Collisions of Three-Component Vector Solitons in Bose-Einstein Condensates

Stefan Lannig, Christian-Marcel Schmied, Maximilian Prüfer, Philipp Kunkel, Robin Strohmaier, Helmut Strobel, Thomas Gasenzer, Panayotis G. Kevrekidis, and Markus K. Oberthaler

Phys. Rev. Lett. 125, 170401 – Published 22 October 2020

Abstract

Ultracold gases provide an unprecedented level of control for the investigation of soliton dynamics and collisions. We present a scheme for deterministically preparing pairs of three-component solitons in a Bose-Einstein condensate. Our method is based on local spin rotations which simultaneously imprint suitable phase and density distributions. This enables us to observe striking collisional properties of the vector degree of freedom which naturally arises for the coherent nature of the emerging multicomponent solitons. We find that the solitonic properties in the quasi-one-dimensional system are quantitatively described by the integrable repulsive three-component Manakov model.

Received 26 May 2020
Accepted 14 September 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.170401

Physics Subject Headings (PhySH)

Atom optics Spinor Bose-Einstein condensates

Solitons

Atomic, Molecular & OpticalNonlinear DynamicsGeneral Physics

Authors & Affiliations

Stefan Lannig ^1,*, Christian-Marcel Schmied¹, Maximilian Prüfer ¹, Philipp Kunkel¹, Robin Strohmaier¹, Helmut Strobel¹, Thomas Gasenzer ¹, Panayotis G. Kevrekidis², and Markus K. Oberthaler¹

¹Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
²Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515 USA

^*vectorsolitons@matterwave.de

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Vol. 125, Iss. 17 — 23 October 2020

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Images

Figure 1
Formation of three-component vector solitons. (a) An amplitude-modulated steerable laser beam (green) is used to implement local spin rotations in an elongated BEC (red) subject to a homogeneous magnetic field $B$ along the $z$ direction. This coherently transfers atoms from the initial state $m_{F} = 0$ (red disk) to $m_{F} = \pm 1$ (green arrows). (b) The upper panel shows absorption images after Stern-Gerlach separation revealing the density distributions of the three $m_{F}$ states after local spin rotations of duration $τ$ . For short Rabi coupling ( $τ = 33 μ s$ ) the population is transferred to $m_{F} = \pm 1$ ; and for longer pulse duration ( $τ = 65 μ s$ ) the population is coherently transferred back to $m_{F} = 0$ in the center of the laser beam, implying a sign change in $ψ_{0}$ . The subsequent dynamics shown below (summed $m_{F} = \pm 1$ densities $n_{\pm 1}$ ) indicates the formation of a soliton pair as a result of the sign change (right column). Each soliton consists of shape-preserving bright components ( $m_{F} = \pm 1$ ) and a corresponding density depletion in the $m_{F} = 0$ component (see lower absorption image). In contrast, without phase jump the initial density distribution disperses (left column).
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Figure 2
Quantitative comparison with a repulsive three-component Manakov vector soliton solution. (a) Experimentally extracted density profiles (markers) of a single realization at $t = 100 ms$ compared to the analytical prediction (solid and dashed lines) of Eq. (1) with independently extracted parameters from the experimental observations (see main text). The spreading of the atomic absorption signal induced by the imaging setup is taken into account by convolving the model densities with a Gaussian with rms radius of $1.2 μ m$ [16, 21]. The inset shows the experimentally extracted soliton positions (solid lines are linear fits). (b) The total density of the three-component Manakov soliton features a small depletion [solid line for parameters used in (a)] which we confirm by taking the difference between the total densities with and without solitons measured by omitting the Stern-Gerlach separation of the components and averaging over 20 realizations. All error bars mark the 1 s.d. interval of the mean.
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Figure 3
Collision of three-component vector solitons. (a) We generate two pairs of solitons by applying two local spin rotations. The resulting evolution of the bright components $n_{1} + n_{- 1}$ , averaged over 6 realizations, is shown in the lower panel. Encircled numbers label the solitons. (b) Detailed view of the collision area marked by the rectangle in (a) for three different relative Larmor phases $Δ φ_{L} = φ_{L}^{(2)} - φ_{L}^{(1)}$ imprinted by corresponding phases of the laser beam modulation. The orientation of the pseudospin $1 / 2$ in the $x − y$ plane is indicated by the green arrows. The color-coded density difference $n_{1} - n_{- 1}$ between the two bright components of the vector soliton after collision reveals a strong dependence on the initial $Δ φ_{L}^{i}$ . The saturation of the color indicates the density $n_{1} + n_{- 1}$ . We confirm that the shape of the solitons remains unaltered and that the polarization features a $Δ φ_{L}$ -dependent change after the collision.
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Figure 4
Quantitative comparison of the experimental soliton polarization dynamics with the analytical solution. We compare the measured polarization after collision (circles, averaged over times $t = 320 - 400 ms$ ) with the predictions using independently determined model parameters (solid lines) for different $Δ φ_{L}^{i}$ measured before collision. (a) $S_{z}$ of both solitons (red and blue). As a reference the dashed lines show the experimental $S_{z}$ before collision averaged over times $t = 40 - 220 ms$ and all measured phases. We attribute the different amplitudes to the differences in initial velocities, widths, and $S_{z}$ of the two solitons. (b) The measured Larmor phase difference $Δ φ_{L}^{f}$ after collision matches the analytical solution. The inset shows the experimentally measured pseudospin $1 / 2$ length before [dashed line, averaged as in (a)] and after (circles) collision, revealing the conservation of coherence. The ticks on all $x$ axes correspond to the same values indicated at the bottom of (b) and all error bars indicate 1 s.d. interval of the mean.
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