Interaction Control and Bright Solitons in Coherently Coupled Bose-Einstein Condensates

J. Sanz, A. Frölian, C. S. Chisholm, C. R. Cabrera, and L. Tarruell

Phys. Rev. Lett. 128, 013201 – Published 4 January 2022

Abstract

We demonstrate fast control of the interatomic interactions in a Bose-Einstein condensate by coherently coupling two atomic states with intra- and interstate scattering lengths of opposite signs. We measure the elastic and inelastic scattering properties of the system and find good agreement with a theoretical model describing the interactions between dressed states. In the attractive regime, we observe the formation of bright solitons formed by dressed-state atoms. Finally, we study the response of the system to an interaction quench from repulsive to attractive values, and observe how the resulting modulational instability develops into a bright soliton train.

Received 12 December 2019
Revised 27 June 2021
Accepted 15 November 2021

DOI:https://doi.org/10.1103/PhysRevLett.128.013201

Physics Subject Headings (PhySH)

Bose-Einstein condensates Mixtures of atomic and/or molecular quantum gases Ultracold collisions

Solitons

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

J. Sanz ^*, A. Frölian , C. S. Chisholm , C. R. Cabrera ^†, and L. Tarruell ^‡

ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

^*Present address: Quside Technologies S. L., C/. Esteve Terradas 1, 08860 Castelldefels (Barcelona), Spain.
^†Present address: Fakultät für Physik, Ludwig-Maximilians-Universität, Schellingstr. 4, D-80799 München, Germany, and Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany.
^‡leticia.tarruell@icfo.eu

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Issue

Vol. 128, Iss. 1 — 7 January 2022

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Images

Figure 1
Elastic scattering properties of the lower dressed state. (a) Energy $E$ of states $| - ⟩$ and $| + ⟩$ vs detuning $δ$ , normalized to the Rabi frequency $Ω$ . $↑$ and $↓$ are the bare atomic states. Color scale: state composition in terms of $P = δ / \sqrt{Ω^{2} + δ^{2}}$ . (b) Sketch of the bare scattering lengths and resulting effective scattering length $a_{- -}$ . (c) Experimental value of $a_{- -}$ obtained by scaling $σ_{x}^{5} / N$ (orange circles, left axis) and $P$ (gray squares, right axis) vs $δ$ . Lines: theory predictions. Brown diamonds: numerical simulation. Color scale of the $a_{- -}$ curve: value of $P$ . Error bars: standard deviation from 5 independent measurements.
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Figure 2
Inelastic decay of the higher dressed state. (a) Sketch of possible dressed state changing collisions ①: $| + + ⟩ \to | - - ⟩$ (orange, solid arrows) and ②: $| + + ⟩ \to (| + - ⟩ + | - + ⟩) / \sqrt{2}$ (green, dashed arrows). Energy $E$ and momentum $k$ are normalized by $\tilde{Ω} = \sqrt{Ω^{2} + δ^{2}}$ and $k_{\tilde{Ω}} = \sqrt{m \tilde{Ω} / ℏ}$ . (b) Momentum distribution of the collision products. Images are the average of 10 independent measurements. The likelihood of processes ① and ② depends on $δ$ . (c) Velocity of the scattered atoms $v_{f}$ vs $\tilde{Ω}$ . (d) Radius of the halos $R_{H}$ for an expansion time $t_{\exp} = 20.1 ms$ . (e) Fraction of scattered atoms $N_{sc} / N$ vs $δ$ . Inset: Inelastic scattering rate $Γ_{1, 2}$ vs $δ$ for $n = 1.3 \times 10^{14} atoms / {cm}^{3}$ . In (c), (d), and (e) orange circles (green squares) correspond to process ① (②). Lines: noninteracting theory. Error bars: fit error (vertical) and uncertainty of $δ$ and $\tilde{Ω}$ (horizontal).
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Figure 3
Formation of a dressed-state bright soliton. (a) $a_{- -}$ vs $δ$ . Near zero detuning $a_{- -} < 0$ . (b) In situ dynamics of the gas after an evolution time $t_{g}$ in the optical waveguide. For $δ / 2 π = 0$ ( $a_{- -} / a_{0} = - 3.5$ ) a self-bound bright soliton forms. For $δ / 2 π = 250 kHz$ [ $N = 9 (2) \times 10^{4}$ ] and $δ / 2 π = - 250 kHz$ [ $N = 1.0 (2) \times 10^{4}$ ], $a_{- -} > 0$ and the gas expands.
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Figure 4
Modulational instability and formation of bright soliton trains. (a) Sketch of the experimental sequence and exemplary in situ images. (b) Number of components observed per image $N_{S}$ vs $δ$ after the quench (orange circles). Error bars: standard deviation of 4 to 6 independent measurements (vertical) and uncertainty of $δ$ (horizontal). Orange line, left axis: theory prediction $N_{S} = L / λ$ (shaded area: uncertainty due to the systematic error in the atom number). Colored line, right axis: $a_{- -}$ (color scale: value of $P$ ).
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