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Repulsively interacting fermions in a two-dimensional deformed trap with spin-orbit coupling

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Abstract

We investigate a two-dimensional system of fermions with two values of the internal (spin) degree of freedom. It is confined by a deformed harmonic trap and subject to a Zeeman field, Rashba or Dresselhaus one-body spin-orbit couplings and two-body short range repulsion. We obtain self-consistent mean-field N-body solutions as functions of the interaction parameters. Single-particle spectra and total energies are computed and compared to the results without interaction. We perform a statistical analysis for the distributions of nearest neighbor energy level spacings and show that quantum signatures of chaos are seen in certain parameters regimes. Furthermore, the effects of two-body repulsion on the nearest neighbor distributions are investigated. This repulsion can either promote or destroy the signatures of potential chaotic behavior depending on relative strengths of parameters. Our findings support the suggestion that cold atoms may be used to study quantum chaos both in the presence and absence of interactions.

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References

  1. W. Ketterle, M.W. Zwierlein, Nuovo Cimento Rivista Serie 31, 247 (2008)

    ADS  Google Scholar 

  2. I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)

    Article  ADS  Google Scholar 

  3. T. Esslinger, Ann. Rev. Cond. Mat. Phys. 1, 129 (2010)

    Article  ADS  Google Scholar 

  4. J.I. Cirac, P. Zoller, Nat. Phys. 8, 264 (2012)

    Article  Google Scholar 

  5. Y.-J. Lin et al., Phys. Rev. Lett. 102, 130401 (2009)

    Article  ADS  Google Scholar 

  6. Y.-J. Lin, R.L. Compton, K. Jiménez-García, J.V. Porto, I.B. Spielman, Nature 462, 628 (2009)

    Article  ADS  Google Scholar 

  7. Y.-J. Lin, K. Jiménez-García, I.B. Spielman, Nature 471, 83 (2011)

    Article  ADS  Google Scholar 

  8. M. Aidelsurger, Phys. Rev. Lett. 107, 255301 (2011)

    Article  ADS  Google Scholar 

  9. J.-Y. Zhang et al., Phys. Rev. Lett. 109, 115301 (2012)

    Article  ADS  Google Scholar 

  10. P. Wang et al., Phys. Rev. Lett. 109, 095301 (2012)

    Article  ADS  Google Scholar 

  11. L. Cheuk et al., Phys. Rev. Lett. 109, 095302 (2012)

    Article  ADS  Google Scholar 

  12. H. Hu, S. Chen, arXiv:1302.5933 (2013)

  13. J. Larson, E. Sjöqvist, Phys. Rev. A 79, 043627 (2009)

    Article  ADS  Google Scholar 

  14. X.Y. Yin, S. Gopalakrishnan, D. Blume, Phys. Rev. A 89, 033606 (2014)

    Article  ADS  Google Scholar 

  15. O.V. Marchukov, A.G. Volosniev, D.V. Fedorov, A.S. Jensen, N.T. Zinner, J. Phys. B 46, 134012 (2013)

    Article  ADS  Google Scholar 

  16. S.M. Reimann, M. Manninen, Rev. Mod. Phys. 74, 1283 (2002)

    Article  ADS  Google Scholar 

  17. S. Avetisyan, P. Pietiläinen, T. Chakraborty, Phys. Rev. B 85, 153301 (2012)

    Article  ADS  Google Scholar 

  18. E.I. Rashba, Sov. Phys. Solid State 2, 1109 (1960)

    Google Scholar 

  19. G. Dresselhaus, Phys. Rev. 100, 580 (1955)

    Article  ADS  MATH  Google Scholar 

  20. O.V. Marchukov, A.G. Volosniev, D.V. Fedorov, A.S. Jensen, N.T. Zinner, J. Phys. B 47, 195303 (2014)

    Article  ADS  Google Scholar 

  21. R.S. Markiewicz, Phys. Rev. E 64, 026216 (2001)

    Article  ADS  Google Scholar 

  22. H. Yamasaki, Y. Natsume, A. Terai, K. Nakamura, Phys. Rev. E 68, 046201 (2003)

    Article  ADS  Google Scholar 

  23. E. Majerníková, S. Shrypko, Phys. Rev. E 73, 057202 (2006)

    Article  ADS  Google Scholar 

  24. E. Majerníková, S. Shrypko, Phys. Rev. E 73, 066215 (2006)

    Article  ADS  Google Scholar 

  25. Q. Guan, X.Y. Yin, S.E. Gharashi, D. Blume, J. Phys. B 47, 161001 (2014)

    Article  ADS  Google Scholar 

  26. X. Cui, W. Yi, Phys. Rev. X 4, 031026 (2014)

    Google Scholar 

  27. P.J. Siemens, A.S. Jensen, Elements of Nuclei: Many-Body Physics with the Strong Interaction (Addison-Wesley Pub. Co., Redwood City, 1987)

  28. M. Olshanii, L. Pricoupenko, Phys. Rev. Lett. 88, 010402 (2002)

    Article  ADS  Google Scholar 

  29. M. Valiente, Phys. Rev. A 85, 014701 (2012)

    Article  ADS  Google Scholar 

  30. D.S. Petrov, M. Holzmann, G.V. Shlyapnikov, Phys. Rev. Lett. 84, 2551 (2000)

    Article  ADS  Google Scholar 

  31. D.S. Petrov, G.V. Shlyapnikov, Phys. Rev. A 64, 012706 (2001)

    Article  ADS  Google Scholar 

  32. M. Valiente, N.T. Zinner, K. Mølmer, Phys. Rev. A 86, 043616 (2012)

    Article  ADS  Google Scholar 

  33. H. Hu, B. Ramachandhran, H. Pu, X.-J. Liu, Phys. Rev. Lett. 108, 010402 (2012)

    Article  ADS  Google Scholar 

  34. L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Non-relativistic Theory) (Pergamon Press, Oxford, 1977)

  35. J.J. Sakurai, Modern Quantum Mechanics (Addison-Wesley Pub. Co., Reading, 1994)

  36. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th edn. (Dover Publications, New York, 1972)

  37. O.V. Marchukov, A.G. Volosniev, D.V. Fedorov, A.S. Jensen, N.T. Zinner, Few-Body Syst. 55, 1045 (2014)

    Article  ADS  Google Scholar 

  38. F. Haake, Quantum Signatures of Chaos, 2nd edn. (Springer-Verlag, Berlin, 2001)

  39. M.V. Berry, Proc. R. Soc. London A 413, 183 (1987)

    Article  ADS  Google Scholar 

  40. L.E. Reichl, The Transition to Chaos: Conservative Classical Systems and Quantum Manifestation, 2nd edn. (Springer-Verlag, Berlin, 2004)

  41. J.R. Armstrong, S. Åberg, S.M. Reimann, V.G. Zelevinsky, Phys. Rev. E 86, 066204 (2012)

    Article  ADS  Google Scholar 

  42. T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey, S.S.M. Wong, Rev. Mod. Phys. 53, 3 (1981)

    Article  MathSciNet  Google Scholar 

  43. L.F. Santos, M. Rigol, Phys. Rev. E 81, 036206 (2010)

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Astronomy, Aarhus University, 8000, Aarhus C, Denmark

    Oleksandr V. Marchukov, Dmitri V. Fedorov, Aksel S. Jensen, Artem G. Volosniev & Nikolaj T. Zinner

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  1. Oleksandr V. Marchukov
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  2. Dmitri V. Fedorov
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  3. Aksel S. Jensen
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  4. Artem G. Volosniev
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  5. Nikolaj T. Zinner
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Correspondence to Nikolaj T. Zinner.

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Marchukov, O.V., Fedorov, D.V., Jensen, A.S. et al. Repulsively interacting fermions in a two-dimensional deformed trap with spin-orbit coupling. Eur. Phys. J. D 69, 73 (2015). https://doi.org/10.1140/epjd/e2015-50682-x

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