Dynamics of inertial vortices in multicomponent Bose-Einstein condensates

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Babajanov, D. Dynamics of inertial vortices in multicomponent Bose-Einstein condensates. American Physical Society.

Авторы: Doniyor Babajanov , Katsuhiro Nakamura , Davron Matrasulov , Michikazu Kobayashi

Просмотры: 1, Страницы: 10, Файлы: 1

Год публикации: 2012

Издатель: American Physical Society

DOI: https://doi.org/10.1103/PhysRevA.86.053613

Ключевые слова: vortex dynamics,Bose-Einstein condensates,Lagrangian formalism,Hamilton equations,Gaussian wave packets,Chaos,inertia

Abstract & Preview

With use of the nonlinear Schroedinger (or Gross-Pitaevskii) equation with strong repulsive cubic nonlinearity, dynamics of multicomponent Bose-Einstein condensates (BECs) with a harmonic trap in two dimensions is investigated beyond the Thomas-Fermi regime. In the case when each component has a single vortex, we obtain an effective nonlinear dynamics for vortex cores (particles). The particles here acquire the inertia, in marked contrast to the standard theory of point vortices widely known in the usual hydrodynamics. The effective dynamics is equivalent to that of charged particles under a strong spring force and in the presence of Lorentz force with the uniform magnetic field. The interparticle (vortex-vortex) interaction is singularly repulsive and short ranged with its magnitude decreasing with increasing distance of the center of mass from the trapping center. “Chaos in the three-body problem” in the three-vortice system can be seen, which is not expected in the corresponding point vortices without inertia in two dimensions.

Files
  • [1] C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2002).
  • [2] L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003). [3] P.G.Kevrekidis,D.J.Frantzeskakis,andR.Carretero-Gonz´alez, Emergent Nonlinear Phenomena in Bose-Einstein Condensates (Springer-Verlag, Berlin, 2008).
  • [4] A. D. Martin, C. S. Adams, and S. A. Gardiner, Phys. Rev. Lett. 98, 020402 (2007).
  • [5] V. M. P´erez-Garc´ıa, Physica D 191, 211 (2004); G. D. Montesinos, V. M. P´erez-Garc´ıa, and H. Michinel, Phys. Rev. Lett. 92, 133901-1 (2004); V. M. P´erez-Garc´ıa et al., Physica D 238, 1289 (2009).
  • [6] H. Yamasaki, Y. Natsume, and K. Nakamura, J. Phys. Soc. Jpn. 74, 1887 (2005).
  • [7] T.W.Neely,E.C.Samson,A.S.Bradley,M.J.Davis,andB.P. Anderson, Phys. Rev. Lett.104, 160401 (2010).
  • [8] D. V. Freilich et al., Science 329, 1182 (2010).
  • [9] S. Middelkamp, P. J. Torres, P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´alez, P. Schmelcher, D. V. Freilich, and D. S. Hall, Phys. Rev. A84, 011605(R) (2011).
  • [10] G.Thalhammer,G.Barontini,L.DeSarlo,J.Catani,F.Minardi, and M. Inguscio, Phys. Rev. Lett. 100, 210402 (2008).
  • [11] S. B. Papp, J. M. Pino, and C. E. Wieman, Phys. Rev. Lett. 101, 040402 (2008).
  • [12] S. Tojo, Y. Taguchi, Y. Masuyama, T. Hayashi, H. Saito, and T. Hirano, Phys. Rev. A 82, 033609 (2010). [13] A.L.FetterandA.A.Svidzinsky,J.Phys.:Condens.Matter13, R135 (2001).
  • [14] A. L. Fetter, Rev. Mod. Phys. 81, 647 (2009).
  • [15] P. J. Torr et al., Phys. Lett. A 375, 3004 (2011).
  • [16] J. C. Neu, Physica D 43, 385 (1990).
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  • [19] K. Nakamura, Prog. Theor. Phys. Suppl. 166, 179 (2007).
  • [20] I. Aranson and V. Steinberg, Phys. Rev. B53, 75 (1996).
  • [21] N. G. Berloff, J. Phys. A 37, 1617 (2004).
  • [22] J. J. Garc´ıa-Ripoll and V. M. P´erez-Garc´ıa, Phys. Rev. Lett.84, 4264 (2000).
  • [23] J. J. Garc´ıa-Ripoll, G. Molina-Terriza, V. M. P´erez-Garc´ıa, and L. Torner, Phys. Rev. Lett. 87, 140403 (2001).
  • [24] L.C.Crasovan,V.Vekslerchik,V.M.P´erez-Garc´ıa,J.P.Torres, D. Mihalache, and L. Torner, Phys. Rev. A68, 063609 (2003).
  • [25] H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1967).
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  • [28] U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
  • [29] J. Roenby and H. Aref, Proc. R. Soc. A466, 1871 (2010).
  • [30] In the usual theory of hydrodynamics, interacting point vortices in two dimensions have three independent constants of motion, i.e., total energy, x (or y) component of momentum and z component of angular momentum. Therefore the number of vortices must be larger than three, to make the system nonintegrable and chaotic.
  • [31] M. Eto, K. Kasamatsu, M. Nitta, H. Takeuchi, and M. Tsubota, Phys. Rev. A 83, 063603 (2011).
Files
  • [1] C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2002).
  • [2] L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003). [3] P.G.Kevrekidis,D.J.Frantzeskakis,andR.Carretero-Gonz´alez, Emergent Nonlinear Phenomena in Bose-Einstein Condensates (Springer-Verlag, Berlin, 2008).
  • [4] A. D. Martin, C. S. Adams, and S. A. Gardiner, Phys. Rev. Lett. 98, 020402 (2007).
  • [5] V. M. P´erez-Garc´ıa, Physica D 191, 211 (2004); G. D. Montesinos, V. M. P´erez-Garc´ıa, and H. Michinel, Phys. Rev. Lett. 92, 133901-1 (2004); V. M. P´erez-Garc´ıa et al., Physica D 238, 1289 (2009).
  • [6] H. Yamasaki, Y. Natsume, and K. Nakamura, J. Phys. Soc. Jpn. 74, 1887 (2005).
  • [7] T.W.Neely,E.C.Samson,A.S.Bradley,M.J.Davis,andB.P. Anderson, Phys. Rev. Lett.104, 160401 (2010).
  • [8] D. V. Freilich et al., Science 329, 1182 (2010).
  • [9] S. Middelkamp, P. J. Torres, P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´alez, P. Schmelcher, D. V. Freilich, and D. S. Hall, Phys. Rev. A84, 011605(R) (2011).
  • [10] G.Thalhammer,G.Barontini,L.DeSarlo,J.Catani,F.Minardi, and M. Inguscio, Phys. Rev. Lett. 100, 210402 (2008).
  • [11] S. B. Papp, J. M. Pino, and C. E. Wieman, Phys. Rev. Lett. 101, 040402 (2008).
  • [12] S. Tojo, Y. Taguchi, Y. Masuyama, T. Hayashi, H. Saito, and T. Hirano, Phys. Rev. A 82, 033609 (2010). [13] A.L.FetterandA.A.Svidzinsky,J.Phys.:Condens.Matter13, R135 (2001).
  • [14] A. L. Fetter, Rev. Mod. Phys. 81, 647 (2009).
  • [15] P. J. Torr et al., Phys. Lett. A 375, 3004 (2011).
  • [16] J. C. Neu, Physica D 43, 385 (1990).
  • [17] A.Aftalion,VorticesinBose-EinsteinCondensates(Birkh¨auser, Boston, 2006).
  • [18] K.Sasaki,N.Suzuki,andH.Saito,Phys.Rev.Lett.104,150404 (2010).
  • [19] K. Nakamura, Prog. Theor. Phys. Suppl. 166, 179 (2007).
  • [20] I. Aranson and V. Steinberg, Phys. Rev. B53, 75 (1996).
  • [21] N. G. Berloff, J. Phys. A 37, 1617 (2004).
  • [22] J. J. Garc´ıa-Ripoll and V. M. P´erez-Garc´ıa, Phys. Rev. Lett.84, 4264 (2000).
  • [23] J. J. Garc´ıa-Ripoll, G. Molina-Terriza, V. M. P´erez-Garc´ıa, and L. Torner, Phys. Rev. Lett. 87, 140403 (2001).
  • [24] L.C.Crasovan,V.Vekslerchik,V.M.P´erez-Garc´ıa,J.P.Torres, D. Mihalache, and L. Torner, Phys. Rev. A68, 063609 (2003).
  • [25] H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1967).
  • [26] L. Onsager, Nuovo Cimento Suppl. 6, 279 (1949).
  • [27] G.K.Batcheor,AnIntroductiontoFluidDynamics(Cambridge University Press, Cambridge, 1967).
  • [28] U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
  • [29] J. Roenby and H. Aref, Proc. R. Soc. A466, 1871 (2010).
  • [30] In the usual theory of hydrodynamics, interacting point vortices in two dimensions have three independent constants of motion, i.e., total energy, x (or y) component of momentum and z component of angular momentum. Therefore the number of vortices must be larger than three, to make the system nonintegrable and chaotic.
  • [31] M. Eto, K. Kasamatsu, M. Nitta, H. Takeuchi, and M. Tsubota, Phys. Rev. A 83, 063603 (2011).
Литература
  • [1] C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2002).
  • [2] L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003). [3] P.G.Kevrekidis,D.J.Frantzeskakis,andR.Carretero-Gonz´alez, Emergent Nonlinear Phenomena in Bose-Einstein Condensates (Springer-Verlag, Berlin, 2008).
  • [4] A. D. Martin, C. S. Adams, and S. A. Gardiner, Phys. Rev. Lett. 98, 020402 (2007).
  • [5] V. M. P´erez-Garc´ıa, Physica D 191, 211 (2004); G. D. Montesinos, V. M. P´erez-Garc´ıa, and H. Michinel, Phys. Rev. Lett. 92, 133901-1 (2004); V. M. P´erez-Garc´ıa et al., Physica D 238, 1289 (2009).
  • [6] H. Yamasaki, Y. Natsume, and K. Nakamura, J. Phys. Soc. Jpn. 74, 1887 (2005).
  • [7] T.W.Neely,E.C.Samson,A.S.Bradley,M.J.Davis,andB.P. Anderson, Phys. Rev. Lett.104, 160401 (2010).
  • [8] D. V. Freilich et al., Science 329, 1182 (2010).
  • [9] S. Middelkamp, P. J. Torres, P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´alez, P. Schmelcher, D. V. Freilich, and D. S. Hall, Phys. Rev. A84, 011605(R) (2011).
  • [10] G.Thalhammer,G.Barontini,L.DeSarlo,J.Catani,F.Minardi, and M. Inguscio, Phys. Rev. Lett. 100, 210402 (2008).
  • [11] S. B. Papp, J. M. Pino, and C. E. Wieman, Phys. Rev. Lett. 101, 040402 (2008).
  • [12] S. Tojo, Y. Taguchi, Y. Masuyama, T. Hayashi, H. Saito, and T. Hirano, Phys. Rev. A 82, 033609 (2010). [13] A.L.FetterandA.A.Svidzinsky,J.Phys.:Condens.Matter13, R135 (2001).
  • [14] A. L. Fetter, Rev. Mod. Phys. 81, 647 (2009).
  • [15] P. J. Torr et al., Phys. Lett. A 375, 3004 (2011).
  • [16] J. C. Neu, Physica D 43, 385 (1990).
  • [17] A.Aftalion,VorticesinBose-EinsteinCondensates(Birkh¨auser, Boston, 2006).
  • [18] K.Sasaki,N.Suzuki,andH.Saito,Phys.Rev.Lett.104,150404 (2010).
  • [19] K. Nakamura, Prog. Theor. Phys. Suppl. 166, 179 (2007).
  • [20] I. Aranson and V. Steinberg, Phys. Rev. B53, 75 (1996).
  • [21] N. G. Berloff, J. Phys. A 37, 1617 (2004).
  • [22] J. J. Garc´ıa-Ripoll and V. M. P´erez-Garc´ıa, Phys. Rev. Lett.84, 4264 (2000).
  • [23] J. J. Garc´ıa-Ripoll, G. Molina-Terriza, V. M. P´erez-Garc´ıa, and L. Torner, Phys. Rev. Lett. 87, 140403 (2001).
  • [24] L.C.Crasovan,V.Vekslerchik,V.M.P´erez-Garc´ıa,J.P.Torres, D. Mihalache, and L. Torner, Phys. Rev. A68, 063609 (2003).
  • [25] H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1967).
  • [26] L. Onsager, Nuovo Cimento Suppl. 6, 279 (1949).
  • [27] G.K.Batcheor,AnIntroductiontoFluidDynamics(Cambridge University Press, Cambridge, 1967).
  • [28] U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
  • [29] J. Roenby and H. Aref, Proc. R. Soc. A466, 1871 (2010).
  • [30] In the usual theory of hydrodynamics, interacting point vortices in two dimensions have three independent constants of motion, i.e., total energy, x (or y) component of momentum and z component of angular momentum. Therefore the number of vortices must be larger than three, to make the system nonintegrable and chaotic.
  • [31] M. Eto, K. Kasamatsu, M. Nitta, H. Takeuchi, and M. Tsubota, Phys. Rev. A 83, 063603 (2011).
Цитирования
  • [1] C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2002).
  • [2] L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003). [3] P.G.Kevrekidis,D.J.Frantzeskakis,andR.Carretero-Gonz´alez, Emergent Nonlinear Phenomena in Bose-Einstein Condensates (Springer-Verlag, Berlin, 2008).
  • [4] A. D. Martin, C. S. Adams, and S. A. Gardiner, Phys. Rev. Lett. 98, 020402 (2007).
  • [5] V. M. P´erez-Garc´ıa, Physica D 191, 211 (2004); G. D. Montesinos, V. M. P´erez-Garc´ıa, and H. Michinel, Phys. Rev. Lett. 92, 133901-1 (2004); V. M. P´erez-Garc´ıa et al., Physica D 238, 1289 (2009).
  • [6] H. Yamasaki, Y. Natsume, and K. Nakamura, J. Phys. Soc. Jpn. 74, 1887 (2005).
  • [7] T.W.Neely,E.C.Samson,A.S.Bradley,M.J.Davis,andB.P. Anderson, Phys. Rev. Lett.104, 160401 (2010).
  • [8] D. V. Freilich et al., Science 329, 1182 (2010).
  • [9] S. Middelkamp, P. J. Torres, P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonz´alez, P. Schmelcher, D. V. Freilich, and D. S. Hall, Phys. Rev. A84, 011605(R) (2011).
  • [10] G.Thalhammer,G.Barontini,L.DeSarlo,J.Catani,F.Minardi, and M. Inguscio, Phys. Rev. Lett. 100, 210402 (2008).
  • [11] S. B. Papp, J. M. Pino, and C. E. Wieman, Phys. Rev. Lett. 101, 040402 (2008).
  • [12] S. Tojo, Y. Taguchi, Y. Masuyama, T. Hayashi, H. Saito, and T. Hirano, Phys. Rev. A 82, 033609 (2010). [13] A.L.FetterandA.A.Svidzinsky,J.Phys.:Condens.Matter13, R135 (2001).
  • [14] A. L. Fetter, Rev. Mod. Phys. 81, 647 (2009).
  • [15] P. J. Torr et al., Phys. Lett. A 375, 3004 (2011).
  • [16] J. C. Neu, Physica D 43, 385 (1990).
  • [17] A.Aftalion,VorticesinBose-EinsteinCondensates(Birkh¨auser, Boston, 2006).
  • [18] K.Sasaki,N.Suzuki,andH.Saito,Phys.Rev.Lett.104,150404 (2010).
  • [19] K. Nakamura, Prog. Theor. Phys. Suppl. 166, 179 (2007).
  • [20] I. Aranson and V. Steinberg, Phys. Rev. B53, 75 (1996).
  • [21] N. G. Berloff, J. Phys. A 37, 1617 (2004).
  • [22] J. J. Garc´ıa-Ripoll and V. M. P´erez-Garc´ıa, Phys. Rev. Lett.84, 4264 (2000).
  • [23] J. J. Garc´ıa-Ripoll, G. Molina-Terriza, V. M. P´erez-Garc´ıa, and L. Torner, Phys. Rev. Lett. 87, 140403 (2001).
  • [24] L.C.Crasovan,V.Vekslerchik,V.M.P´erez-Garc´ıa,J.P.Torres, D. Mihalache, and L. Torner, Phys. Rev. A68, 063609 (2003).
  • [25] H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1967).
  • [26] L. Onsager, Nuovo Cimento Suppl. 6, 279 (1949).
  • [27] G.K.Batcheor,AnIntroductiontoFluidDynamics(Cambridge University Press, Cambridge, 1967).
  • [28] U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
  • [29] J. Roenby and H. Aref, Proc. R. Soc. A466, 1871 (2010).
  • [30] In the usual theory of hydrodynamics, interacting point vortices in two dimensions have three independent constants of motion, i.e., total energy, x (or y) component of momentum and z component of angular momentum. Therefore the number of vortices must be larger than three, to make the system nonintegrable and chaotic.
  • [31] M. Eto, K. Kasamatsu, M. Nitta, H. Takeuchi, and M. Tsubota, Phys. Rev. A 83, 063603 (2011).
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