Origins of bright soliton transparency to Bogoliubov quasi-particles

Chiquillo Márquez, Emerson Evaristo

Argha Debnath, Ayan Khan, Prasanta Kumar Panigrahi

Dmitry K. Efimkin, Johannes Hofmann, Victor M. Galitski

We explore the quantum dynamics of a bright matter-wave soliton in a quasi-one-dimensional bosonic superfluid with attractive interactions. Specifically, we focus on the dissipative forces experienced by the soliton due to its interaction with Bogoliubov excitations. Using the collective coordinate approach and the Keldysh formalism, a Langevin equation of motion for the soliton is derived from first principles. The equation contains a stochastic Langevin force (associated with quantum noise) and a nonlocal in time dissipative force, which appears due to inelastic scattering of Bogoliubov quasiparticles off of the moving soliton. It is shown that Ohmic friction (i.e., a term proportional to the soliton's velocity) is absent in the integrable setup. However, the Markovian approximation gives rise to the Abraham-Lorentz force (i.e., a term proportional to the derivative of the soliton's acceleration), which is known from classical electrodynamics of a charged particle interacting with its own radiation. These Abraham-Lorentz equations famously contain a fundamental causality paradox, where the soliton (particle) interacts with excitations (radiation) originating from future events. We show, however, that the causality paradox is an artifact of the Markovian approximation, and our exact non-Markovian dissipative equations give rise to physical trajectories. We argue that the quantum friction discussed here should be observable in current quantum gas experiments.

F. Kh. Abdullaev, Josselin C. Garnier

Krzysztof Sacha, Dominique Delande, Jakub Zakrzewski

At very low temperature, a quasi-one-dimensional ensemble of atoms with attractive interactions tend to form a bright soliton.When exposed to a sufficiently weak external potential, the shape of the soliton is not modified, but its external motion is affected.We develop in detail the Bogoliubov approach for the problem, treating, in a non-perturbative way, the motion of the center of mass of the soliton.Quantization of this motion allows us to discuss its long time properties.In particular, in the presence of a disordered potential, the quantum motion of the center of mass of a bright soliton may exhibit Anderson localization, on a localization length which may be much larger than the soliton size and could be observed experimentally.

Xueli Feng

We have numerically studied the head-on collisions of the bright-bright solitons and bright-dark solitons with different relative phases, based on Gross-Pitaevskii(GP) equation of the quasi-one-dimensional heteronuclear two-component Bose-Einstein condensates. If there is no external potential well, the relative phase zc leads to elastic collision of the bright-bright solitons, but they collide with each other accompanied by some energy transfer for the relative phase π /2. If there is external potential well, they collide periodically with the relative phase π, but with the relative phase π /2, the two solitons combine to one soliton after collision with energy escape. For the bright-dark solitons, their bright-bright solitons in the first component collide periodically with the relative phase 0 or π. The difference of them is that the former has one collision point, the latter two collision points. Furthermore, we have found that the bright-bright solitons are always stable and the bright-dark solitons are unstable by solving its co~esponding Bogoliubov-de Gennes equations.