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Coherent multi-flavour spin dynamics in a fermionic quantum gas

Abstract

Microscopic spin-interaction processes are fundamental for global static and dynamical magnetic properties of many-body systems. Quantum gases as pure and well-isolated systems offer intriguing possibilities to study basic magnetic processes including non-equilibrium dynamics. Here, we report on the realization of a well-controlled fermionic spinor gas in an optical lattice with tunable effective spin ranging from 1/2 to 9/2. We observe long-lived intrinsic spin oscillations and investigate the transition from two-body to many-body dynamics. The latter involves a complex interplay of spin and spatial degrees of freedom and implies an instability of an initially band insulating state. Using an external magnetic field we control the dimensionality of the system and tune the spin oscillations in and out of resonance. Our results open new routes to study quantum magnetism of fermionic particles beyond conventional spin 1/2 systems.

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Figure 1: Principles of fermionic lattice spin dynamics.
Figure 2: Coherent fermionic spin dynamics.
Figure 3: Coherent multi-flavour spin dynamics of fermionic atoms.
Figure 4: Transition from on-site to many-body spin dynamics.
Figure 5: Simplified sketch of processes originating from the combination of spin-changing collisions and tunnelling.
Figure 6: Numerical simulation of a four-well system.

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References

  1. Rüegg, C. et al. Quantum magnets under pressure: Controlling elementary excitations in TlCuCl3 . Phys. Rev. Lett. 100, 205701 (2008).

    Article  ADS  Google Scholar 

  2. Beaulac, R., Schneider, L., Archer, P. I., Bacher, G. & Gamelin, D. R. Light-induced spontaneous magnetization in doped colloidal quantum dots. Science 325, 973–976 (2009).

    Article  ADS  Google Scholar 

  3. Kim, K. et al. Quantum simulation of frustrated Ising spins with trapped ions. Nature 465, 590–593 (2010).

    Article  ADS  Google Scholar 

  4. Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011).

    Article  ADS  Google Scholar 

  5. Stenger, J. et al. Spin domains in ground-state Bose–Einstein condensates. Nature 396, 345–348 (1998).

    Article  ADS  Google Scholar 

  6. Schmaljohann, H. et al. Dynamics of F = 2 spinor Bose–Einstein condensates. Phys. Rev. Lett. 92, 040402 (2004).

    Article  ADS  Google Scholar 

  7. Chang, M. S., Qin, Q., Zhang, W., You, L. & Chapman, M. S. Coherent spinor dynamics in a spin-1 Bose condensate. Nature Phys. 1, 111–116 (2005).

    Article  ADS  Google Scholar 

  8. Sadler, L. E., Higbie, J. M., Leslie, S. R., Vengalattore, M. & Stamper-Kurn, D. M. Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate. Nature 443, 312–315 (2006).

    Article  ADS  Google Scholar 

  9. Widera, A. et al. Coherent collisional spin dynamics in optical lattices. Phys. Rev. Lett. 95, 190405 (2005).

    Article  ADS  Google Scholar 

  10. Struck, J. et al. Quantum simulation of frustrated classical magnetism in triangular optical lattices. Science 333, 996–999 (2011).

    Article  ADS  Google Scholar 

  11. Simon, J. et al. Quantum simulation of antiferromagnetic spin chains in an optical lattice. Nature 472, 307–312 (2011).

    Article  ADS  Google Scholar 

  12. Lücke, B. et al. Twin matter waves for interferometry beyond the classical limit. Science 334, 773–776 (2011).

    Article  ADS  Google Scholar 

  13. Gross, C. et al. Atomic homodyne detection of continuous-variable entangled twin-atom states. Nature 480, 219–223 (2011).

    Article  ADS  Google Scholar 

  14. Becker, C. et al. Ultracold quantum gases in triangular optical lattices. New J. Phys. 12, 065025 (2010).

    Article  ADS  Google Scholar 

  15. Jo, G. B. et al. Itinerant ferromagnetism in a Fermi gas of ultracold atoms. Science 325, 1521–1524 (2009).

    Article  ADS  Google Scholar 

  16. Zhang, S. & Ho, T. L. Atom loss maximum in ultra-cold Fermi gases. New J. Phys. 13, 055003 (2011).

    Article  ADS  Google Scholar 

  17. Pekker, D. et al. Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances. Phys. Rev. Lett. 106, 050402 (2011).

    Article  ADS  Google Scholar 

  18. Conduit, G. J. & Altman, E. Effect of three-body loss on itinerant ferromagnetism in an atomic Fermi gas. Phys. Rev. A 83, 043618 (2011).

    Article  ADS  Google Scholar 

  19. Sommer, A., Ku, M., Roati, G. & Zwierlein, M. W. Universal spin transport in a strongly interacting Fermi gas. Nature 472, 201–204 (2011).

    Article  ADS  Google Scholar 

  20. Taie, S. et al. Realization of a SU(2)×SU(6) system of fermions in a cold atomic gas. Phys. Rev. Lett. 105, 190401 (2010).

    Article  ADS  Google Scholar 

  21. Stellmer, S., Grimm, R. & Schreck, F. Detection and manipulation of nuclear spin states in fermionic strontium. Phys. Rev. A 84, 043611 (2011).

    Article  ADS  Google Scholar 

  22. Lompe, T. et al. Radio-frequency association of Efimov trimers. Science 330, 940–944 (2010).

    Article  ADS  Google Scholar 

  23. Lecheminant, P., Boulat, E. & Azaria, P. Confinement and superfluidity in one-dimensional degenerate fermionic cold atoms. Phys. Rev. Lett. 95, 240402 (2005).

    Article  ADS  Google Scholar 

  24. Wu, C. Competing orders in one-dimensional spin-3/2 fermionic systems. Phys. Rev. Lett. 95, 266404 (2005).

    Article  ADS  Google Scholar 

  25. Rapp, Á., Zaránd, G., Honerkamp, C. & Hofstetter, W. Color superfluidity and ‘Baryon’ formation in ultracold fermions. Phys. Rev. Lett. 98, 160405 (2007).

    Article  ADS  Google Scholar 

  26. Honerkamp, C. & Hofstetter, W. Ultracold fermions and the SU(N) Hubbard model. Phys. Rev. Lett. 92, 170403 (2004).

    Article  ADS  Google Scholar 

  27. Hermele, M., Gurarie, V. & Rey, A. M. Mott insulators of ultracold fermionic alkaline earth atoms: Underconstrained magnetism and chiral spin liquid. Phys. Rev. Lett. 103, 135301 (2009).

    Article  ADS  Google Scholar 

  28. Cazalilla, M. A., Ho, A. F. & Ueda, M. Ultracold gases of ytterbium: Ferromagnetism and Mott states in an SU(6) Fermi system. New J. Phys. 11, 103033 (2009).

    Article  ADS  Google Scholar 

  29. Gorshkov, A. V. et al. Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms. Nature Phys. 6, 289–295 (2010).

    Article  ADS  Google Scholar 

  30. Ho, T. L. & Yip, S. Pairing of fermions with arbitrary spin. Phys. Rev. Lett. 82, 247–250 (1999).

    Article  ADS  Google Scholar 

  31. Wu, C., Hu, J. P. & Zhang, S. C. Exact SO(5) symmetry in the spin-3/2 fermionic system. Phys. Rev. Lett. 91, 186402 (2003).

    Article  ADS  Google Scholar 

  32. Tu, H. H., Zhang, G. M. & Yu, L. Spin-quadrupole ordering of spin-3/2 ultracold fermionic atoms in optical lattices in the one-band Hubbard model. Phys. Rev. B 74, 174404 (2006).

    Article  ADS  Google Scholar 

  33. Rodríguez, K., Argüelles, A., Colomé-Tatché, M., Vekua, T. & Santos, L. Mott-insulator phases of spin-3/2 fermions in the presence of quadratic Zeeman coupling. Phys. Rev. Lett. 105, 050402 (2010).

    Article  ADS  Google Scholar 

  34. Köhl, M., Moritz, H., Stoferle, T., Günter, K. & Esslinger, T. Fermionic atoms in a three dimensional optical lattice: Observing fermi surfaces, dynamics, and interactions. Phys. Rev. Lett. 94, 080403 (2005).

    Article  ADS  Google Scholar 

  35. Jördens, R., Strohmaier, N., Günter, K., Moritz, H. & Esslinger, T. A Mott insulator of fermionic atoms in an optical lattice. Nature 455, 204–207 (2008).

    Article  ADS  Google Scholar 

  36. Schneider, U. et al. Metallic and insulating phases of repulsively interacting fermions in a 3D optical lattice. Science 322, 1520–1525 (2008).

    Article  ADS  Google Scholar 

  37. Ho, T. L. Spinor Bose condensates in optical traps. Phys. Rev. Lett. 81, 742–745 (1998).

    Article  ADS  Google Scholar 

  38. Law, C. K., Pu, H. & Bigelow, N. P. Quantum spins mixing in spinor Bose–Einstein condensates. Phys. Rev. Lett. 81, 5257–5261 (1998).

    Article  ADS  Google Scholar 

  39. Ohmi, T. & Machida, K. Bose–Einstein condensation with internal degrees of freedom in alkali atom gases. J. Phys. Soc. Jpn 67, 1822–1825 (1998).

    Article  ADS  Google Scholar 

  40. Bornemann, N., Hyllus, P. & Santos, L. Resonant spin-changing collisions in spinor Fermi gases. Phys. Rev. Lett. 100, 205302 (2008).

    Article  ADS  Google Scholar 

  41. Kronjäger, J., Becker, C., Navez, P., Bongs, K. & Sengstock, K. Magnetically tuned spin dynamics resonance. Phys. Rev. Lett. 97, 110404 (2006).

    Article  ADS  Google Scholar 

  42. Black, A. T., Gomez, E., Turner, L. D., Jung, S & Lett, P. D. Spinor dynamics in an antiferromagnetic spin-1 condensate. Phys. Rev. Lett. 99, 070403 (2007).

    Article  ADS  Google Scholar 

  43. Klempt, C. et al. Multiresonant spinor dynamics in a Bose–Einstein condensate. Phys. Rev. Lett. 103, 195302 (2009).

    Article  ADS  Google Scholar 

  44. Auerbach, A. Interacting Electrons and Quantum Magnetism (Springer, 1998).

    Google Scholar 

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Acknowledgements

We acknowledge stimulating discussions with E. Demler, F. Deuretzbacher, A. Eckardt, T.-L. Ho, M. Lewenstein, A. Sotnikov and M.W. Zwierlein and thank T. Hanna and L. Cook for providing us with calculated values of the scattering lengths. This work has been financially supported by DFG grant FOR 801.

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Contributions

J.S.K., J.H. and N.F. performed the measurements and collected the data. J.H. performed the numerical two-body calculations. O.J. and D.S.L. performed the numerical simulations of the four-well system. All authors contributed substantially to the discussion and interpretation of the data and results and to the writing of the manuscript.

Corresponding author

Correspondence to Klaus Sengstock.

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The authors declare no competing financial interests.

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Krauser, J., Heinze, J., Fläschner, N. et al. Coherent multi-flavour spin dynamics in a fermionic quantum gas. Nature Phys 8, 813–818 (2012). https://doi.org/10.1038/nphys2409

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