Research projects - Joachim Brand

Soliton collisions in BECs
Solitonenkollisionen in Bose-Einstein-Kondensaten

Solitons and vortex rings are examples of nonlinear wave phenomena, which maintain their shape during propagation. The collisions of such waves were recently observed in a Bose-Einstein condensate for the first time. The experiment at Harvard University showed evidence of unexpected shell-like structures. Simulations give evidence that these structures are hybride objects composed of soliton fronts and vortex rings.

Phys. Rev. Lett. 95, 110401 (2005)
Phys. Rev. Lett. 94, 040403 (2005)
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Dynamics of the 1D Bose gas

The 1D Bose gas at zero temperature has many surprising properties that are very distinct from 3D Bose-Einstein condensates including the loss of phase coherence and a fermionic excitation spectrum with appearance of two branches of elementary excitations. We approach the subject by making use of an exact mapping of the 1D Bose system to an interacting Fermi gas and by applying fermionic density functional theory in a local density approximation. An appealing feature of this approach is that the approximations become exact in the limit of strong interactions in the bosonic system and thus both the fermionic excitation spectrum and phase coherence properties are recovered. A time-dependent version of this theory may be used to simulate the time-dependent dynamics as it may become important in narrow atomic guides, e.g. on atom chips. In this project, we can make a connection between well established approximation methods from the field of quantum chemistry and solid state physics to the study of 1D quantum degenerate gases. Another promising direction is the development of a many-body perturbation theory starting from the strongly interacting limit, which is equivalent to a non-interacting Fermi gas.

Phys. Rev. A. 72, 033619 (2005)
Preprint cond-mat/0507086
J. Phys. B: At. Mol. Opt. Phys. 37 (2004) S287-S300

Spontaneous formation and dynamics of bright solitons

When attractive Bose-Einstein condensates are confined to cigar-shaped harmonic traps they can avoid collapse and show features previously known from non-linear fiber optics like modulational instability and bright solitons. Motivated by the recent creation of the first matter-wave bright soliton train [Strecker et al. Nature 417 150 (2002)], we study the effect of modulational instability in inhomogeneous density profiles and external trapping potentials. Also the dynamics of bright solitons in a harmonic trap is considered.

Phys. Rev. Lett. 92, 040401 (2004)
Phys. Rev. A. 70, 033607 (2004)

Self-consistent determination of the coupling constant

The coupling constant in the Gross-Pitaevskii equation is renormalized due to medium effects and the trapping potential, e.g. most dramatically in quasi 1D or quasi 2D. Usually this  renormalization is determined either from a pseudopotential replacement or using a T-matix approach. We propose a different approach which is more powerful than  the pseudopotential and much simpler than comparable T-matrix methods. Starting from the bare potential we suggest a self-consistent scheme that allows to treat medium effects as well as the influence of the trapping potential. This approach is particularly useful for situations where the range of the interaction is comparable to the characteristic scale of the trapping potentials, as they may arise for molecular condensates in quasi-low-dimensional traps or optical lattices.

Phys. Rev. A. 70, 043622 (2004)

Levinson's theorem for Bose-Einstein Condensates

Levinson's theorem of potential scattering connects the number of bound states of a given potential to the phase shifts of scattering solutions. Excitations of a weakly interacting Bose condensate are described by the coupled Bogoliubov equations. Scattering solutions for a finite trapping potential describe the scattering of single, identical particles. Can Levinson's theorem be generalized and the number of bound collective excitations of a condensate be linked with the phase shifts of single-particle scattering? Particularly interesting situations occur for kinks or vortices in shallow traps as they can give rise to 'bound states in the continuum' of single particle scattering.

Phys. Rev. Lett. 91 , 070403 (2003)

Solitonic vortices and the snake instability

What happens to vortices when they are put into a narrow channel? What is the 1D analog of a vortex? Svortex generated by transverse instability We study the effects of transverse confinement on vortices in a repulsive, elongated BEC. In a regime where the width of the elongated trap is about 6 to 12 healing lengths, vortices show properties usually associated with solitons. In particular, their velocity may be associated with a characteristic phase step and collision properties are soliton-like. Thus we speak of solitonic vortices. A connection can be made to the snake instability of soliton stripes which is also a mechanism that may be exploited to experimentally create solitonic vortices [1 ]. A different way of producing solitonic vortices in a controlled manner is stirring in a toroidal trap [2 ]. Properties are studied using 2 and 3D simulations of the Gross-Pitaevskii equation but also using the method of image charges which yields an exactly solvable model of vortex dynamics.

[1] J. Brand and W. P. Reinhardt, Phys. Rev. A, 65 (2002) 043612

[2] J. Brand and W. P. Reinhardt, J. Phys. B: At. Mol. Opt. Phys., 34 (2001) L113-L119

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