Linear superpositions of nonlinear matter waves in optical lattices

¹ Centro de Física, Universidade do Minho, Campus de Gualtar - Braga 4710-057, Portugal, EU
² Centro de Física Teórica e Computacional and Departamento de Física, Universidade de Lisboa Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal, EU
³ Dipartimento di Fisica “E.R. Caianiello”, CNISM and INFN, Gruppo Collegato di Salerno, Università di Salerno Via Ponte don Melillo, 84084 Fisciano (SA), Italy, EU

^a bludov@fisica.uminho.pt

Received: 8 December 2010
Accepted: 17 January 2011

Abstract

It is shown that by a proper design of the nonlinearity it is possible to obtain linear superposition of matter waves in optical lattices. In particular, the possibility to create non-stationary states of Bose-Einstein condensates which are linear superposition of stationary nonlinear matter waves is demonstrated. This is achieved by means of spatial variation of the interatomic interaction which suppresses the nonlinear overlapping terms, which otherwise would destroy the superposition, and at the same time retaining all the nonlinearity necessary for each component state to exist. The superposition state is shown to be long lived and can be split into constituent parts by accelerating the lattice.