Two-body physics in quasi-low-dimensional atomic gases under spin–orbit coupling

doi:10.1007/s11467-015-0529-2

Frontiers of Physics

2016, Vol. 11

Issue (3): 118102 https://doi.org/10.1007/s11467-015-0529-2

本期目录

Two-body physics in quasi-low-dimensional atomic gases under spin–orbit coupling

Jing-Kun Wang^1,²,Wei Yi^3,^4,^*(

),Wei Zhang^1,^2,^*(

)

¹. Department of Physics, Renmin University of China, Beijing 100872, China
². Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, China
³. Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
⁴. Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China

全文: PDF(835 KB)

Abstract：

One of the most dynamic directions in ultracold atomic gas research is the study of low-dimensional physics in quasi-low-dimensional geometries, where atoms are confined in strongly anisotropic traps. Recently, interest has significantly intensified with the realization of synthetic spin–orbit coupling (SOC). As a first step toward understanding the SOC effect in quasi-low-dimensional systems, the solution of two-body problems in different trapping geometries and different types of SOC has attracted great attention in the past few years. In this review, we discuss both the scattering-state and the bound-state solutions of two-body problems in quasi-one and quasi-two dimensions. We show that the degrees of freedom in tightly confined dimensions, in particular with the presence of SOC, may significantly affect system properties. Specifically, in a quasi-one-dimensional atomic gas, a one-dimensional SOC can shift the positions of confinement-induced resonances whereas, in quasitwo-dimensional gases, a Rashba-type SOC tends to increase the two-body binding energy, such that more excited states in the tightly confined direction are occupied and the system is driven further away from a purely two-dimensional gas. The effects of the excited states can be incorporated by adopting an effective low-dimensional Hamiltonian having the form of a two-channel model. With the bare parameters fixed by two-body solutions, this effective Hamiltonian leads to qualitatively different many-body properties compared to a purely low-dimensional model.

Key words： artificial gauge field synthetic spin–orbit coupling quasi-low dimensional sysem

收稿日期: 2015-08-15 出版日期: 2016-06-08

Corresponding Author(s): Wei Yi,Wei Zhang

引用本文:

. [J]. Frontiers of Physics, 2016, 11(3): 118102.
Jing-Kun Wang,Wei Yi,Wei Zhang. Two-body physics in quasi-low-dimensional atomic gases under spin–orbit coupling. Front. Phys. , 2016, 11(3): 118102.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-015-0529-2
https://academic.hep.com.cn/fop/CN/Y2016/V11/I3/118102

1	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. 102(13), 130401 (2009) https://doi.org/10.1103/PhysRevLett.102.130401
2	Y. J. Lin, K. Jiménez-García, and I. B. Spielman, Spin–orbit-coupled Bose–Einstein condensates, Nature 471(7336), 83 (2011) https://doi.org/10.1038/nature09887
3	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. 109(11), 115301 (2012) https://doi.org/10.1103/PhysRevLett.109.115301
4	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, Phys. Rev. A 88, 021604(R) (2013)
5	S. C. Ji, J. Y. Zhang, L. Zhang, Z. D. Du, W. Zheng, Y. J. Deng, H. Zhai, S. Chen, and J. W. Pan, Experimental determination of the finite-temperature phase diagram of a spin–orbit coupled Bose gas, Nat. Phys. 10(4), 314 (2014) https://doi.org/10.1038/nphys2905
6	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. 109(9), 095301 (2012) https://doi.org/10.1103/PhysRevLett.109.095301
7	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. 109(9), 095302 (2012) https://doi.org/10.1103/PhysRevLett.109.095302
8	Z. Fu, L. Huang, Z. Meng, P. Wang, L. Zhang, S. Zhang, H. Zhai, P. Zhang, and J. Zhang, Production of Feshbach molecules induced by spin–orbit coupling in Fermi gases, Nat. Phys. 10(2), 110 (2014) https://doi.org/10.1038/nphys2824
9	P. J. Wang and J. Zhang, Spin–orbit coupling in Bose–Einstein condensate and degenerate Fermi gases, Front. Phys. 9(5), 612 (2014) https://doi.org/10.1007/s11467-013-0377-x
10	H. Zhai, Spin–orbit coupled quantum gases, Int. J. Mod. Phys. B 26(01), 1230001 (2012) https://doi.org/10.1142/S0217979212300010
11	V. Galitski and I. B. Spielman, Spin–orbit coupling in quantum gases, Nature 494(7435), 49 (2013) https://doi.org/10.1038/nature11841
12	X. Zhou, Y. Li, Z. Cai, and C. Wu, Unconventional states of bosons with the synthetic spin–orbit coupling, J. Phys. B 46(13), 134001 (2013) https://doi.org/10.1088/0953-4075/46/13/134001
13	N. Goldman, G. Juzeliūnas, P. Öhberg, and I. B. Spielman, Light-induced gauge fields for ultracold atoms, Rep. Prog. Phys. 77(12), 126401 (2014) https://doi.org/10.1088/0034-4885/77/12/126401
14	H. Zhai, Degenerate quantum gases with spin–orbit coupling: A review, Rep. Prog. Phys. 78(2), 026001 (2015) https://doi.org/10.1088/0034-4885/78/2/026001
15	J. Zhang, H. Hu, X. J. Liu, and H. Pu, Fermi gases with synthetic spin–orbit coupling, Annu. Rev. Cold At. Mol. 2, 81 (2014) https://doi.org/10.1142/9789814590174_0002
16	Y. Xu and C. Zhang, Topological Fulde–Ferrell superfluids of a spin–orbit coupled Fermi gas, Int. J. Mod. Phys. B 29(01), 1530001 (2015) https://doi.org/10.1142/S0217979215300017
17	W. Yi, W. Zhang, and X. Cui, Pairing superfluidity in spin–orbit coupled ultracold Fermi gases, Sci. China- Phys. Mech. Astron. 58(1), 014201 (2015) https://doi.org/10.1007/s11433-014-5609-8
18	J. P. Vyasanakere and V. B. Shenoy, Bound states of two spin-1/2 fermions in a synthetic non-Abelian gauge field, Phys. Rev. B 83(9), 094515 (2011) https://doi.org/10.1103/PhysRevB.83.094515
19	J. P. Vyasanakere, S. Zhang, and V. B. Shenoy, BCS–BEC crossover induced by a synthetic non-Abelian gauge field, Phys. Rev. B 84(1), 014512 (2011) https://doi.org/10.1103/PhysRevB.84.014512
20	X. Cui, Mixed-partial-wave scattering with spin–orbit coupling and validity of pseudopotentials, Phys. Rev. A 85(2), 022705 (2012) https://doi.org/10.1103/PhysRevA.85.022705
21	Z. F. Xu and L. You, Dynamical generation of arbitrary spin–orbit couplings for neutral atoms, Phys. Rev. A 85(4), 043605 (2012) https://doi.org/10.1103/PhysRevA.85.043605
22	F. Wu, R. Zhang, T. S. Deng, W. Zhang, W. Yi, and G. C. Guo, BCS–BEC crossover and quantum phase transition in an ultracold Fermi gas under spin–orbit coupling, Phys. Rev. A 89(6), 063610 (2014) https://doi.org/10.1103/PhysRevA.89.063610
23	Z. Y. Shi, X. Cui, and H. Zhai, Universal trimers induced by spin–orbit coupling in ultracold Fermi gases, Phys. Rev. Lett. 112(1), 013201 (2014) https://doi.org/10.1103/PhysRevLett.112.013201
24	X. Cui, and W. Yi, Universal Borromean binding in spin–orbit-coupled ultracold fermi gases, Phys. Rev. X 4(3), 031026 (2014) https://doi.org/10.1103/PhysRevX.4.031026
25	M. Sato, Y. Takahashi, and S. Fujimoto, Non-Abelian topological order in s-wave superfluids of ultracold fermionic atoms, Phys. Rev. Lett. 103(2), 020401 (2009) https://doi.org/10.1103/PhysRevLett.103.020401
26	J. P. Kestner and L. M. Duan, Conditions of low dimensionality for strongly interacting atoms under a transverse trap, Phys. Rev. A 74(5), 053606 (2006) https://doi.org/10.1103/PhysRevA.74.053606
27	J. P. Kestner and L. M. Duan, Effective low-dimensional Hamiltonian for strongly interacting atoms in a transverse trap, Phys. Rev. A 76(6), 063610 (2007) https://doi.org/10.1103/PhysRevA.76.063610
28	Z. Q. Yu and H. Zhai, Spin–orbit coupled Fermi gases across a Feshbach resonance, Phys. Rev. Lett. 107(19), 195305 (2011) https://doi.org/10.1103/PhysRevLett.107.195305
29	R. Zhang, F. Wu, J. R. Tang, G. C. Guo, W. Yi, and W. Zhang, Significance of dressed molecules in a quasi-two-dimensional Fermi gas with spin–orbit coupling, Phys. Rev. A 87(3), 033629 (2013) https://doi.org/10.1103/PhysRevA.87.033629
30	T. Stöferle, H. Moritz, K. Günter, M. Köhl, and T. Esslinger, Molecules of fermionic atoms in an optical lattice, Phys. Rev. Lett. 96(3), 030401 (2006) https://doi.org/10.1103/PhysRevLett.96.030401
31	B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G. V. Shlyapnikov, T. W. Hänsch, and I. Bloch, Tonks–Girardeau gas of ultracold atoms in an optical lattice, Nature 429(6989), 227 (2004) https://doi.org/10.1038/nature02530
32	T. Kinoshita, T. Wenger, and D. S. Weiss, Observation of a one-dimensional Tonks–Girardeau gas, Science 305(5687), 1125 (2004) https://doi.org/10.1126/science.1100700
33	M. Köhl, H. Moritz, T. Stöferle, K. Günter, and T. Esslinger, Fermionic atoms in a three dimensional optical lattice: Observing Fermi surfaces, dynamics, and interactions, Phys. Rev. Lett. 94(8), 080403 (2005) https://doi.org/10.1103/PhysRevLett.94.080403
34	Y. Castin, Simple theoretical tools for low dimension Bose gases, J. Phys. IV 116, 89 (2004) https://doi.org/10.1051/jp4:2004116004
35	D. E. Sheehy and L. Radzihovsky, Quantum decoupling transition in a one-dimensional Feshbach-resonant superfluid, Phys. Rev. Lett. 95(13), 130401 (2005) https://doi.org/10.1103/PhysRevLett.95.130401
36	E. Orignac and R. Citro, Phase transitions in the boson–fermion resonance model in one dimension, Phys. Rev. A 73(6), 063611 (2006) https://doi.org/10.1103/PhysRevA.73.063611
37	M. Olshanii, Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons, Phys. Rev. Lett. 81(5), 938 (1998) https://doi.org/10.1103/PhysRevLett.81.938
38	T. Bergeman, M. G. Moore, and M. Olshanii, Atom–atom scattering under cylindrical harmonic confinement: Numerical and analytic studies of the confinement induced resonance, Phys. Rev. Lett. 91(16), 163201 (2003) https://doi.org/10.1103/PhysRevLett.91.163201
39	T. Busch, B. G. Englert, K. Rzażewski, and M. Wilkens, Two cold atoms in a harmonic trap, Found. Phys. 28(4), 549 (1998) https://doi.org/10.1023/A:1018705520999
40	D. S. Petrov, M. Holzmann, and G. V. Shlyapnikov, Bose–Einstein condensation in quasi-2D trapped gases, Phys. Rev. Lett. 84(12), 2551 (2000) https://doi.org/10.1103/PhysRevLett.84.2551
41	D. S. Petrov and G. V. Shlyapnikov, Interatomic collisions in a tightly confined Bose gas, Phys. Rev. A 64(1), 012706 (2001) https://doi.org/10.1103/PhysRevA.64.012706
42	P. O. Fedichev, M. J. Bijlsma, and P. Zoller, Extended molecules and geometric scattering resonances in optical lattices, Phys. Rev. Lett. 92(8), 080401 (2004) https://doi.org/10.1103/PhysRevLett.92.080401
43	M. Holland, S. J. J. M. F. Kokkelmans, M. L. Chiofalo, and R. Walser, Resonance superfluidity in a quantum degenerate Fermi gas, Phys. Rev. Lett. 87(12), 120406 (2001) https://doi.org/10.1103/PhysRevLett.87.120406
44	M. H. Szymańska, K. Góral, T. Köhler, and K. Burnett, Conventional character of the BCS–BEC crossover in ultracold gases of K40, Phys. Rev. A 72(1), 013610 (2005) https://doi.org/10.1103/PhysRevA.72.013610
45	Q. Chen, J. Stajic, S. Tan, and K. Levin, BCS–BEC crossover: From high temperature superconductors to ultracold superfluids, Phys. Rep. 412(1), 1 (2005) https://doi.org/10.1016/j.physrep.2005.02.005
46	Q. Chen and J. Wang, Pseudogap phenomena in ultracold atomic Fermi gases, Front. Phys. 9(5), 570 (2014) https://doi.org/10.1007/s11467-014-0448-7
47	L. M. Duan, Effective Hamiltonian for fermions in an optical lattice across a Feshbach resonance, Phys. Rev. Lett. 95(24), 243202 (2005) https://doi.org/10.1103/PhysRevLett.95.243202
48	R. B. Diener and T. L. Ho, Fermions in optical lattices swept across Feshbach resonances, Phys. Rev. Lett. 96(1), 010402 (2006) https://doi.org/10.1103/PhysRevLett.96.010402
49	C. A. Regal, M. Greiner, and D. S. Jin, Observation of resonance condensation of fermionic atom pairs, Phys. Rev. Lett. 92(4), 040403 (2004) https://doi.org/10.1103/PhysRevLett.92.040403
50	K. Huang, Statistical Mechanics, 2nd Ed., New York: Wiley, 1987
51	L. Tonks, The complete equation of state of one, two and three-dimensional gases of hard elastic spheres, Phys. Rev. 50(10), 955 (1936) https://doi.org/10.1103/PhysRev.50.955
52	H. Moritz, T. Stöferle, K. Günter, M. Köhl, and T. Esslinger, Confinement induced molecules in a 1D Fermi gas, Phys. Rev. Lett. 94(21), 210401 (2005) https://doi.org/10.1103/PhysRevLett.94.210401
53	J. K. Chin, D. E. Miller, Y. Liu, C. Stan, W. Setiawan, C. Sanner, K. Xu, and W. Ketterle, Evidence for superfluidity of ultracold fermions in an optical lattice, Nature 443(7114), 961 (2006) https://doi.org/10.1038/nature05224
54	Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas, Nature 441(7097), 1118 (2006) https://doi.org/10.1038/nature04851
55	W. Zhang, G. D. Lin, and L. M. Duan, BCS–BEC crossover of a quasi-two-dimensional Fermi gas: The significance of dressed molecules, Phys. Rev. A 77(6), 063613 (2008) https://doi.org/10.1103/PhysRevA.77.063613
56	P. Dyke, E. D. Kuhnle, S. Whitlock, H. Hu, M. Mark, S. Hoinka, M. Lingham, P. Hannaford, and C. J. Vale, Crossover from 2D to 3D in a weakly interacting Fermi gas, Phys. Rev. Lett. 106(10), 105304 (2011) https://doi.org/10.1103/PhysRevLett.106.105304
57	A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, 2nd Ed., New York: Dover, 1975
58	L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd Ed., Oxford: Butterworth–Heinemann, 1999
59	Y. Kagan, B. V. Svistunov, and G. V. Shlyapnikov, Influence on inelastic processes of the phase transition in a weakly collisional two-dimensional Bose gas, Sov. Phys. JETP 66, 480 (1987)
60	R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, 2nd Ed., New York: McGraw-Hill, 1995
61	W. Zhang and P. Zhang, Confinement-induced resonances in quasi-one-dimensional traps with transverse anisotropy, Phys. Rev. A 83(5), 053615 (2011) https://doi.org/10.1103/PhysRevA.83.053615
62	A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series, 2nd Ed., New York: Gordon and Breach, 1986
63	Z. Idziaszek and T. Calarco, Analytical solutions for the dynamics of two trapped interacting ultracold atoms, Phys. Rev. A 74(2), 022712 (2006) https://doi.org/10.1103/PhysRevA.74.022712
64	X. J. Liu and H. Hu, Topological superfluid in one-dimensional spin–orbit-coupled atomic Fermi gases, Phys. Rev. A 85(3), 033622 (2012) https://doi.org/10.1103/PhysRevA.85.033622
65	J. R. Taylor, Scattering Theory, 2nd Ed., New York: Wiley, 1972
66	P. Zhang, L. Zhang, and W. Zhang, Interatomic collisions in two-dimensional and quasi-two-dimensional confinements with spin–orbit coupling, Phys. Rev. A 86(4), 042707 (2012) https://doi.org/10.1103/PhysRevA.86.042707
67	Y. C. Zhang, S. W. Song, and W. M. Liu, The confinement induced resonance in spin–orbit coupled cold atoms with Raman coupling, Sci. Rep. 4, 4992 (2014) https://doi.org/10.1038/srep04992
68	R. Zhang and W. Zhang, Effective Hamiltonians for quasi-one-dimensional Fermi gases with spin–orbit coupling, Phys. Rev. A 88(5), 053605 (2013) https://doi.org/10.1103/PhysRevA.88.053605
69	L. Dell'Anna, G. Mazzarella, and L. Salasnich, Condensate fraction of a resonant Fermi gas with spin–orbit coupling in three and two dimensions, Phys. Rev. A 84(3), 033633 (2011) https://doi.org/10.1103/PhysRevA.84.033633
70	A. J. Leggett, Modern Trends in the Theory of Condensed Matter, 2nd Ed., Berlin: Springer-Verlag, 1980
71	P. Nozières and S. Schmitt-Rink, Bose condensation in an attractive fermion gas: From weak to strong coupling superconductivity, J. Low Temp. Phys. 59(3), 195 (1985) https://doi.org/10.1007/BF00683774
72	C. A. R. S. de Melo, M. Randeria, and J. R. Engelbrecht, Crossover from BCS to Bose superconductivity– transition temparetaure and time-dependent Ginzburg–Landau theory, Phys. Rev. Lett. 71, 3202 (1993) https://doi.org/10.1103/PhysRevLett.71.3202
73	J. Zhou, W. Zhang, and W. Yi, Topological superfluid in a trapped two-dimensional polarized Fermi gas with spin–orbit coupling, Phys. Rev. A 84(6), 063603 (2011) https://doi.org/10.1103/PhysRevA.84.063603
74	W. Yi and L. M. Duan, BCS–BEC crossover and quantum phase transition for Li6 and K40 atoms across the Feshbach resonance, Phys. Rev. A 73(6), 063607 (2006) https://doi.org/10.1103/PhysRevA.73.063607
75	P. Fulde and R. A. Ferrell, Superconductivity in a strong spin-exchange field, Phys. Rev. 135(3A), A550 (1964) https://doi.org/10.1103/PhysRev.135.A550
76	A. I. Larkin and Y. N. Ovchinnikov, Inhomogeneous state of superconductors, Sov. Phys. JETP 20, 762 (1965)
77	W. V. Liu and F. Wilczek, Interior gap superfluidity, Phys. Rev. Lett. 90(4), 047002 (2003) https://doi.org/10.1103/PhysRevLett.90.047002
78	C. Zhang, S. Tewari, R. M. Lutchyn, and S. Das Sarma, px+ipy superfluid from s-wave interactions of fermionic cold atoms, Phys. Rev. Lett. 101(16), 160401 (2008) https://doi.org/10.1103/PhysRevLett.101.160401

Viewed

Full text

Abstract

Cited

Shared

Discussed