Nondecaying Bloch modes of a dissipative lattice
1 Centro de Ciências Naturais e Humanas, Universidade Federal do ABC - Santo André, São Paulo 09210-170, Brazil
2 Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa - Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal, EU
Received: 14 May 2012
Accepted: 1 September 2012
We consider a Bose-Einstein condensate in a periodic optical lattice having a periodic sublattice of dissipative sites (which we call the dissipative lattice). The optical analog of this system consisting of lossy optical waveguides arranged in a checkerboard order is also presented. Using numerical simulations within the mean-field theory we demonstrate the existence of nondecaying (or propagating, in optical applications) Bloch-like coherent modes, which are eigenstates of the non-Hermitian operator with the dissipative lattice serving as a spatially periodic potential. The nondecaying modes have the Bloch index confined to the boundary of the Brillouin zone of the dissipative lattice. Besides the numerical simulations for a finite lattice, we use the Fourier space perturbation theory for a weak dissipative lattice and the single-band tight-binding approximation for a strong lattice to show that the effect is a universal property of the dissipative lattice.
PACS: 03.75.Lm – Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations / 03.75.Kk – Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow / 03.75.Nt – Other Bose-Einstein condensation phenomena
© EPLA, 2012