The spin Hall effect in a quantum gas

Subjects

Abstract

Electronic properties such as current flow are generally independent of the electron’s spin angular momentum, an internal degree of freedom possessed by quantum particles. The spin Hall effect, first proposed 40 years ago1, is an unusual class of phenomena in which flowing particles experience orthogonally directed, spin-dependent forces—analogous to the conventional Lorentz force that gives the Hall effect, but opposite in sign for two spin states. Spin Hall effects have been observed for electrons flowing in spin–orbit-coupled materials such as GaAs and InGaAs (refs 2, 3) and for laser light traversing dielectric junctions4. Here we observe the spin Hall effect in a quantum-degenerate Bose gas, and use the resulting spin-dependent Lorentz forces to realize a cold-atom spin transistor. By engineering a spatially inhomogeneous spin–orbit coupling field for our quantum gas, we explicitly introduce and measure the requisite spin-dependent Lorentz forces, finding them to be in excellent agreement with our calculations. This ‘atomtronic’ transistor behaves as a type of velocity-insensitive adiabatic spin selector, with potential application in devices such as magnetic5 or inertial6 sensors. In addition, such techniques for creating and measuring the spin Hall effect are clear prerequisites for engineering topological insulators7,8 and detecting their associated quantized spin Hall effects in quantum gases. As implemented, our system realizes a laser-actuated analogue to the archetypal semiconductor spintronic device, the Datta–Das spin transistor9,10.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Schematic of experimental set-up.
Figure 2: Spin Hall shear.
Figure 3: Spin-polarized SHE.
Figure 4: Spin Hall currents.

References

  1. 1

    Dyakonov, M. I. & Perel, V. I. Possibility of orienting electron spins with current. Sov. Phys. JETP 13, 467–469 (1971)

    Google Scholar 

  2. 2

    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)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimental observation of the spin-Hall effect in a two-dimensional spin-orbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Hosten, O. & Kwiat, P. Observation of the spin Hall effect of light via weak measurements. Science 319, 787–790 (2008)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Kitching, J., Knappe, S. & Donley, E. Atomic sensors – a review. Sensors J. IEEE 11, 1749–1758 (2011)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Anderson, B. M., Taylor, J. M. & Galitski, V. M. Interferometry with synthetic gauge fields. Phys. Rev. A 83, 031602 (2011)

    ADS  Article  Google Scholar 

  7. 7

    Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Vaishnav, J. Y., Ruseckas, J., Clark, C. W. & Juzeliūnas, G. Spin field effect transistors with ultracold atoms. Phys. Rev. Lett. 101, 265302 (2008)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Datta, S. & Das, B. Electronic analog of the electro-optic modulator. Appl. Phys. Lett. 56, 665–667 (1990)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Jungwirth, T., Wunderlich, J. & Olejnik, K. Spin Hall effect devices. Nature Mater. 11, 382–390 (2012)

    ADS  CAS  Article  Google Scholar 

  12. 12

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

    ADS  Article  Google Scholar 

  13. 13

    Hirsch, J. E. Spin Hall effect. Phys. Rev. Lett. 83, 1834–1837 (1999)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Ruseckas, J., Juzeliūnas, G., Öhberg, P. & Fleischhauer, M. Non-Abelian gauge potentials for ultracold atoms with degenerate dark states. Phys. Rev. Lett. 95, 010404 (2005)

    ADS  CAS  Article  Google Scholar 

  15. 15

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

    ADS  CAS  Article  Google Scholar 

  16. 16

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

    ADS  Article  Google Scholar 

  17. 17

    Lyanda-Geller, Y. Quantum interference and electron-electron interactions at strong spin-orbit coupling in disordered systems. Phys. Rev. Lett. 80, 4273–4276 (1998)

    ADS  CAS  Article  Google Scholar 

  18. 18

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

    ADS  CAS  Article  Google Scholar 

  19. 19

    Stanescu, T. D., Galitski, V., Vaishnav, J. Y., Clark, C. W. & Das Sarma, S. Topological insulators and metals in atomic optical lattices. Phys. Rev. A 79, 053639 (2009)

    ADS  Article  Google Scholar 

  20. 20

    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)

    ADS  Article  Google Scholar 

  21. 21

    Lin, Y. J., Jiménez-García, K. & Spielman, I. B. Spin–orbit-coupled Bose–Einstein condensates. Nature 471, 83–86 (2011)

    ADS  CAS  Article  Google Scholar 

  22. 22

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

    ADS  Article  Google Scholar 

  23. 23

    Wang, P. et al. Spin-orbit coupled degenerate Fermi gases. Phys. Rev. Lett. 109, 095301 (2012)

    ADS  Article  Google Scholar 

  24. 24

    Cheuk, L. W. et al. Spin-injection spectroscopy of a spin-orbit coupled Fermi gas. Phys. Rev. Lett. 109, 095302 (2012)

    ADS  Article  Google Scholar 

  25. 25

    Liu, X.-J., Liu, X., Kwek, L. C. & Oh, C. H. Optically induced spin-Hall effect in atoms. Phys. Rev. Lett. 98, 026602 (2007)

    ADS  Article  Google Scholar 

  26. 26

    Zhang, Y., Mao, L. & Zhang, C. Mean-field dynamics of spin-orbit coupled Bose-Einstein condensates. Phys. Rev. Lett. 108, 035302 (2012)

    ADS  Article  Google Scholar 

  27. 27

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

    ADS  Article  Google Scholar 

  28. 28

    Lin, Y.-J. et al. A synthetic electric force acting on neutral atoms. Nature Phys. 7, 531–534 (2011)

    ADS  CAS  Article  Google Scholar 

  29. 29

    LeBlanc, L. J. et al. Observation of a superfluid Hall effect. Proc. Natl Acad. Sci. USA 109, 10811–10814 (2012)

    ADS  CAS  Article  Google Scholar 

  30. 30

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

    ADS  CAS  Article  Google Scholar 

  31. 31

    Palima, D., Alonzo, C. A., Rodrigo, P. J. & Glückstad, J. Generalized phase contrast matched to Gaussian illumination. Opt. Express 15, 11971–11977 (2007)

    ADS  Article  Google Scholar 

  32. 32

    Pasienski, M. & DeMarco, B. A high-accuracy algorithm for designing arbitrary holographic atom traps. Opt. Express 16, 2176–2190 (2008)

    ADS  Article  Google Scholar 

  33. 33

    Gaunt, A. L. & Hadzibabic, Z. Robust digital holography for ultracold atom trapping. Sci. Rep. 2, 721 (2012)

    ADS  Article  Google Scholar 

  34. 34

    Lee, J. G., McIlvain, B. J., Lobb, C. J. & Hill, W. T., III Analogs of basic electronic circuit elements in a free-space atom chip. Sci. Rep. 3, 1034 (2013)

    ADS  Article  Google Scholar 

  35. 35

    Lin, Y.-J. et al. Bose-Einstein condensate in a uniform light-induced vector potential. Phys. Rev. Lett. 102, 130401 (2009)

    ADS  Article  Google Scholar 

  36. 36

    Schliemann, J. Spin Hall effect. Int. J. Mod. Phys. B 20, 1015–1036 (2006)

    ADS  CAS  Article  Google Scholar 

  37. 37

    Sakurai, J. J. Modern Quantum Mechanics 130–131 (Addison-Wesley, 1994)

    Google Scholar 

  38. 38

    Peskin, M. E. & Schroeder, D. V. An Introduction to Quantum Field Theory 481–502 (Westview, 1995)

    Google Scholar 

  39. 39

    Yang, C. N. & Mills, R. L. Conservation of isotopic spin and isotopic gauge invariance. Phys. Rev. 96, 191–195 (1954)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  40. 40

    Estienne, B., Haaker, S. M. & Schoutens, K. Particles in non-Abelian gauge potentials: Landau problem and insertion of non-Abelian flux. N. J. Phys. 13, 045012 (2011)

    MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the DARPA OLE programme; the ARO atomtronics MURI, NIST, and the US NSF through the PFC at the JQI. M.C.B. acknowledges NIST-ARRA, L.J.L. acknowledges support from NSERC and K.J.-G. acknowledges CONACYT.

Author information

Affiliations

Authors

Contributions

M.C.B. led the data-taking effort, in which all co-authors participated. M.C.B. carried out the analysis, M.C.B. and I.B.S. performed theoretical and analytical calculations, and all authors contributed to writing the manuscript.

Corresponding author

Correspondence to I. B. Spielman.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains a Supplementary Discussion, additional references and a Supplementary Figure. The Supplementary Discussion and figure contain a specific proposal to extend the technique used in our manuscript to realize the quantum spin Hall effect in a similar experimental system. Calculations are explained and illustrated for realistic example experimental parameters. (PDF 194 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Beeler, M., Williams, R., Jiménez-García, K. et al. The spin Hall effect in a quantum gas. Nature 498, 201–204 (2013). https://doi.org/10.1038/nature12185

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing