Observing Bethe strings in an attractive Bose gas far from equilibrium

TL;DR

This paper reports the experimental observation of Bethe string bound states in an ultracold Bose gas, demonstrating the creation of complex many-particle bound states out of equilibrium and confirming predictions from generalized hydrodynamics.

Contribution

First experimental realization of intermixtures of Bethe strings in a nearly integrable 1D Bose gas, including large strings with more than six particles, out of equilibrium.

Findings

Observed bound states of more than six particles.

Measured average binding energy consistent with theoretical predictions.

Confirmed results with generalized hydrodynamics simulations.

Abstract

Bethe strings are bound states of constituent particles in a variety of interacting many-body one-dimensional (1D) integrable quantum models relevant to magnetism, nanophysics, cold atoms and beyond. As emergent fundamental excitations, they are predicted to collectively reshape observable equilibrium and dynamical properties. Small individual Bethe strings have recently been observed in quantum magnets and superconducting qubits. However, creating states featuring intermixtures of many, including large, strings remains an outstanding experimental challenge. Here, using nearly integrable ultracold Bose gases, we realize such intermixtures of Bethe strings out of equilibrium, by dynamically tuning interactions from repulsive to attractive. We measure the average binding energy of the strings, revealing the presence of bound states of more than six particles. We find further evidence for them in the momentum distribution and in Tan's contact, connected to the correlated density. Our data quantitatively agree with predictions from generalized hydrodynamics (GHD). Manipulating intermixtures of Bethe strings opens new avenues for understanding quantum coherence, nonlinear dynamics and thermalization in strongly-interacting 1D systems.