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

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