Spread complexity and dynamical transition in multimode Bose-Einstein condensates

TL;DR

This paper investigates how spread complexity can detect dynamical transitions in multimode Bose-Einstein condensates, linking quantum phase transitions with classical dynamical behavior and chaos.

Contribution

It introduces the use of spread complexity as a probe for dynamical and excited state quantum phase transitions in multimode BECs, revealing sharp transitions and spectral singularities.

Findings

Spread complexity signals the transition from self-trapping to Josephson oscillation.

Spectral singularities at critical energy characterize quantum phase transitions.

Dynamical behavior varies with initial state stability and chaos in triple-well models.

Abstract

We study the spread complexity in two-mode Bose-Einstein condensations and unveil that the long-time average of the spread complexity $\overline{C}_{K}$ can probe the dynamical transition from self-trapping to Josephson oscillation. When the parameter $\omega$ increases over a critical value $\omega_{c}$, we reveal that the spread complexity exhibits a sharp transition from lower to higher value, with the corresponding phase space trajectory changing from self-trapping to Josephson oscillation. Moreover, we scrutinize the eigen-spectrum and uncover the relation between the dynamical transition and the excited state quantum phase transition, which is characterized by the emergence of singularity in the density of states at critical energy $E_{c}$. In the thermodynamical limit, the cross point of $E_{c}(\omega)$ and the initial energy $E_{0}(\omega)$ determines the dynamical transition point $\omega_{c}$. Furthermore, we show that the different dynamical behavior for the initial state at a fixed point can be distinguished by the long-time average of the spread complexity, when the fixed point changes from unstable to stable. Finally, we also examine the sensitivity of $\overline{C}_{K}$ for the triple-well bosonic model which exibits the transition from chaotic dynamics to regular dynamics.