arXiv:2208.08192 · Physical review. E

Chaos and bipartite entanglement between Bose-Josephson junctions

Amichay Vardi

Published Dec 23, 2022• 2 citations

Abstract

The entanglement between two weakly coupled bosonic Josephson junctions is studied in relation to the classical mixed phasespace structure of the system, containing symmetry-related regular islands separated by chaos. The symmetry-resolved entanglement spectrum and bipartite entanglement entropy of the system's energy eigenstates are calculated and compared to their expected structure for random states that exhibit complete or partial ergodicity. The entanglement spectra of chaos-supported eigenstates match the microcanonical structure of a Generalized Gibbs Ensemble due to the existence of an adiabatic invariant that restricts ergodization on the energy shell. The symmetry-resolved entanglement entropy of these quasistochastic states consists of a mean-field maximum entanglement term and a fluctuation correction due to the finite size of the constituent subsystems. The total bipartite entanglement entropy of the eigenstates correlates with their chaoticity. Island-supported eigenstates are macroscopic Schrödinger cat states for particles and excitations with substantially lower entanglement.

DOI: 10.1103/physreve.106.064210

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arXiv:2208.08192 · Physical review. E

Chaos and bipartite entanglement between Bose-Josephson junctions

Amichay Vardi

Published Dec 23, 2022• 2 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreve.106.064210

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ρ_{AA^*}^{(2)}

,which controls the Rényi-2 reflected entropy. We show that

ρ_{AA^*}^{(2)}

in a chaotic eigenstate is well-described by this ensemble average which, unlike an ordinary reduced density matrix, takes three qualitatively distinct forms across subsystem-size regimes, which may be viewed as a tripartite generalization of subsystem ETH. We benchmark our analytical predictions against exact diagonalization of the mixed-field Ising model.

N

, the volume

V

, and the subsystem fraction

f={V}_{A}/V

, where

{V}_{A}

is the volume of the subsystem. We expand our result as a power series ${\ensuremath{\langle}{S}_{A}\ensuremath{\rangle}}_{N}=afV+b\sqrt{V}+c+o(1)$, and find that

c

is universal (i.e., independent of the system type), while

a

and

b

can be obtained from a generating function characterizing the local Hilbert space dimension. We illustrate the generality of our findings by studying a wide range of different systems, e.g., bosons, fermions, spins, and mixtures thereof. We provide evidence that our analytical results describe the entanglement entropy of highly excited eigenstates of quantum-chaotic spin and boson systems, which is distinct from that of integrable counterparts.