Abstract
A theoretical study of vortex-lattice formation in atomic Bose-Einstein condensates confined by a rotating elliptical trap is presented. For the conventional case of purely s-wave interatomic interactions, this is done through a consideration of both hydrodynamic equations and time-dependent simulations of the Gross-Pitaevskii equation. We discriminate three distinct, experimentally testable regimes of instability: ripple, interbranch, and catastrophic. Additionally, we generalize the classical hydrodynamical approach to include long-range dipolar interactions, showing how the static solutions and their stability in the rotating frame are significantly altered. This enables us to examine the routes towards unstable dynamics, which, in analogy to conventional condensates, may lead to vortex-lattice formation.
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K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, Phys. Rev. Lett. 84, 806 (2000).
K. W. Madison, F. Chevy, V. Bretin, and J. Dalibard, Phys. Rev. Lett. 86, 4443 (2001).
E. Hodby et al., Phys. Rev. Lett. 88, 010405 (2001).
A. Recati, F. Zambelli, and S. Stringari, Phys. Rev. Lett. 86, 377 (2001).
S. Sinha and Y. Castin, Phys. Rev. Lett. 87, 190402 (2001).
C. Lobo, A. Sinatra, and Y. Castin, Phys. Rev. Lett. 92, 020403 (2004).
M. Tsubota, K. Kasamatsu, and M. Ueda, Phys. Rev. A 65, 023603 (2002); K. Kasamatsu, M. Tsubota, and M. Ueda, Phys. Rev. A 67, 033610 (2003).
A. A. Penckwitt, R. J. Ballagh, and C. W. Gardiner, Phys. Rev. Lett. 89, 260402 (2002).
E. Lundh, J.-P. Martikainen, and K.-A. Suominen, Phys. Rev. A 67, 063604 (2003).
N. G. Parker and C. S. Adams, Phys. Rev. Lett. 95, 145301 (2005).
N. G. Parker and C. S. Adams, J. Phys. B 39, 43 (2006).
N. G. Parker, R. M. W. van Bijnen, and A. M. Martin, Phys. Rev. A 73, 061603(R) (2006).
I. Corro, N. G. Parker, and A. M. Martin, J. Phys. B 40, 3615 (2007).
J. R. Abo-Shaeer, C. Raman, and W. Ketterle, Phys. Rev. Lett. 88, 070409 (2002).
A. Griesmaier et al., Phys. Rev. Lett. 94, 160401 (2005).
N. R. Cooper, E. H. Rezayi, and S. H. Simon, Phys. Rev. Lett. 95, 200402 (2005).
J. Zhang and H. Zhai, Phys. Rev. Lett. 95, 200403 (2005).
S. Yi and H. Pu, Phys. Rev. A 73, 061602(R) (2006).
R. M. W. van Bijnen, D. H. J. O’Dell, N. G. Parker, and A. M. Martin, Phys. Rev. Lett. 98, 150401 (2007).
D. H. J. O’Dell, S. Giovanazzi, and C. Eberlein, Phys. Rev. Lett. 92, 250401 (2004).
M. Marinescu and L. You, Phys. Rev. Lett. 81, 4596 (1998).
S. Yi and L. You, Phys. Rev. A 61, 041604(R) (2000).
K. Góral, K. Rzążewski, and T. Pfau, Phys. Rev. A 61, 051601(R) (2000).
L. Santos, G. V. Shlyapnikov, P. Zoller, and M. Lewenstein, Phys. Rev. Lett. 85, 1791 (2000).
The limit where the zero-point kinetic energy (quantum pressure) is negligible compared to the potential and interaction energies.
C. Eberlein, S. Giovanazzi, and D. H. J. O’Dell, Phys. Rev. A 71, 033618 (2005).
Y. Castin, in Coherent Matter Waves, Lecture Notes of Les Houches Summer School, Ed. by R. Kaiser, C. Westbrook, and F. David (Springer-Verlag, Berlin, 2001), p. 1–136.
L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford Univ. Press, London, 2003).
For n > 3 we find that although there are more eigenvalues the region of instability, defined by max[Re(λ) > 0], remains the same.
E. Lundh, C.J. Pethick and H. Smith, Phys. Rev. A 55, 2126 (1997).
D. H. J. O’Dell and C. Eberlein, Phys. Rev. A. 75, 013604 (2007).
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Martin, A.M., Parker, N.G., van Bijnen, R.M.W. et al. Instabilities and vortex-lattice formation in rotating conventional and dipolar dilute-gas Bose-Einstein condensates. Laser Phys. 18, 322–330 (2008). https://doi.org/10.1134/S1054660X08030225
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DOI: https://doi.org/10.1134/S1054660X08030225