We experimentally study the excitation modes of bright matter-wave solitons in a quasi-one-dimensional geometry. The solitons are created by quenching the interactions of a Bose-Einstein condensate of cesium atoms from repulsive to attractive in combination with a rapid reduction of the longitudinal confinement. A deliberate mismatch of quench parameters allows for the excitation of breathing modes of the emerging soliton and for the determination of its breathing frequency as a function of atom number and confinement. In addition, we observe signatures of higher-order solitons and the splitting of the wave packet after the quench. Our experimental results are compared to analytical predictions and to numerical simulations of the one-dimensional Gross-Pitaevskii equation.The dispersionless propagation of solitary waves is one of the most striking features of nonlinear dynamics, with multiple applications in hydrodynamics, nonlinear optics and broadband long-distance communications [1]. In fiber optics, one-dimensional (1D) "bright" solitons, i.e. solitons presenting a local electric field maximum with one-dimensional propagation, have been observed [2]. They exhibit a dispersionless flow and excitation modes such as breathing or higher-order modes [2][3][4]. Matter waves can also display solitary dispersion properties. Typically, bright matter-wave solitons are created in quasi-1D systems by quenching the particle interaction in a Bose-Einstein condensate (BEC) from repulsive to attractive [5]. Recent experiments demonstrated the collapse [6], collisions [7], reflection from a barrier [8], and the formation of trains [9-11] of bright solitons.In this letter, we experimentally study the excitation modes of a single bright matter-wave soliton. In previous studies, other dynamical properties have been observed, such as center-of-mass oscillations of solitons in an external trap [7], excitations following the collapse of attractive BECs [6,12], and quadrupole oscillations of attractive BECs in three dimensions (3D) [13]. Here, we probe the fundamental breathing mode of a single soliton by measuring its oscillation frequency and the time evolution of its density profile. In addition, we observe signatures of higher-order matter-wave solitons, which can be interpreted as stable excitations with periodic oscillations of the density profile and phase, or as a bound state of overlapping modes [3,14].The shape-preserving evolution of a matter-wave soliton is due to a balancing of dispersive and attractive terms in the underlying 3D Gross-Pitaevskii equation (GPE) [15]. For quasi-1D systems with tight radial confinement, we can approximate the matter wave in the 3D-GPE by the product of a Gaussian wave function for the radial direction and a function f (z) for the longitudinal direction (see [16]). Depending on the ansatz for the Gaussian with either constant or varying radial sizes, f (z) satisfies either the 1D-GPE or the non-polynomial Schrödinger equation (NPSE) [17]. We reference to the analytical solutions of the 1D-G...

We study the evolution of a collisionally inhomogeneous matter wave in a spatial gradient of the interaction strength. Starting with a Bose-Einstein condensate with weak repulsive interactions in quasi-one-dimensional geometry, we monitor the evolution of a matter wave that simultaneously extends into spatial regions with attractive and repulsive interactions. We observe the formation and the decay of soliton-like density peaks, counter-propagating self-interfering wave packets, and the creation of cascades of solitons. The matter-wave dynamics is well reproduced in numerical simulations based on the nonpolynomial Schrödinger equation with three-body loss, allowing us to better understand the underlying behaviour based on a wavelet transformation. Our analysis provides new understanding of collapse processes for solitons, and opens interesting connections to other nonlinear instabilities.

We model propagation of far-red-detuned optical vortex beams through a Bose-Einstein Condensate using nonlinear Schrödinger and Gross-Pitaevskii equations. We show the formation of coupled light/atomic solitons that rotate azimuthally before moving off tangentially, carrying angular momentum. The number, and velocity, of solitons, depends on the orbital angular momentum of the optical field. Using a Bessel-Gauss beam increases radial confinement so that solitons can rotate with fixed azimuthal velocity. Our model provides a highly controllable method of channelling a BEC and atomic transport.

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