Dynamics of dark–bright solitons in cigar-shaped Bose–Einstein condensates

Abstract

We explore the stability and dynamics of dark-bright solitons in two-component elongated BoseEinstein condensates by developing effective 1D vector equations as well as solving the corresponding 3D Gross-Pitaevskii equations. A strong dependence of the oscillation frequency and of the stability of the dark-bright (DB) soliton on the atom number of its components is found. Spontaneous symmetry breaking leads to oscillatory dynamics in the transverse degrees of freedom for a large occupation of the component supporting the dark soliton. Moreover, the interactions of two DB solitons are investigated with special emphasis on the importance of their relative phases. Experimental results showcasing dark-bright soliton dynamics and collisions in a BEC consisting of two hyperfine states of 87 Rb confined in an elongated optical dipole trap are presented.Introduction. Multi-component systems of nonlinear waves are a fascinating topic with a rich and diverse history spanning a variety of areas, including Bose-Einstein condensates (BECs) in atomic physics [1], optical fibers and crystals in nonlinear optics [2], and integrable systems in mathematical physics [3]. Of particular interest are the so-called "symbiotic solitons", namely structures that would not otherwise exist in one-component settings, but can be supported by the interaction between the optical or atomic species components. A prototypical example of such a structure is the dark-bright (DB) soliton in self-defocusing, two-component systems, whereby the dark soliton (density dip) which typically arises in self-defocusing media [1][2][3][4] creates, through nonlinearity, a trapping mechanism that localizes a density hump (bright soliton) in the second component.

Statics and dynamics of atomic dark-bright solitons in the presence of impurities

“…[34], or the states |1, − 1 and |2, − 2 used in the experiments of Refs. [17][18][19]. In the first case the scattering lengths take the values a 11 = 100.4a 0 , a 12 = 97.66a 0 , and a 22 = 95.00a 0 , while in the second case the respective values are a 11 = 100.4a 0 , a 12 = 98.98a 0 , and a 22 = 98.98a 0 (where a 0 is the Bohr radius).…”

“…Eq. (19)], i.e., when the number of atoms of the bright soliton is only a small fraction of the total number of atoms [16][17][18][19], we may approximate the above integrals as I 1 ≈ I 2 ≈ (2/3)sech 2 (Dx 0 ) tanh(Dx 0 ). This way, we accordingly simplify Eq.…”

“…Furthermore, they have recently been analyzed in discrete settings [12], while higher-dimensional generalizations-namely, vortex-bright-soliton structureswere studied as well [13]. Importantly, dark-bright solitons have been observed in experiments conducted both in optics [14,15] and, more recently, in BECs [16][17][18][19].…”

“…More specifically, we consider a quasione-dimensional (1D) two-component repulsive BEC, composed by two hyperfine states of the same alkali-metal species (as, e.g., in the experiments of Refs. [17][18][19])-a system that can be approximated by two coupled 1D Gross-Pitaevskii equations (GPEs) (see, e.g., Refs. [3,4,7]).…”

Multiple dark-bright solitons in atomic Bose-Einstein condensates

“…[10] by means of a phase-imprinting method, and they were observed more recently in Refs. [22][23][24] by means of the counterflow of the two BEC components. The above efforts led to a renewed interest in theoretical aspects of this theme: in this way, DB-soliton interactions were studied from the viewpoint of the integrable systems theory in Ref.…”