Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates

Abstract

We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates (BECs). Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multi-soliton states emerge as a nonlinear continuation of the appropriate excited eigensates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states may be dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally we present experimental realizations of multi-soliton states including a three-soliton state consisting of two solitons oscillating around a stationary one.Comment: 17 pages, 11 figure

Multiple Fluxon Analogues and Dark Solitons in Linearly Coupled Bose–Einstein Condensates

“…In this section, we shall first derive the interaction potential of two dark solitons given by (5) in the absence of the magnetic trap, which was discussed rather briefly in [25,30]. We shall then generalize the concept for the interaction of n solitons.…”

“…This problem has been considered in details in [25]. Since the domain of inverse hyperbolic cosine is [1, ∞[, Eq.…”

“…The dynamics of a dark soliton in BECs in the uncoupled system with magnetic trap has been considered before theoretically [22,23] (see also [24] and references therein) and experimentally [25,27,28,26,29]. Interesting phenomena on the collective behavior of a quantum degenerate bosonic gas, such as soliton oscillations [28,26,25] and frequency shifts due to soliton collisions [29] were observed. A theoretical analysis based on variational formulation was developed in [30,31] that is in good agreement with numerics as well as with experiments (see, e.g., [32,33]).…”

“…the critical coupling for a pitchfork bifurcation between dark solitons and FAs, the oscillation frequency of dark solitons in a harmonic trap is recovered [35](see also [32,23,25]). When the FAs are moving with the velocity v, critical value of the coupling constant is [16] …”

Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: An example of an antidamped Josephson junction

“…Within this plot, the (blue) star represents the theoretical frequency ±0.0302, which nearly coincides with one of the eigenvalues ±0.0292i of L. As has been analyzed in detail in previous works (see, e.g., Refs. [2,11,66]) for the Hamiltonian case, and even for the thermal BEC setting [20,22], this eigenvalue represents the so-called anomalous (or negative energy, or negative Krein signature in the Hamiltonian case) [2] mode, which is the one that pertains to the (eigenfrequency of the) motion of the dark soliton around its equilibrium position. As seen in the bottom left panel of Fig.…”