Statistical properties of spectra in harmonically trapped spin-orbit coupled systems

O. V. Marchukov*, A. G. Volosniev, D. V. Fedorov, A. S. Jensen, N. T. Zinner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We compute single-particle energy spectra for a one-body Hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choice of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding the Zeeman field we can reproduce a Brody distribution, which is known to describe a transition between the Poisson and linear Wigner distributions.

Original languageEnglish
Article number195303
JournalJournal of Physics B: Atomic, Molecular and Optical Physics
Issue number19
StatePublished - 14 Oct 2014
Externally publishedYes


  • chaotic behavior
  • cold atoms
  • spin-orbit coupling


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