Density matrix negativity for two oscillators in an Agarwal bath

Abstract

A system of two harmonic oscillators is placed in an Agarwal bath. The resulting quantum master equations

are studied with the help of quantum characteristic functions. The density matrix positivity is investigated in

view of the recent interest in searching for a sound quantum dissipation theory. An analytical criterion is

derived for density matrix negativity for two uncoupled oscillators. It is found that, for an initial two-oscillator

squeezed state with a real squeezing parameter s, density matrix negativity occurs for two uncoupled oscillators

at temperatures lower than \v/(kB ln cothusu) with v the oscillator frequency and kB the Boltzmann factor. As

a by-product an analytical expression is also obtained for determining the quantum separability of two uncoupled

oscillators. The effects of interoscillator coupling on density matrix negativity are discussed.