Spin–orbit coupling in Bose–Einstein condensate and degenerate Fermi gases

doi:10.1007/s11467-013-0377-x

Front. Phys.

2014, Vol. 9

Issue (5) : 598-612 https://doi.org/10.1007/s11467-013-0377-x

REVIEW ARTICLE

Spin–orbit coupling in Bose–Einstein condensate and degenerate Fermi gases

Peng-Jun Wang,Jing Zhang(

)

State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China

Download: PDF(1264 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

We review our recent experimental realization and investigation of a spin–orbit (SO) coupled Bose–Einstein condensate (BEC) and quantum degenerate Fermi gas. By using two counter-propagating Raman lasers and controlling the different frequency of two Raman lasers to engineer the atom–light interaction, we first study the SO coupling in BEC. Then we study SO coupling in Fermi gas. We observe the spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state as hallmarks of SO coupling in a Fermi gas. To clearly reveal the property of SO coupling Fermi gas, we also study the momentum-resolved radio-frequency spectroscopy which characterizes the energy–momentum dispersion and spin composition of the quantum states. We observe the change of fermion surfaces in different helicity branches with different atomic density, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system. At last, we study the momentum-resolved Raman spectroscopy of an ultracold Fermi gas.

Keywords spin–orbit coupling Bose–Einstein condensate Fermi gases topological change momentum-resolved radio-frequency spectroscopy momentum-resolved Raman spectroscopy

Corresponding Author(s): Jing Zhang

Issue Date: 15 October 2014

Cite this article:

Peng-Jun Wang,Jing Zhang. Spin–orbit coupling in Bose–Einstein condensate and degenerate Fermi gases[J]. Front. Phys. , 2014, 9(5): 598-612.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-013-0377-x
https://academic.hep.com.cn/fop/EN/Y2014/V9/I5/598

1	W. Ketterle and M. W. Zwierlein, Making, probing and understanding ultracold Fermi gases, Rivista del Nuovo Cimento, 2008, 31: 247; arXiv: 0801.2500
2	C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Rev. Mod. Phys., 2010, 82(2): 647 https://doi.org/10.1103/RevModPhys.82.1225
3	I. Bloch, J. Dalibard, and S. Nascimbène, Quantum simulations with ultracold quantum gases, Nat. Phys., 2012, 8(4): 267 https://doi.org/10.1038/nphys2259
4	M. Greiner, O. Mandel, T. Esslinger, T. W. H?nsch, and I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature, 2002, 415(6867): 39 https://doi.org/10.1038/415039a
5	F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, Three-dimensional localization of ultracold atoms in an optical disordered potential, Nat. Phys., 2012, 8: 398 https://doi.org/10.1038/nphys2256
6	E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman, Dynamics of collapsing and exploding Bose–Einstein condensates, Nature, 2001, 412(6844): 295 https://doi.org/10.1038/35085500
7	E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, Atom–molecule coherence in a Bose–Einstein condensate, Nature, 2002, 417(6888): 529 https://doi.org/10.1038/417529a
8	C. A. Regal, M. Greiner, and D. S. Jin, Observation of resonance condensation of fermionic atom pairs, Phys. Rev. Lett., 2004, 92(4): 040403 https://doi.org/10.1103/PhysRevLett.92.040403
9	T. Kraemer, M. Mark, P. Waldburger, J. G. Danzl, C. Chin, B. Engeser, A. D. Lange, K. Pilch, A. Jaakkola, H.-C. N?gerl, and R. Grimm, Evidence for Efimov quantum states in an ultracold gas of caesium atoms, Nature, 2006, 440(7082): 315 https://doi.org/10.1038/nature04626
10	B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science, 2006, 314(5806): 1757 https://doi.org/10.1126/science.1133734
11	M. K?nig, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X. L. Qi, and S. C. Zhang, Quantum spin hall insulator state in HgTe quantum wells, Science, 2007, 318(5851): 766 https://doi.org/10.1126/science.1148047
12	K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Vortex formation in a stirred Bose–Einstein condensate, Phys. Rev. Lett., 2000, 84(5): 806 https://doi.org/10.1103/PhysRevLett.84.806
13	J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Observation of vortex lattices in Bose–Einstein condensates, Science, 2001, 292(5516): 476 https://doi.org/10.1126/science.1060182
14	E. Hodby, G. Hechenblaikner, S. A. Hopkins, O. M. Maragò, and C. J. Foot, Vortex nucleation in Bose–Einstein condensates in an oblate, purely magnetic potential, Phys. Rev. Lett., 2002, 88(1): 010405 https://doi.org/10.1103/PhysRevLett.88.010405
15	A. S. Sorensen, E. Demler, and M. D. Lukin, Fractional quantum Hall states of atoms in optical lattices, Phys. Rev. Lett., 2005, 94(8): 086803 https://doi.org/10.1103/PhysRevLett.94.086803
16	V. Schweikhard, I. Coddington, P. Engels, V. P. Mogendorff, and E. A. Cornell, Rapidly rotating Bose–Einstein condensates in and near the lowest Landau level, Phys. Rev. Lett., 2004, 92(4): 040404 https://doi.org/10.1103/PhysRevLett.92.040404
17	M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, Vortices and superfluidity in a strongly interacting Fermi gas, Nature, 2005, 435(7045): 1047 https://doi.org/10.1038/nature03858
18	Y. J. Lin, R. L. Compton, A. R. Perry, W. D. Phillips, J. V. Porto, and I. B. Spielman, Bose–Einstein condensate in a uniform light-induced vector potential, Phys. Rev. Lett., 2009, 102(13): 130401 https://doi.org/10.1103/PhysRevLett.102.130401
19	Y. J. Lin, R. L. Compton, K. Jiménez-García, J. V. Porto, and I. B. Spielman, Synthetic magnetic fields for ultracold neutral atoms, Nature, 2009, 462(7273): 628 https://doi.org/10.1038/nature08609
20	Y. J. Lin, R. L. Compton, K. Jimnez-Garca, W. D. Phillips, J. V. Porto, and I. B. Spielman, A synthetic electric force acting on neutral atoms, Nat. Phys., 2011, 7(7): 531 https://doi.org/10.1038/nphys1954
21	Y. J. Lin, K. Jiménez-García, and I. B. Spielman, Spin–orbit-coupled Bose-Einstein condensates, Nature, 2011, 471(7336): 83 https://doi.org/10.1038/nature09887
22	Z. Fu, P. Wang, S. Chai, L. Huang, and J. Zhang, Bose–Einstein condensate in a light-induced vector gauge potential using 1064-nm optical-dipole-trap lasers, Phys. Rev. A, 2011, 84(4): 043609 https://doi.org/10.1103/PhysRevA.84.043609
23	J. Y. Zhang, S. C. Ji, Z. Chen, L. Zhang, Z. D. Du, B. Yan, G. S. Pan, B. Zhao, Y. J. Deng, H. Zhai, S. Chen, and J. W. Pan, Collective dipole oscillations of a spin-orbit coupled Bose–Einstein condensate, Phys. Rev. Lett., 2012, 109(11): 115301 https://doi.org/10.1103/PhysRevLett.109.115301
24	C. Qu, C. Hamner, M. Gong, C. Zhang, and P. Engels, Non-equilibrium spin dynamics and Zitterbewegung in quenched spin-orbit coupled Bose–Einstein condensates, arXiv: 1301.0658, 2013
25	M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys., 2010, 82(4): 3045 https://doi.org/10.1103/RevModPhys.82.3045
26	X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys., 2011, 83(4): 1057 https://doi.org/10.1103/RevModPhys.83.1057
27	P. Wang, Z. Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, and J. Zhang, Spin–orbit coupled degenerate Fermi gases, Phys. Rev. Lett., 2012, 109(9): 095301 https://doi.org/10.1103/PhysRevLett.109.095301
28	L. W. Cheuk, A. T. Sommer, Z. Hadzibabic, T. Yefsah, W. S. Bakr, and M. W. Zwierlein, Spin-injection spectroscopy of a spin–orbit coupled Fermi gas, Phys. Rev. Lett., 2012, 109(9): 095302 https://doi.org/10.1103/PhysRevLett.109.095302
29	M. Gong, S. Tewari, and C. W. Zhang, BCS-BEC crossover and topological phase transition in 3D spin–orbit coupled degenerate Fermi gases, Phys. Rev. Lett., 2011, 107(19): 195303 https://doi.org/10.1103/PhysRevLett.107.195303
30	Z. Q. Yu and H. Zhai, Spin–orbit coupled Fermi gases across a Feshbach resonance, Phys. Rev. Lett., 2011, 107(19): 195305 https://doi.org/10.1103/PhysRevLett.107.195305
31	L. Jiang, X. J. Liu, H. Hu, and H. Pu, Rashba spin–orbitcoupled atomic Fermi gases, Phys. Rev. A, 2011, 84(6): 063618 https://doi.org/10.1103/PhysRevA.84.063618
32	X. J. Liu, L. Jiang, H. Pu, and H. Hu, Probing Majorana fermions in spin–orbit-coupled atomic Fermi gases, Phys. Rev. A, 2012, 85(2): 021603 https://doi.org/10.1103/PhysRevA.85.021603
33	R. Liao, Y. X. Yu, and W. M. Liu, Tuning the tricritical point with spin–orbit coupling in polarized fermionic condensates, Phys. Rev. Lett., 2012, 108(8): 080406 https://doi.org/10.1103/PhysRevLett.108.080406
34	M. Gong, G. Chen, S. T. Jia, and C. W. Zhang, Searching for Majorana fermions in 2D spin–orbit coupled Fermi superfluids at finite temperature, Phys. Rev. Lett., 2012, 109(10): 105302 https://doi.org/10.1103/PhysRevLett.109.105302
35	H. Hu, H. Pu, J. Zhang, S. G. Peng, and X. J. Liu, Radiofrequency spectroscopy of weakly bound molecules in spin–orbit coupled atomic Fermi gases, arXiv: 1208.5841, 2012
36	Z. Zheng, M. Gong, Y. C. Zhang, X. B. Zou, C. W. Zhang, and G. Guo, Fulde–Ferrell–Larkin–Ovchinnikov phases in two-dimensional spin–orbit coupled degenerate Fermi gases, arXiv: 1212.6826, 2012
37	V. Galitski and I. B. Spielman, Spin–orbit coupling in quantum gases, Nature, 2013, 494(7435): 49 https://doi.org/10.1038/nature11841
38	J. Radi, A. Di Ciolo, K. Sun, and V. Galitski, Exotic quantum spin models in spin–orbit-coupled Mott insulators, Phys. Rev. Lett., 2012, 109(8): 085303 https://doi.org/10.1103/PhysRevLett.109.085303
39	W. S. Cole, S. Zhang, A. Paramekanti, and N. Trivedi, Bose–Hubbard models with synthetic spin–orbit coupling: Mott insulators, spin textures, and superfluidity, Phys. Rev. Lett., 2012, 109(8): 085302 https://doi.org/10.1103/PhysRevLett.109.085302
40	Z. Cai, X. Zhou, and C. Wu, Magnetic phases of bosons with synthetic spin–orbit coupling in optical lattices, Phys. Rev. A, 2012, 85(6): 061605 https://doi.org/10.1103/PhysRevA.85.061605
41	D. Wei, D. Zh. Xiong, H. X. Chen, and J. Zhang, An enriched 40K source for atomic cooling, Chin. Phys. Lett., 2007, 24: 679 https://doi.org/10.1088/0256-307X/24/3/025
42	D. Xiong, H. Chen, P. Wang, X. Yu, F. Gao, and J. Zhang, Quantum degenerate Fermi–Bose mixtures of 40K and 87Rb atoms in a quadrupole-Ioffe configuration trap, Chin. Phys. Lett., 2008, 25: 843 https://doi.org/10.1088/0256-307X/25/3/011
43	P. Wang, H. Chen, D. Xiong, X. Yu, F. Gao, and J. Zhang, The design of quadrapole-Ioffe configuration trap for quantum degenerate Fermi–Bose mixtures, Acta. Phys. Sin., 2008, 57(8): 4840 (in Chinese)
44	D. Xiong, P. Wang, Z. Fu, S. Chai, and J. Zhang, Evaporative cooling of 87Rb atoms into Bose–Einstein condensate in an optical dipole trap, Chin. Opt. Lett., 2010, 8: 627 (in Chinese) https://doi.org/10.3788/COL20100807.0627
45	D. Xiong, P. Wang, Z. Fu, and J. Zhang, Transport of Bose–Einstein condensate in QUIC trap and separation of trapping spin states, Opt. Express, 2010, 18(2): 1649 https://doi.org/10.1364/OE.18.001649
46	I. B. Spielman, Raman processes and effective gauge potentials, Phys. Rev. A, 2009, 79(6): 063613 https://doi.org/10.1103/PhysRevA.79.063613
47	L. Zhang, J. Y. Zhang, S. C. Ji, Z. D. Du, H. Zhai, Y. J. Deng, S. Chen, P. Zhang, and J. W. Pan, Stability of excited dressed states with spin–orbit coupling, Phys. Rev. A, 2012, 87(1): 011601 https://doi.org/10.1103/PhysRevA.87.011601
48	X. J. Liu and H. Hu, Topological superfluid in onedimensional spin–orbit-coupled atomic Fermi gases, Phys. Rev. A, 2012, 85(3): 033622 https://doi.org/10.1103/PhysRevA.85.033622
49	X. J. Liu, L. Jiang, H. Pu, and H. Hu, Probing Majorana fermions in spin–orbit-coupled atomic Fermi gases, Phys. Rev. A, 2012, 85(2): 021603 https://doi.org/10.1103/PhysRevA.85.021603
50	X. J. Liu, Zh. X. Liu, and M. Cheng, Manipulating topological edge spins in a one-dimensional optical lattice, Phys. Rev. Lett., 2013, 110(7): 076401 https://doi.org/10.1103/PhysRevLett.110.076401
51	L. Zhou, H. Pu, and W. Zhang, Anderson localization of cold atomic gases with effective spin–orbit interaction in a quasiperiodic optical lattice, Phys. Rev. A, 2013, 87(2): 023625 https://doi.org/10.1103/PhysRevA.87.023625
52	R. Wei and E. J. Mueller, Majorana fermions in onedimensional spin–orbit-coupled Fermi gases, Phys. Rev. A, 2012, 86(6): 063604 https://doi.org/10.1103/PhysRevA.86.063604
53	P. Wang, Z. Fu, L. Huang, and J. Zhang, Momentumresolved Raman spectroscopy of a noninteracting ultracold Fermi gas, Phys. Rev. A, 2012, 85(5): 053626 https://doi.org/10.1103/PhysRevA.85.053626
54	Z. Fu, P. Wang, L. Huang, Z. Meng, and J. Zhang, Momentum-resolved Raman spectroscopy of bound molecules in ultracold Fermi gas, Phys. Rev. A, 2012, 86(3): 033607 https://doi.org/10.1103/PhysRevA.86.033607
55	C. Chin, M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, J. H. Denschlag, and R. Grimm, Observation of the pairing gap in a strongly interacting Fermi gas, Science, 2004, 305(5687): 1128 https://doi.org/10.1126/science.1100818
56	J. T. Stewart, J. P. Gaebler, and D. S. Jin, Using photoemission spectroscopy to probe a strongly interacting Fermi gas, Nature, 2008, 454(7205): 744 https://doi.org/10.1038/nature07172
57	J. Simon, W. S. Bakr, R. Ma, M. E. Tai, P. M. Preiss, and M. Greiner, Quantum simulation of antiferromagnetic spin chains in an optical lattice, Nature, 2011, 472(7343): 307 https://doi.org/10.1038/nature09994
58	E. Altman, E. Demler, and M. D. Lukin, Probing manybody states of ultracold atoms via noise correlations, Phys. Rev. A, 2004, 70(1): 013603 https://doi.org/10.1103/PhysRevA.70.013603
59	C. A. Regal and D. S. Jin, Measurement of positive and negative scattering lengths in a Fermi gas of atoms, Phys. Rev. Lett., 2003, 90(23): 230404 https://doi.org/10.1103/PhysRevLett.90.230404
60	S. Gupta, Z. Hadzibabic, M. W. Zwierlein, C. A. Stan, K. Dieckmann, C. H. Schunck, E. G. M. Van Kempen, B. J. Verhaar, and W. Ketterle, Radio-frequency spectroscopy of ultracold fermions, Science, 2003, 300(5626): 1723 https://doi.org/10.1126/science.1085335
61	Y. Shin, C. H. Schunck, A. Schirotzek, and W. Ketterle, Tomographic rf spectroscopy of a trapped Fermi gas at unitarity, Phys. Rev. Lett., 2007, 99(9): 090403 https://doi.org/10.1103/PhysRevLett.99.090403
62	Q. Chen and K. Levin, Momentum resolved radio frequency spectroscopy in trapped fermi gases, Phys. Rev. Lett., 2009, 102(19): 190402 https://doi.org/10.1103/PhysRevLett.102.190402
63	Q. Chen, Y. He, C. C. Chien, and K. Levin, Theory of radio frequency spectroscopy experiments in ultracold Fermi gases and their relation to photoemission in the cuprates, Rep. Prog. Phys., 2009, 72: 12250<?Pub Caret?>1 https://doi.org/10.1088/0034-4885/72/12/122501
64	T. L. Dao, A. Georges, J. Dalibard, C. Salomon, and I. Carusotto, Measuring the one-particle excitations of ultracold fermionic atoms by stimulated Raman spectroscopy, Phys. Rev. Lett., 2007, 98(24): 240402 https://doi.org/10.1103/PhysRevLett.98.240402
65	T. L. Dao, I. Carusotto, and A. Georges, Probing quasiparticle states in strongly interacting atomic gases by momentumresolved Raman photoemission spectroscopy, Phys. Rev. A, 2009, 80(2): 023627 https://doi.org/10.1103/PhysRevA.80.023627
66	G. Veeravalli, E. Kuhnle, P. Dyke, and C. J. Vale, Bragg spectroscopy of a strongly interacting Fermi gas, Phys. Rev. Lett., 2008, 101(25): 250403 https://doi.org/10.1103/PhysRevLett.101.250403
67	E. D. Kuhnle, S. Hoinka, P. Dyke, H. Hu, P. Hannaford, and C. J. Vale, Temperature dependence of the universal contact parameter in a unitary Fermi gas, Phys. Rev. Lett., 2011, 106(17): 170402 https://doi.org/10.1103/PhysRevLett.106.170402

[1]	Qian Chen,Xiaohui Yang,Xiaojun Yang,Jian Chen,Chenyi Shen,Pan Zhang,Yupeng Li,Qian Tao,Zhu-An Xu. Enhanced superconductivity in hole-doped Nb₂PdS₅[J]. Front. Phys. , 2017, 12(5): 127402-.
[2]	Jian-Lei Ge,Tian-Ru Wu,Ming Gao,Zhan-Bin Bai,Lu Cao,Xue-Feng Wang,Yu-Yuan Qin,Feng-Qi Song. Weak localization of bismuth cluster-decorated graphene and its spin–orbit interaction[J]. Front. Phys. , 2017, 12(4): 127210-.
[3]	Cong Xiao,Dingping Li,Zhongshui Ma. Thermoelectric response of spin polarization in Rashba spintronic systems[J]. Front. Phys. , 2016, 11(3): 117201-.
[4]	Yongping Zhang,Maren Elizabeth Mossman,Thomas Busch,Peter Engels,Chuanwei Zhang. Properties of spin–orbit-coupled Bose–Einstein condensates[J]. Front. Phys. , 2016, 11(3): 118103-.
[5]	Jing-Kun Wang,Wei Yi,Wei Zhang. Two-body physics in quasi-low-dimensional atomic gases under spin–orbit coupling[J]. Front. Phys. , 2016, 11(3): 118102-.
[6]	Yi-Bin Hu, Yong-Hong Zhao, Xue-Feng Wang. A computational investigation of topological insulator Bi₂Se₃ film[J]. Front. Phys. , 2014, 9(6): 760-767.
[7]	Qijin Chen, Jibiao Wang. Pseudogap phenomena in ultracold atomic Fermi gases[J]. Front. Phys. , 2014, 9(5): 539-570.

Viewed

Full text

Abstract

Cited

Shared

Discussed