Matter-wave soliton tunneling in driven potentials

S. E. Pollack, D. Dries, E.J. Olson +1 more

Paul Dyke, Sidong Lei, S. E. Pollack +2 more

Kimberley Anne Heenan

In this thesis we study, analytically and numerically, the dynamics of a bright matter-wave soliton formed from a Bose-Einstein condensate with attractive interatomic interactions, confined by a one dimensional harmonic or double-well trapping potential, and subject to weak periodic driving. Such systems have potential applications in metrology, specifically in the use of atom interferometers for high precision inertial and gravitational field sensing. The localised and dynamically robust nature of matter-wave solitons may help overcome limitations such as wavepacket spreading in current atom interferometry experiments. A typical matter-wave interferometer involves a condensate trapped in a double-well potential. Being able to manipulate the tunnelling behaviour of a matter-wave soliton in potentials such as a double-well would thus give greater control in setting up these experiments. This also has a bearing upon the broader problem of transport of matter-wave solitons across potential barriers. These are questions which are largely unanswered in the current literature. We understand the tunnelling behaviour of a matter-wave soliton in a driven double well potential by first studying the fundamental mechanisms by which energy is transferred to a soliton in a driven harmonic potential. In this way our work also contributes more generally to the problem of transport in driven potentials. Within the mean field approximation, we show that efficient energy transfer to the soliton occurs in two frequency regimes: on resonance with the trapping frequency and on resonance with the internal mode frequency of the soliton. The former regime is well described by modelling the soliton effectively as a rigid particle, and in this regime energy transfer occurs due to parametric driving. In the latter regime, the extended nature of the soliton is important and energy transfer occurs due to internal mode coupling: a coupling between the width oscillations of the soliton and its translational motion. We find that in this internal mode coupling regime the soliton is unstable to decay. We thus show that effective particle regime is the more promising for efficiently exciting a bright matter-wave soliton to tunnel across a potential barrier, while preserving its form.

Jasur A. Abdullaev, Dario Poletti, Elena A. Ostrovskaya +1 more

We study the transport of quasi-two-dimensional matter-wave solitons in a Bose-Einstein condensate with attractive atomic interactions in a two-dimensional driven optical lattice potential.In order to describe the dynamics of 2D matter-wave soliton analytically we use the effective Hamiltonian theory.We also present numerical studies of the soliton evolution in the system.

Jason Nguyen, Paul Dyke, De Luo +2 more

F. Kh. Abdullaev, Josselin C. Garnier

The bright matter-wave soliton propagation through a barrier with a rapidly oscillating position is investigated. The averaged-over rapid oscillations Gross-Pitaevskii equation is derived, where the effective potential has the form of a finite well. Dynamical trapping and quantum tunneling of the soliton in the effective finite well are investigated. The analytical predictions for the effective soliton dynamics is confirmed by numerical simulations of the full Gross-Pitaevskii equation.