Ripplon Modes of Two Segregated Bose-Einstein Condensates in Confined Geometry

Tran Huu Phat, Hoang Van Quyet


The ripplon modes of two segregated Bose-Einstein condensates (BECs) confined by one and two hard walls are respectively studied by means of the hydrodynamic approach within the Gross-Pitaevskii (GP) theory. For the system at rest we find that due to the spatial restriction the dispersion relations are of the form \(\omega \sim {k^2}\) in low momentum limit for both cases, while for the system in motion parallel to the interface the dispersion relations for both cases are \(\omega \sim k\) at low momentum limit and, furthermore, the system becomes unstable.


Bose-Einstein condensates, hydrodynamic approach, ripplon modes, Kelvin-Helmholtz instability, Bernoulli equation

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C. J. Myatt, E. A. Burt, R. W. Ghrist, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 78, 586 (1997).

D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman and E.A.Cornell, Phys. Rev. Lett. 81 , 1539 (1998).

D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, S. Inouye, J. Stenger and W. Ketterle, Phys. Rev. Lett. 83,


M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman and E. A. Cornell, Phys. Rev. Lett. 83,


H. J. Miesner , D. M. Stamper-Kurn, J. Stenger, S. Inouye, A. P. Chikkatur and W. Ketterle, Phys. Rev. Lett. 82,


D. J. McCarron, H.W. Cho, D. L. Jenkin, M. P. Koppinger and S. L. Cornish, Phys. Rev. A 84, 011603(R) (2011).

S. B. Papp, J. M. Pino and C. E. Wieman, Phys. Rev. Lett. 101, 040402 (2008).

D. S. Hall, in Emergent Nonlinear Phenomena in Bose-Einstein condensates, edited by P.G.Kevrekidis , D. J.

Frantzeskakis and R. Carretero-Gonzales ( Springer-Verlag, Berlin, (2008 ), Chap.16 , p.307.

E. Timmermans, Phys. Rev. Lett. 81, 5718 (1998).

P.Ao and S.T.Chui, Phys. Rev. A 58, 4836, (1998).

A. Bezett, V. Bychkov, E. Lundh, D. Kobyakov, and M.Marklund, Phys. Rev. A 82, 043623 (2010).

D. Kobyakov, V. Bychkov , E. Lundh, A. Bezett, V. Akkerman and M. Marklund, Phys. Rev. A 83, 043623


J. O. Indekeu and B. Van Schaeybroeck, Phys. Rev. Lett . 93, 210402 (2004).

B. Van Schaeybroeck, Phys. Rev. A 78 023624 (2008); 80, 06560(addendum ) (2009); 93, 210402 (2004).

B. Van Schaeybroeck and J. O. Indekeu, Phys. Rev. A 91, 013626 (2015).

J. O. Indekeu, Chang-You Lin, N. V. Thu, B. Van Schaeybroeck and T. H. Phat, Phys. Rev. A 91, 033615 (2015).

K. Sasaki, N. Suzuki and H. Saito, Phys. Rev. A 83, 033602 (2011); 83, 053606 (2011).

C. Ticknor , Phys. Rev. A 89, 053601 (2014).

D. A. Takahashi , M. Kobayashi and M. Nitta, Phys. Rev. B 91, 184501 (2015).

T. Kadokura, T. Aioi, K. Sasaki, T. Kishimoto and H. Saito, Phys. Rev. A 85, 013602 (2012).

F. V. Pepe, P. Facchi, G. Florio and S. Pascazio, Phys. Rev. A 86, 023629 (2012).

T. H. Phat, L. V. Hoa, N. T. Anh and N. V. Long, Ann. Phys.(NY). 324, 2074 (2009) .

B. Van Schaeybroeck, Phys. Rev. A 392, 3806 (2013).

A. Roy, S. Gautam and D. Angom, Phys. Rev. A 89, 013617 (2014).

G. Ceccarelli, J. Nespolo, A. Pelissetto and E. Vicari, Phys. Rev. A 92, 043613 (2015).

L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 4th ed. (Academic Press, NY, 2008).

I. K. Kundu, I. M. Cohen and D. R. Dowling, Fluid Mechanics, 5th edition, Elsevier 2012, Amsterdam, Netherlands.

This approximation corresponds to the Boussinesq approximation in classic hydrodynamics, see [27], p.135 for

detail .

A. N. Malmi - Kakkada, O. T. Valls and C. Dasgupta, J. Phys. B 47, 055301 (2014).

D. A. Takahashi and M. Nitta, Ann. Phys.(NY). 354, 101 (2015).

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