 Rev. Mod. Phys. 80 1009
[7] Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[8] Davis K B, Mewes M O, Andrews M R, van Druten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969
[9] Bradley C C, Sacket C A, Tollett J J, Hulet R G 1995 Phys. Rev. Lett. 75 1687
[10] Khl M, Moritz H, Stferle T, Schori C, Esslinger T 2005 J. Low. Temp. Phys. 138 635
[11] Polkovnikov A, Altman E, Demler E 2006 Proc. Natl. Acad. Sci. U.S.A 103 6125
[12] Hadzibabic Z, Kruger P, Cheneau M, Battelier B, Dalibard J 2006 Nature 441 1118
[13] Bezett A, Blakie P B 2009 Phys. Rev. A 79 033611
[14] Donner T, Ritter S, Bourdel T, Ottl A, Khl M, Esslinger T 2007 Science 315 1556
[15] Xiong W, Zhou X J, Yue X G, Chen X Z, Wu B, Xiong H W 2013 Laser Phys. Lett. 10 125502
[16] Sondhi S L, Girvin S M, Carini J P, Shahar D 1997 Rev. Mod. Phys. 69 315
[17] Buckingham M J, Fairbank W M 1961 Progress in Low Temperature Physics (Vol. 3) (Amserdam: North-Holland) pp80-122
[18] Feng M, Zhong Y P, Liu T, Yan L L, Yang W L, Twamley J, Wang H 2015 Nat. Commun. 6 7111
[19] Damle K, Senthil T, Majumdar S N, Sachdev S 1996 Euro. Phys. Lett. 36 7
[20] Giorgini S, Pitaevskii L P, Stringari S 1996 Phys. Rev. A 54 R4633
[21] Pethick C J, Smith H 2008 Bose-Einstein Condensation in Dilute Gases (2nd Ed.) (New York: Cambridge University Press) pp21-28
[22] L B L, Tan X Z, Wang B, Cao L J, Xiong H W 2010 Phys. Rev. A 82 053629
[23] Mewes M O, Andrews M R, van Druten N J, Kurn D M, Durfee D S, Ketterle W 1996 Phys. Rev. Lett. 77 416
[24] Ma S K 2000 Modern Theory of Critical Phenomena (New York: Westview Press) pp16-32
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