Entanglement production in bosonic systems: Linear and logarithmic growth

Oct 11, 2017
19 pages
Published in:
  • Phys.Rev.A 97 (2018) 3, 032321
  • Published: Mar 19, 2018
e-Print:
Report number:
  • IGC-17-10-1

Citations per year

201720192021202320240246810
Abstract: (APS)
We study the time evolution of the entanglement entropy in bosonic systems with time-independent, or time-periodic, Hamiltonians. In the first part, we focus on quadratic Hamiltonians and Gaussian initial states. We show that all quadratic Hamiltonians can be decomposed into three parts: (a) unstable, (b) stable, and (c) metastable. If present, each part contributes in a characteristic way to the time dependence of the entanglement entropy: (a) linear production, (b) bounded oscillations, and (c) logarithmic production. In the second part, we use numerical calculations to go beyond Gaussian states and quadratic Hamiltonians. We provide numerical evidence for the conjecture that entanglement production through quadratic Hamiltonians has the same asymptotic behavior for non-Gaussian initial states as for Gaussian ones. Moreover, even for nonquadratic Hamiltonians, we find a similar behavior at intermediate times. Our results are of relevance to understanding entanglement production for quantum fields in dynamical backgrounds and ultracold atoms in optical lattices.
Note:
  • 15+6 pages, 7 figures
  • entropy: entanglement
  • entanglement: time dependence
  • lattice: optical
  • Hamiltonian
  • initial state
  • numerical calculations
  • field theory
  • asymptotic behavior
  • non-Gaussianity
  • oscillation