Observation of vector rogue waves in repulsive three-component atomic mixtures

TL;DR

This work demonstrates the experimental observation of vector rogue waves in repulsive three-component Bose-Einstein condensates by exploiting a weak attractive well to induce effective attraction among minority components. A general reduction scheme maps the N-component repulsive system to an effective attractive two-component (or single-component) dynamics, and the authors validate it with quantitative 3D mean-field simulations that include three-body losses as well as a non-polynomial 1D GPE reduction. The experiments reveal multiple vector Peregrine soliton configurations, including single and twin Peregrines, by tuning hyperfine-state combinations and harnessing inter- and intra-species modulational instability. Together, these results establish cold-atom quantum simulators as a versatile platform for multi-component rogue-wave dynamics and lay groundwork for exploring higher-order and collisional rogue waves in quantum gases.

Abstract

We report the experimental observation of vector extensions of Peregrine solitons in highly particle-imbalanced, pairwise immiscible three-component repulsive Bose-Einstein condensates (BECs). The possibility of an effectively attractive character of the minority components is established by constructing a generalized reduction scheme for an imbalanced N-component setup with arbitrary interaction signs. These components may suffer intra- and inter-component modulation instability, which along with the presence of an attractive potential well induces the dynamical formation of highly reproducible vector rogue waves. Exploiting different Rb hyperfine states, it is possible to flexibly tune the effective interactions stimulating the realization of a plethora of vector rogue waves, including single and double Peregrine-like wave peaks. The experimental findings are in quantitative agreement with suitable three-dimensional mean-field simulations, while quasi-one-dimensional analysis of the non-polynomial Schrödinger model provides additional insights into the rogue wave characteristics.

Figures (10)

• Figure 1: Observation of vector PS configurations. Spatiotemporal evolution of the integrated absorption images [(a$i$), (b$i$), (c$i$); with $i = 1, 3, 5$] is presented, averaged over 15 independent experimental realizations. Corresponding density distributions [(a$i$), (b$i$), (c$i$); with $i = 2, 4, 6$] are obtained from 3D mean-field simulations. The setups pertain to (ai) S1 , (bi) S2 and (ci) S3 consisting of $\ket{1} \equiv \ket{1,-1}$, $\ket{2} \equiv \ket{1,0}$ and $\ket{3} \equiv \ket{2,0}$ hyperfine states of $^{87}$Rb (see experimental panels). In S1 and S3 (S2) the majority-minority population imbalance reads $f_{\rm{m}}=10\% ~ (15\%)$. A PS forms in $\ket{3}$ followed by a density dip in $\ket{2}$ state for S1 and S3, while twin PS structures build upon both $\ket{1}$ and $\ket{2}$ accompanied by a PS in $\ket{3}$ in S2. Excellent agreement between the experiment and the 3D computations can be readily seen.
• Figure 2: Twin PS structure. Density profiles within the quasi-1D NPGPE of the (a), (c) $\ket{1}$ minority state and the (b), (d) $\ket{3}$ majority component of S2 at selected time-instants (see legends) for (a), (b) $f_{\rm{m}}=15\%$ and (c), (d) $f_{\rm{m}} = 1\%$ population imbalances. A twin (single) PS appears in the minority (majority) component for different imbalances captured by the phase (colormap) and the fitted analytical PS waveform (black dashed lines). Evidently, the twin PS is fully formed for larger imbalances, i.e. smaller $f_{\rm{m}}$.
• Figure 3: Zoo of vector PS configurations in three-component BECs. Selected density profile snapshots of different $^{87}$Rb minority states (see legends) within the NPGPE. The three-component settings (all not considered in Fig. \ref{['Fig:Spacetimes']}) have fixed particle-imbalance $f_{\rm{m}} =10 ~ \%$ and demonstrate different vector PS structures. The majority components are denoted by the black box and are not shown (see also Table I in SM supp).
• Figure Supp. 1: Averaged integrated cross sections over 15 experimental realizations of (a) Setup S1 and (b) Setup S2 at evolution times of 50 ms and 35 ms, respectively. Shading represents one standard deviation of variation in the density.
• Figure Supp. 2: (a)-(c) Experimentally extracted population fraction dynamics, $n_j(t)/N$ with $j=1,2,3$, of the individual hyperfine states (see legends) participating in the three different Setups S1-S3 (from left to right), discussed in the main text. The shaded regions indicate one standard deviation. It can be seen that the $\ket{3} = \ket{2,0}$ hyperfine state features the most prominent losses. The dashed line in panel (b) represents the fit characterizing three-body losses used in the simulations.