Nearly-one-dimensional self-attractive Bose-Einstein condensates in optical lattices

Abstract

Within the framework of a mean-field description, we investigate atomic Bose-Einstein condensates, with attraction between atoms, under the action of a strong transverse confinement and periodic [optical-lattice (OL)] axial potential. Using a combination of the variational approximation, one-dimensional (1D) nonpolynomial Schrodinger equation, and direct numerical solutions of the underlying 3D Gross-Pitaevskii equation, we show that the ground state of the condensate is a soliton belonging to the semi-infinite band gap of the periodic potential. The soliton may be confined to a single cell of the lattice or extended to several cells, depending on the effective self-attraction strength g (which is proportional to the number of atoms bound in the soliton) and depth of the potential, V-0, the increase of V-0 leading to strong compression of the soliton. We demonstrate that the OL is an effective tool to control the soliton's shape. It is found that, due to the 3D character of the underlying setting, the ground-state soliton collapses at a critical value of the strength, g=g(c), which gradually decreases with the increase of V-0; under typical experimental conditions, the corresponding maximum number of Li-7 atoms in the soliton, N-max, ranges between 8000 and 4000. Examples of stable multipeaked solitons are also found in the first finite band gap of the lattice spectrum. The respective critical value g(c) again slowly decreases with the increase of V-0, corresponding to N-max similar or equal to 5000

Dynamics of kicked matter-wave solitons in an optical lattice

“…Such solitons were created in condensates of 7 Li [12] and 85 Rb [13] atoms, with the sign of the atomic interactions switched to attraction by means of the Feshbach-resonance technique (in the latter case, the solitons were observed in a post-collapse state of the condensate). In the presence of a periodic potential, such solitons should exist too, with the chemical potential falling in the semi-infinite gap of the spectrum, as first shown in the context of the optical setting [14], and later demonstrated in detail in the framework of GPEs [15,16,5].…”

“…The NPSE including axial OL potential (3) was derived too [16,5], assuming the following factorization of the 3D wave function in Eq. (1),…”

“…( 7) by means of the numerical scheme described in Refs. [16,5], for values of the interaction strength g belonging to the above-mentioned existence range, g min < g < g coll .…”

Double-layer Bose-Einstein condensates: A quantum phase transition in the transverse direction, and reduction to two dimensions

“…In particular, studies of quasi-two-dimensional (quasi-2D) BEC with embedded 2D potentials have drawn much interest [35,55]. In this connection, approximations which make it possible to reduce the underlying 3D Gross-Pitaevskii equation (GPE) to effective 1D [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70] and 2D [62,63,65,66,[71][72][73][74][75][76] equations have been elaborated. In particular, different effective low-dimensional equations were developed in Refs.…”

Finite number of trapped bosons interacting through the harmonic Calogero interaction in one dimension

“…However in a nice paper, Druten and Ketterle [6] consider the ideal gas in 1D and showed that with an appropriate choice of N and trap parameters BEC is possible; but the effect of interaction on the calculated properties was not discussed. The system of interacting bosons in 1D optical lattice and the study of different transport properties is another interesting area of research [7][8][9][10][11] both experimentally and theoretically. Although the low-lying excitation frequency in reduced dimension has been studied [11,12]; however, the thermodynamic properties of trapped bosons and their dependence on interaction are not yet studied in detail.…”