4 research outputs found
Multi-mode entanglement of N harmonic oscillators coupled to a non-Markovian reservoir
Multi-mode entanglement is investigated in the system composed of coupled
identical harmonic oscillators interacting with a common environment. We treat
the problem very general by working with the Hamiltonian without the
rotating-wave approximation and by considering the environment as a
non-Markovian reservoir to the oscillators. We invoke an -mode unitary
transformation of the position and momentum operators and find that in the
transformed basis the system is represented by a set of independent harmonic
oscillators with only one of them coupled to the environment. Working in the
Wigner representation of the density operator, we find that the covariance
matrix has a block diagonal form that it can be expressed in terms of multiples
of and matrices. This simple property allows to treat
the problem to some extend analytically. We illustrate the advantage of working
in the transformed basis on a simple example of three harmonic oscillators and
find that the entanglement can persists for long times due to presence of
constants of motion for the covariance matrix elements. We find that, in
contrast to what one could expect, a strong damping of the oscillators leads to
a better stationary entanglement than in the case of a weak damping.Comment: 21 pages, 4 figure