Discrete breathers in Bose–Einstein condensates

Discrete breathers, originally introduced in the context of biopolymers and
coupled nonlinear oscillators, are also localized modes of excitation of Bose–
Einstein condensates (BEC) in periodic potentials such as those generated by
counter-propagating laser beams in an optical lattice. Static and dynamical
properties of breather states are analysed in the discrete nonlinear Schrödinger
equation that is derived in the limit of deep potential wells, tight-binding and
the superfluid regime of the condensate. Static and mobile breathers can
be formed by progressive re-shaping of initial Gaussian wave-packets or by
transporting atomic density towards dissipative boundaries of the lattice. Static
breathers generated via boundary dissipations are determined via a transfer matrix approach and discussed in the two analytic limits of highly localized
and very broad profiles. Mobile breathers that move across the lattice are
well approximated by modified analytical expressions derived from integrable
models with two independent parameters: the core-phase gradient and the peak
amplitude. Finally, possible experimental realizations of discrete breathers
in BEC in optical lattices are discussed in the presence of residual harmonic
trapping and in interferometry configurations suitable to investigate discrete
breathers’ interactions.