Oscillations and interactions of dark and dark–bright solitons in Bose–Einstein condensates

Abstract

Solitons are among the most distinguishing fundamental excitations in a wide range of non-linear systems such as water in narrow channels, high speed optical communication, molecular biology and astrophysics. Stabilized by a balance between spreading and focusing, solitons are wavepackets, which share some exceptional generic features like form-stability and particle-like properties. Ultracold quantum gases represent very pure and well-controlled non-linear systems, therefore offering unique possibilities to study soliton dynamics. Here we report on the first observation of long-lived dark and dark-bright solitons with lifetimes of up to several seconds as well as their dynamics in highly stable optically trapped 87 Rb Bose-Einstein condensates. In particular, our detailed studies of dark and dark-bright soliton oscillations reveal the particle-like nature of these collective excitations for the first time. In addition, we discuss the collision between these two types of solitary excitations in Bose-Einstein condensates. The dynamics of non-linear systems plays an essential role in nature, ranging from strong non-linear interactions of elementary particles to non-linear wave phenomena in oceanography and meteorology. A special class of non-linear phenomena are solitons with interesting particle and wave-like behaviour. Reaching back to the observation of "waves of translation" in a narrow water channel by Scott-Russell in 1834 [1], solitons are nowadays recognized to appear in various systems as different as astrophysics, molecular biology and non-linear optics [2]. They are characterized as localized solitary wavepackets that maintain their shape and amplitude caused by a self-stabilization against dispersion via a non-linear interaction. While an early theoretical explanation of this non-dispersive wave phenomenon was given by Korteweg and de Vries in the late 19th century it was not before 1965 that numerical simulations of Zabusky and Kruskal theoretically proved that these solitary waves preserve their identity in collisions [3,4]. This revelation led to the term "soliton" for this type of collective excitation. Nowadays solitons are a very active field of research in many areas of science. In the field of non-linear optics they attract enormous attention due to applications in fast data transfer. Bose-Einstein condensates (BEC) of weakly interacting atoms offer fascinating possibilities for the study of nonlinear phenomena, as they are very pure samples of ultracold gases building up an effective macroscopic wave function of up to mm size. Non-linear effects like collective excitations [5], four-wave mixing [6] and vortices [7,8] have been studied, to name only a few examples. The existence and some fundamental properties of solitons have been deduced from few experiments employing ultra-cold quantum gases. Bright solitons, characterized as non-spreading matter-wave packets, have been observed in BEC with attractive interaction [9,10,11] where they represent the ground state of the system. In a repulsively...

Spontaneous creation of Kibble–Zurek solitons in a Bose–Einstein condensate

“…More solitons are shown in the other panels, including cases where the solitonic planes are bent and/or collide as in f) and g). As opposed to artificially created solitons via phase imprinting techniques [27][28][29] or by exciting the superfluid with laser pulses or through collisions [30,31], our solitons spontaneously form when the BEC is created by crossing the transition temperature.The identification of these defects as dark/grey solitons is based on several arguments: they are simultaneously observed as lines from two orthogonal directions in the radial plane, demonstrating their planar structure, mostly perpendicular to the weak axis of confinement; sometimes they exhibit a bent shape as we expect for snake oscillations [32] of soliton planes; when two of these defects overlap, they appear as solitons in a collision [33], whose individual structure is preserved except in the crossing region. Finally their size after TOF is of the right order of magnitude.…”

Dark soliton oscillations in Bose–Einstein condensates with multi-body interactions

“…The remarkable theoretical prediction (6) was confirmed in the experiment [20]. Equation (6) then implies that the motion of the dark soliton must be accompanied by a deformation of the density distribution which re-tunes the oscillation of the whole condensate to the trap frequency.…”

Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

“…These hybrid structures, termed dark-bright solitons, have analogs in nonlinear optics [151] and were first predicted to exist in inhomogeneous BECs by Busch and Anglin [152]. Since then they have been generated and observed in several experiments [153][154][155]. Possessing only repulsive interactions, they are free from the collapse instability and behave more akin to dark solitary waves (see reference [8] for a review) than bright solitary waves.…”