Multiparticle Bound-State Formation following a Quantum Quench to the One-Dimensional Bose Gas with Attractive Interactions

We consider quantum quenches from an ideal Bose condensate to the Lieb-Liniger model with an arbitrary attractive interaction strength. We focus on the properties of the stationary state reached at late times after the quench. Using recently developed methods based on integrability, we obtain an exact description of the stationary state for a large number of bosons. A distinctive feature of this state is the presence of a hierarchy of multiparticle bound states. We determine the dependence of their densities on interaction strength and obtain an exact expression for the stationary value of the local pair correlation $g_2$. We discuss ramifications of our results for cold atom experiments.

Figure 1

Numerical value of $g_2(\gamma )$ given in Eq. (11) (solid line) and asymptotic analytical expansion as given in Eq. (14) (dashed line).

Figure 2

Density distributions for the string centers ${\rho }_n(\lambda )$ for (a) $\gamma =0.5$ and (b) $\gamma =2$.

Figure 3

Density $D_n$ and absolute value of the energy $|E_n|$ of the particles forming $n$ strings, as defined in Eq. (16), at fixed density $D=1$ and for (a) $\gamma =20$, (b) $\gamma =2$, and (c) $\gamma =0.2$.