Vortex lines attached to dark solitons in Bose-Einstein condensates and boson-vortex duality in 3+1 dimensions

Abstract

We demonstrate the existence of stationary states composed of vortex lines attached to planar dark solitons in scalar Bose-Einstein condensates. Dynamically stable states of this type are found at low values of the chemical potential in channeled condensates, where the long-wavelength instability of dark solitons is prevented. In oblate, harmonic traps, U-shaped vortex lines attached by both ends to a single planar soliton are shown to be long-lived states. Our results are reported for parameters typical of current experiments, and open up a way to explore the interplay of different topological structures. These configurations provide Dirichlet boundary conditions for vortex lines and thereby mimic open strings attached to D-branes in string theory. We show that these similarities can be formally established by mapping the Gross-Pitaevskii theory into a dual effective string theory for open strings via a boson-vortex duality in 3+1 dimensions. Combining a one-form gauge field living on the soliton plane which couples to the endpoints of vortex lines and a two-form gauge field which couples to vortex lines, we obtain a gauge-invariant dual action of open vortex lines with their endpoints attached to dark solitons. * amunoz@fqa.ub.edu † xiaoquan.yu@otago.ac.nz ‡ nian@ihes.fr arXiv:1606.02776v3 [cond-mat.quant-gas]

Note on nonlinear Schrödinger equation, KdV equation and 2D topological Yang–Mills–Higgs theory

“…In this paper, we would like to pursue their relation from some new perspectives, e.g. the boson/vortex duality [2][3][4][5].…”

“…Recently, in Refs. [4,5] this (3+1)D duality was generalized to include boundaries, and the dual theory is an effective open string theory. The same steps can be repeated in (1+1)D, however, instead of an effective string theory the dual theory is another scalar field theory, and the bulk equation of motion in a certain limit becomes the KdV equation.…”

Dark solitons, D-branes and noncommutative tachyon field theory

“…More recently, some numerical work in BEC [4] has demonstrated that the vortex lines can be attached directly to dark solitons, which mimics the configuration of open strings attached to D-branes in string theory. Hence, it is very conceivable that there should be some explanations about this similarity from theoretical point of view.…”

Vortex force in compressible spin-orbit-coupled Bose-Einstein condensates

“…We note that φ l is not a new degree of freedom, but rather a short-hand for the integral (8), fixed by the divergence of j (l) (Eq. (7)).…”

“…This is especially manifest in the presence of a quantised vortex, which creates a logarithmic branch cut in the phase of the incompressible sector. To this end, various gauge fields have been introduced to address this problem [5][6][7][8], but it remains unclear what happens in the presence of a two-component compressible BEC under SO coupling.…”