Correlated many-body quantum dynamics of the Peregrine soliton

TL;DR

This work investigates how quantum correlations in a 1D Bose gas alter the rogue-wave Peregrine soliton during a repulsive-to-attractive quench in a box trap. Using ab initio ML-MCTDHX/MCTDHB simulations, the authors demonstrate that beyond-mean-field effects populate higher orbitals, reshaping the Peregrine structure: reduced peak, wider core, and absence of MF side dips. They quantify fragmentation and entropy growth and map the evolving coherence and two-body correlations, revealing edge coherence loss, intracore bunching, and inter-side anti-bunching. The study shows that system size and particle number act as control parameters for seeding and tuning the quantum PS and related Kuznetsov-Ma breather regimes, highlighting a path toward quantum dispersive hydrodynamics in non-integrable settings.

Abstract

We explore the correlated dynamics underlying the formation of the quantum Peregrine soliton, a prototypical rogue-wave excitation, utilizing interaction quenches from repulsive to attractive couplings in an ultracold bosonic gas confined in a one-dimensional box trap. The latter emulates the so-called semi-classical initial conditions and the associated gradient catastrophe scenario facilitating the emergence of a high-density, doubly localized waveform. The ensuing multi-orbital variant of the Peregrine soliton features notable deviations from its mean-field sibling, including a reduced peak amplitude, wider core, absence of the side density dips, and earlier formation times. Moreover, Peregrine soliton generation yields coherence losses, while experiencing two-body bunching within each of its sides which show anti-bunching between each other. Controllable seeding of the Peregrine soliton is also demonstrated by tuning the atom number or the box length, while reducing the latter favors the generation of the time-periodic Kuznetsov-Ma breather. Our results highlight that correlations reshape the morphology of rogue-waves in the genuinely quantum, non-integrable realm, while setting the stage for the emergent field of quantum dispersive hydrodynamics.

Figures (8)

• Figure 1: Time-evolution of the one-body density, $\rho^{(1)}(x,t)$, within (a) the MF and (b) the MB approaches following an interaction quench from $g_i=0.05$ to $g_f=-0.05$. The quantum PS (panel b) forms at slightly earlier times and it is characterized by a relatively reduced (larger) peak amplitude (core) compared to its MF analogue as can also be seen in Fig. \ref{['fig3:density profile']}(a), (b). (c)-(f) Dynamics of the different orbital distributions, participating in the genuine MB evolution after the quench, weighted by their occupations, i.e., $n_i(t) \left| \phi_i(x,t) \right|^2$ (see legends). The first orbital (panel (c)) resembles the MF configuration (panel (a)), while higher-order ones accommodate progressively more spatially delocalized structures. In all cases, the system consists of $N=20$ bosons trapped in a 1D box of length $L=20$, and it is prepared in its ground state with $g_i=0.05$.
• Figure 2: Density snapshots (see legends) of the bosonic gas in the course of the interaction quench dynamics depicted in Fig. \ref{['fig1:1b-density']} as captured by (a) the MF and (b) the MB methods. PS formation occurs at $t \sim 26$ ($t\sim 25$) in the MF (MB) evolution. The quantum PS edges are not fully dipped in contrast to the MF PS, and its peak amplitude (core) is reduced (increased) compared to its MF counterpart. Good agreement with the analytical PS solution at the integrable limit (see black dashed lines) takes place in the MF dynamics, while more prominent deviations are evident in the quantum variant. Other system parameters are the same as in Fig. \ref{['fig1:1b-density']}.
• Figure 3: (a)-(f) Density profiles of the various orbital distributions (see legend) at the time-instant of the quantum PS formation, $t=25$. The first orbital is reminiscent of the MF density, see also Fig. \ref{['fig1:1b-density']}(a). The inset in panel (a) shows the $\sim \pi$ phase jump between the core and the wings of the PS building atop the first orbital which attests its nature. The spatial delocalization of higher orbitals is responsible for the observed deviations from the MF PS predominantly enforcing finite tails, a wider core and reduced peak amplitude of the quantum PS. The color shading in each orbital density configuration represents its phase. Almost $\sim \pi$ phase jumps occur between the density nodes appearing in the orbital densities. The remaining system parameters are the same as in Fig. \ref{['fig1:1b-density']}.
• Figure 4: (a) Time-evolution of the natural populations of the eight orbitals participating in the MB wave function expansion. It is evident that the second and third orbitals are significantly occupied in the course of the evolution, while the remaining ones are mainly suppressed. The horizontal dashed line marks orbital population $n_{i}(t)=0.5$. (b) Dynamics of the information entropy measures [Eq. (\ref{['Shannon']})], namely $S(t)$ (solid lines), $S^{(2)}(t)$ (dashed lines), stemming from the one- and two-body reduced densities respectively, for different post-quench attractive interaction strengths $g_f$ (see legend). As expected, quenches to stronger interactions yield a larger amount of fragmentation and hence degree of correlations. Other system parameters are the same as in Fig. \ref{['fig1:1b-density']}.
• Figure 5: Profiles of (a)-(e) the one-body and (f)-(i) the two-body coherence functions at different time-instants (see legends) of the MB evolution obtained with MCTDHB. The quantum PS structure is characterized by loss of one-body coherence between its edges, see off-diagonals in panel (d), although recurrence of coherence arises at later times (panel (e)). It features a strong bunching effect within its left and right parts as well as anti-bunching between them [panel (i)]. System parameters are the ones used in Fig. \ref{['fig1:1b-density']}.