EGAS41 - Swansea University

41 st EGAS CP 129 Gdańsk 2009
Discrete soliton collisions in two-species Bose-Einstein
condensates confined to a one-dimensional optical lattice
M. Borkowski 1,∗ , G.-L. Oppo 2
1 Instytut Fizyki, Uniwersytet Miko̷laja Kopernika, ul. Grudzi¸adzka 5/7, 87–100 Toruń,
Poland.
2 SUPA and Department of Physics, University of Strathclyde, 107 Rottenrow, Glasgow G4
0NG, Scotland, UK.
∗ Corresponding author: mateusz.borkowski@fizyka.umk.pl,
We generalize the tight-binding approximation [1] to model a two-species Bose-Einstein
condensate (BEC) in a one-dimensional optical lattice. We obtain a set of two coupledchannel
discrete nonlinear Schrödinger equations, which we use to model interactions in
two systems – the anticipated mixtures of two Ytterbium isotopes and a mixture of 87 Rb
and 41 K recently reported by Thalhammer et al. [2]. We study collisions between solitons
composed of different species. We observe that these collisions tend to be inelastic when
the interspecies scattering length is positive and lead to destruction of the two solitons
and creation of mutually-trapped states, while when the interspecies scattering length is
negative the collision is – counterintuitively – elastic over a wide range of parameters.
Figure 1: Left: collision of two travelling breathers in the case where the interaction between
the two species is attractive (ie. described by a negative scattering length [3]), as it is in the
case of 170 Yb and 174 Yb. The two solitons collide elastically. Right: a collision of a travelling
breather ( 170 Yb) and a self-trapped state ( 168 Yb) with the interspecies interaction repulsive.
The travelling breather is destroyed and becomes part of a two-species self-trapped state.
References
[1] A. Trombettoni, A. Smerzi, Phys. Rev. Lett. 86, 002353 (2001)
[2] G. Thalhammer, G. Barontini, L. De Sarlo, J. Catani, F. Minardi, M. Inguscio, Phys.
Rev. Lett 100, 210402 (2008)
[3] M. Kitagawa, K. Enomoto, K. Kasa, Y. Takahashi, R. Ciury̷lo, P. Naidon, P.S. Julienne,
Phys. Rev. A 77, 012719 (2008)
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