Entanglement dynamics for two-level quantum systems coupled with massive scalar fields

Abstract

Entanglement is essential in quantum information science. Typically, the inevitable coupling between quantum systems and environment inhibits entanglement from being created between long-distance subsystems and being maintained for a long time. In this paper, we show that when the environment is composed of a bath of massive scalar fields, the region of the separation within which entanglement can be generated is significantly enlarged, and the decay rate of entanglement is significantly slowed down compared with those in the massless case, when the mass of the field m is smaller than but close to the transition frequency of the qubits ω. When m ≥ ω, the initial entanglement can be maintained for an arbitrarily long time, regardless of the environmental temperature. Therefore, in principle, it is possible to achieve long-distance entanglement generation and long-lived entanglement by manipulating the energy level spacing of the two-level systems with respect to the mass of the field.

Entanglement dynamics for Unruh-DeWitt detectors interacting with massive scalar fields: The Unruh and anti-Unruh effects

“…( 12) and ( 13), one finds that, for uniformly accelerated Unruh-DeWitt detectors in the Minkowski vacuum, Ω a is not only related to the field mass m/ω, but also to the acceleration a/ω. However, for the static ones in a thermal bath, Ω β is only related to m/ω but not to the temperature of the bath T U [41]. This leads to significant differences between the two cases.…”

“…6 and 7, it is shown that, compared with the massless case, the region of separation ωL within which entanglement can be created is expanded when the acceleration a/ω is smaller than a critical value a crit /ω determined by the field mass m/ω, and is compressed when a > a crit . This is distinct from the fact that the region of separation for entanglement generation is always expanded for a static quantum system coupled with massive fields (in vacuum or in a thermal bath), compared with the massless case [41].…”

“…This is in sharp contrast to the case of a static quantum system in a thermal bath, where this time delay brought by the field being massive is not affected by the temperature. Secondly, in the thermal case, when m/ω ≥ 1, Ω β = 0, which means that the quantum system is locked up in its initial state ρ(τ ) = ρ(0), and the concurrence is a constant [41]. However, in the acceleration case, as long as a = 0, Ω a = 0, and so the entanglement still evolves, although the evolution may be very slow because Ω a → 0 when a → 0.…”

“…7, we find that the behaviors of the factor λ a at a → 0 is completely different for m < ω and m > ω, resulting in a significant difference in the possible regions of separation ωL for entanglement creation. In the acceleration case, when the mass of the field exceeds the energy level spacing of the Unruh-DeWitt detectors, longdistance entanglement creation can be achieved when the acceleration is small, in contrast to the static case in which the mass of the field has to be smaller than but close to the energy level spacing in order to achieve long-distance entanglement [41].…”

“…Recently, the entanglement dynamics of two static detectors coupled with massive scalar fields has been studied in Ref. [41]. It has been found that, compared with the massless field case, the evolution of entanglement is slower and the region of spatial separation between the detectors within which entanglement can be generated is significantly enlarged.…”