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Spin–orbit coupling in quantum gases

Abstract

Spin–orbit coupling links a particle’s velocity to its quantum-mechanical spin, and is essential in numerous condensed matter phenomena, including topological insulators and Majorana fermions. In solid-state materials, spin–orbit coupling originates from the movement of electrons in a crystal’s intrinsic electric field, which is uniquely prescribed in any given material. In contrast, for ultracold atomic systems, the engineered ‘material parameters’ are tunable: a variety of synthetic spin–orbit couplings can be engineered on demand using laser fields. Here we outline the current experimental and theoretical status of spin–orbit coupling in ultracold atomic systems, discussing unique features that enable physics impossible in any other known setting.

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Figure 1: Physical origin of SOC in conventional systems.
Figure 2: Laser coupling schemes.
Figure 3: Generalized SOC.

References

  1. Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010)

    Article  ADS  CAS  PubMed  Google Scholar 

  2. Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010)

    Article  ADS  CAS  Google Scholar 

  3. von Klitzing, K., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980)

    Article  ADS  CAS  Google Scholar 

  4. Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982)

    Article  ADS  CAS  Google Scholar 

  5. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008)

    Article  ADS  CAS  Google Scholar 

  6. Osterloh, K., Baig, M., Santos, L., Zoller, P. & Lewenstein, M. Cold atoms in non-abelian gauge potentials: from the Hofstadter “Moth” to lattice gauge theory. Phys. Rev. Lett. 95, 010403 (2005)This paper was an initial proposal suggesting a method of creating SOC in cold atoms (equivalent to a non-Abelian gauge field), in a lattice potential.

    Article  ADS  CAS  PubMed  Google Scholar 

  7. Ruseckas, J., Juzeliūnas, G., Ohberg, P. & Fleischhauer, M. Non-abelian gauge potentials for ultracold atoms with degenerate dark states. Phys. Rev. Lett. 95, 010404 (2005)This paper was an initial proposal suggesting a method of creating SOC in cold atoms (equivalent to a non-Abelian gauge field) in the continuum.

    Article  ADS  CAS  PubMed  Google Scholar 

  8. Liu, X.-J., Borunda, M. F., Liu, X. & Sinova, J. Effect of induced spin–orbit coupling for atoms via laser fields. Phys. Rev. Lett. 102, 046402 (2009)

    Article  ADS  PubMed  CAS  Google Scholar 

  9. Juzeliūnas, G., Ruseckas, J. & Dalibard, J. Generalized Rashba-Dresselhaus spin–orbit coupling for cold atoms. Phys. Rev. A 81, 053403 (2010)

    Article  ADS  CAS  Google Scholar 

  10. Anderson, B. M., Juzeliūnas, G., Galitski, V. M. & Spielman, I. B. Synthetic 3D spin–orbit coupling. Phys. Rev. Lett. 108, 235301 (2012)

    Article  ADS  PubMed  CAS  Google Scholar 

  11. Lin, Y.-J., Compton, R. L., Jiménez-García, K., Porto, J. V. & Spielman, I. B. Synthetic magnetic fields for ultracold neutral atoms. Nature 462, 628–632 (2009)

    Article  ADS  CAS  PubMed  Google Scholar 

  12. Lin, Y.-J., Jiménez-García, K. & Spielman, I. B. Spin-orbit-coupled Bose–Einstein condensates. Nature 471, 83–86 (2011)This work demonstrated the first observation of SOC in an atomic quantum gas, and observed a quantum phase transition in the resulting two-component spin–orbit-coupled BECs.

    Article  ADS  CAS  PubMed  Google Scholar 

  13. Sau, J. D., Lutchyn, R. M., Tewari, S. & Das Sarma, S. Generic new platform for topological quantum computation using semiconductor heterostructures. Phys. Rev. Lett. 104, (2010)

  14. Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546–570 (1989)

    Article  ADS  CAS  Google Scholar 

  15. Greiner, M., Mandel, O., Esslinger, T., Hansch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002)

    Article  ADS  CAS  PubMed  Google Scholar 

  16. Radić, J., Di Ciolo, A., Sun, K. & Galitski, V. Exotic quantum spin models in spin–orbit-coupled Mott insulators. Phys. Rev. Lett. 109, 085303 (2012)

    Article  ADS  PubMed  CAS  Google Scholar 

  17. Cole, W., Zhang, S., Paramekanti, A. & Trivedi, N. Bose-Hubbard models with synthetic spin–orbit coupling: Mott insulators, spin textures, and superfluidity. Phys. Rev. Lett. 109, 085302 (2012)

    Article  ADS  PubMed  CAS  Google Scholar 

  18. Levin, M. & Stern, A. Fractional topological insulators. Phys. Rev. Lett. 103, 196803 (2009)

    Article  ADS  PubMed  CAS  Google Scholar 

  19. Sedrakyan, T. A., Kamenev, A. & Glazman, L. I. Composite fermion state of spin–orbit-coupled bosons. Phys. Rev. A 86, 063639 (2012)

    Article  ADS  CAS  Google Scholar 

  20. Ashhab, S. & Leggett, A. J. Bose-Einstein condensation of spin-1/2 atoms with conserved total spin. Phys. Rev. A 68, 063612 (2003)

    Article  ADS  CAS  Google Scholar 

  21. Cai, Z., Zhou, X. & Wu, C. Magnetic phases of bosons with synthetic spin–orbit coupling in optical lattices. Phys. Rev. A 85, 061605 (2012)

    Article  ADS  CAS  Google Scholar 

  22. Stanescu, T., Anderson, B. & Galitski, V. Spin-orbit coupled Bose-Einstein condensates. Phys. Rev. A 78, 023616 (2008)

    Article  ADS  CAS  Google Scholar 

  23. Bychkov, Y. A. & Rashba, E. I. Oscillatory effects and the magnetic susceptibility of carriers in inversion layers. J. Phys. Chem. 17, 6039–6045 (1984)

    Google Scholar 

  24. Meier, L. et al. Measurement of Rashba and Dresselhaus spin–orbit magnetic fields. Nature Phys. 3, 650–654 (2007)

    Article  ADS  CAS  Google Scholar 

  25. Dresselhaus, G. Spin-orbit coupling effects in zinc blende structures. Phys. Rev. 100, 580–586 (1955)

    Article  ADS  CAS  MATH  Google Scholar 

  26. von Zutic, I., Fabian, J. & Das Sarma, S. Spintronics: fundamentals and applications. Rev. Mod. Phys. 76, 323–410 (2004)

    Article  ADS  CAS  Google Scholar 

  27. Sinova, J. et al. Universal intrinsic spin Hall effect. Phys. Rev. Lett. 92, 126603 (2004)

    Article  ADS  PubMed  CAS  Google Scholar 

  28. Kato, Y. K., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Observation of the spin Hall effect in semiconductors. Science 306, 1910–1913 (2004)

    Article  ADS  CAS  PubMed  Google Scholar 

  29. Burkov, A. A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011)

    Article  ADS  CAS  PubMed  Google Scholar 

  30. Koralek, J. D. et al. Emergence of the persistent spin helix in semiconductor quantum wells. Nature 458, 610–613 (2009)

    Article  ADS  CAS  PubMed  Google Scholar 

  31. Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Phys.-Usp. 44, 131–136 (2001)This paper proposed that Majorana fermions can exist at the end of one-dimensional superconducting wires, an idea that is directly relevant to one-dimensional atomic Fermi gases with SOC.

    Article  ADS  Google Scholar 

  32. Alicea, J., Oreg, Y., Refael, G., von Oppen, F. & Fisher, M. P. A. Non-Abelian statistics and topological quantum information processing in 1D wire networks. Nature Phys. 7, 412–417 (2011)

    Article  ADS  CAS  Google Scholar 

  33. Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336, 1003–1007 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  34. Higbie, J. & Stamper-Kurn, D. M. Periodically dressed Bose-Einstein condensate: a superfluid with an anisotropic and variable critical velocity. Phys. Rev. Lett. 88, 090401 (2002)This paper proposed loading quantum degenerate gases into the laser-dressed states used in current SOC experiments.

    Article  ADS  CAS  PubMed  Google Scholar 

  35. Fu, Z., Wang, P., Chai, S., Huang, L. & Zhang, J. Bose-Einstein condensate in a light-induced vector gauge potential using 1064-nm optical-dipole-trap lasers. Phys. Rev. A 84, 043609 (2011)

    Article  ADS  CAS  Google Scholar 

  36. Zhang, J.-Y. et al. Collective dipole oscillations of a spin–orbit coupled Bose-Einstein condensate. Phys. Rev. Lett. 109, 115301 (2012)

    Article  ADS  PubMed  CAS  Google Scholar 

  37. Wang, P. et al. Spin-orbit coupled degenerate Fermi gases. Phys. Rev. Lett. 109, 095301 (2012)This was the first observation of SOC in an atomic Fermi gas.

    Article  ADS  PubMed  CAS  Google Scholar 

  38. Cheuk, L. et al. Spin-injection spectroscopy of a spin–orbit coupled Fermi gas. Phys. Rev. Lett. 109, 095302 (2012)This paper describes the observation of SOC in an atomic Fermi gas, and a direct spectroscopic measurement of the SOC dispersion relation.

    Article  ADS  PubMed  CAS  Google Scholar 

  39. Campbell, D. L., Juzeliūnas, G. & Spielman, I. B. Realistic Rashba and Dresselhaus spin–orbit coupling for neutral atoms. Phys. Rev. A 84, 025602 (2011)

    Article  ADS  CAS  Google Scholar 

  40. Wang, C., Gao, C., Jian, C.-M. & Zhai, H. Spin-orbit coupled spinor Bose-Einstein condensates. Phys. Rev. Lett. 105, 160403 (2010)

    Article  ADS  PubMed  CAS  Google Scholar 

  41. Ho, T.-L. & Zhang, S. Bose-Einstein condensates with spin–orbit interaction. Phys. Rev. Lett. 107, 150403 (2011)

    Article  ADS  PubMed  CAS  Google Scholar 

  42. Wu, C.-J., Mondragon-Shem, I. & Zhou, X.-F. Unconventional Bose–Einstein condensations from spin–orbit coupling. Chin. Phys. Lett. 28, 097102 (2011)

    Article  ADS  Google Scholar 

  43. Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of ultracold atomic Fermi gases. Rev. Mod. Phys. 80, 1215–1274 (2008)

    Article  ADS  CAS  Google Scholar 

  44. Ketterle, W. & Zwierlein, M. W. Making, probing and understanding ultracold Fermi gases. In Proc. International School of Physics “Enrico Fermi”, Course CLXIV (Varenna, 20–30 June 2006) (eds Inguscio, M., Ketterle, W. & Salomon, C. ) 95–287 (IOS Press, 2008)

    Google Scholar 

  45. Chaplik, A. V. & Magarill, L. I. Bound states in a two-dimensional short range potential induced by the spin–orbit interaction. Phys. Rev. Lett. 96, 126402 (2006)

    Article  ADS  CAS  PubMed  Google Scholar 

  46. Gong, M., Tewari, S. & Zhang, C. BCS-BEC crossover and topological phase transition in 3D spin–orbit coupled degenerate Fermi gases. Phys. Rev. Lett. 107, 195303 (2011)

    Article  ADS  PubMed  CAS  Google Scholar 

  47. Yu, Z.-Q. & Zhai, H. Spin-orbit coupled Fermi gases across a Feshbach resonance. Phys. Rev. Lett. 107, 195305 (2011)

    Article  ADS  PubMed  CAS  Google Scholar 

  48. Veillette, M., Sheehy, D., Radzihovsky, L. & Gurarie, V. Superfluid transition in a rotating Fermi gas with resonant interactions. Phys. Rev. Lett. 97, 250401 (2006)

    Article  ADS  PubMed  CAS  Google Scholar 

  49. Levinsen, J., Cooper, N. R. & Gurarie, V. Strongly resonant p-wave superfluids. Phys. Rev. Lett. 99, 210402 (2007)

    Article  ADS  CAS  PubMed  Google Scholar 

  50. Regal, C. A., Ticknor, C., Bohn, J. L. & Jin, D. S. Tuning p-wave interactions in an ultracold Fermi gas of atoms. Phys. Rev. Lett. 90, 053201 (2003)

    Article  ADS  CAS  PubMed  Google Scholar 

  51. Williams, R. A. et al. Synthetic partial waves in ultracold atomic collisions. Science 335, 314–317 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  52. Zhang, C., Tewari, S., Lutchyn, R. M. & Das Sarma, S. p x +ip y superfluid from s-wave interactions of fermionic cold atoms. Phys. Rev. Lett. 101, 160401 (2008)

    Article  ADS  PubMed  CAS  Google Scholar 

  53. Massignan, P., Sanpera, A. & Lewenstein, M. Creating p-wave superfluids and topological excitations in optical lattices. Phys. Rev. A 81, 031607 (2010)

    Article  ADS  CAS  Google Scholar 

  54. Seo, K., Han, L. & Sá de Melo, C. Emergence of Majorana and Dirac particles in ultracold fermions via tunable interactions, spin–orbit effects, and Zeeman fields. Phys. Rev. Lett. 109, 105303 (2012)

    Article  ADS  PubMed  CAS  Google Scholar 

  55. Schnyder, A. P., Ryu, S., Furusaki, A. & Ludwig, A. W. W. Classification of topological insulators and superconductors in three spatial dimensions. Phys. Rev. B 78, 195125 (2008)

    Article  ADS  CAS  Google Scholar 

  56. Kitaev, A. Periodic table for topological insulators and superconductors. AIP Conf. Proc. 1134, 22–30 (2009)

    Article  ADS  CAS  MATH  Google Scholar 

  57. Moore, J. E. & Balents, L. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306(R) (2007)

    Article  ADS  CAS  Google Scholar 

  58. Gell-Mann, M. Symmetries of baryons and mesons. Phys. Rev. 125, 1067–1084 (1962)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  59. Lindner, N. H., Refael, G. & Galitski, V. Floquet topological insulator in semiconductor quantum wells. Nature Phys. 7, 490–495 (2011)

    Article  ADS  CAS  Google Scholar 

  60. Jiang, L. et al. Majorana fermions in equilibrium and driven cold atom quantum wires. Phys. Rev. Lett. 106, 220402 (2011)

    Article  ADS  PubMed  CAS  Google Scholar 

  61. Shapere, A. & Wilczek, F. Geometric Phases in Physics (World Pacific, 1989)

    MATH  Google Scholar 

  62. Dalibard, J., Gerbier, F., Juzeliūnas, G. & Öhberg, P. Artificial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523–1543 (2011)

    Article  ADS  CAS  Google Scholar 

  63. Jaksch, D. & Zoller, P. Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms. N. J. Phys. 5, 56 (2003)

    Article  Google Scholar 

  64. Aidelsburger, M. et al. Experimental realization of strong effective magnetic fields in an optical lattice. Phys. Rev. Lett. 107, 255301 (2011)

    Article  ADS  CAS  PubMed  Google Scholar 

  65. Struck, J. et al. Tunable gauge potential for neutral and spinless particles in driven optical lattices. Phys. Rev. Lett. 108, 225304 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  66. Zhu, S.-L., Fu, H., Wu, C. J., Zhang, S. C. & Duan, L. M. Spin Hall effects for cold atoms in a light-induced gauge potential. Phys. Rev. Lett. 97, 240401 (2006)

    Article  ADS  PubMed  CAS  Google Scholar 

  67. Bermudez, A. et al. Wilson fermions and axion electrodynamics in optical lattices. Phys. Rev. Lett. 105, 190404 (2010)

    Article  ADS  CAS  PubMed  Google Scholar 

  68. Zohar, E., Cirac, J. & Reznik, B. Simulating compact quantum electrodynamics with ultracold atoms: probing confinement and nonperturbative effects. Phys. Rev. Lett. 109, 125302 (2012)

    Article  ADS  PubMed  CAS  Google Scholar 

  69. Banerjee, D. et al. Atomic quantum simulation of dynamical gauge fields coupled to fermionic matter: from string breaking to evolution after a quench. Phys. Rev. Lett. 109, 175302 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

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Acknowledgements

We acknowledge the financial support of the NSF through the Physics Frontier Center at JQI; the ARO with funds from the Atomtronics MURI, DARPA’s OLE Program (I.B.S.), and directly (V.G.).

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Correspondence to Ian B. Spielman.

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Galitski, V., Spielman, I. Spin–orbit coupling in quantum gases. Nature 494, 49–54 (2013). https://doi.org/10.1038/nature11841

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