Level statistics and entanglement entropy of Rydberg dressed bosons in a triple-well potential

<p>We study the signatures of quantum chaos in Rydberg dressed bosonic atoms held in a 1&nbsp;triple-well potential. Dynamics of the bosons&nbsp;are governed by an extended Bose-Hubbard model (EBHM) where long-range nearest-neighbor and next-nearest-neighbor&nbsp;interactions are induced by&nbsp;laser coupling the ground state to Rydberg state. We analyze the level statistics of the EBHM for finite&nbsp;number N of atoms through numerical diagonalization. In the presence of a tilting potential, the&nbsp;level statistics are Poissonian distribution for weak dressed interaction. It becomes a Wigner-Dyson&nbsp;distribution for strong interaction, signifying the emergence of&nbsp;quantum chaos. A hybrid distribution&nbsp;is obtained when the dressed interaction is much stronger than the hopping rate. Using the Fock&nbsp;basis, we further calculate dynamical evolution of the entanglement entropy. The maximal value&nbsp;(upper bound) of the entanglement&nbsp;entropy is proved to depend on particle numbers in the form&nbsp;ln(N + 1). It is found that the maximum of the time-averaged entanglement entropy appears when&nbsp;the chaos is strong. The location of the maximum as a function of the dressed interaction and tilting&nbsp;potential is independent of atom number N.</p>