Entanglement invariant for the double Jaynes-Cummings model

Abstract

We study entanglement dynamics between four qubits interacting through two isolated Jaynes-Cummings hamiltonians, via the entanglement measure based on the wedge product. We compare the results with similar results obtained using bipartite concurrence resulting in what is referred to as "entanglement sudden death". We find a natural entanglement invariant under evolution demonstrating that entanglement sudden death is caused by ignoring (tracing over) some of the system's degrees of freedom that become entangled through the interaction.Comment: Sec. V has largely been rewritten. An error pertaining to the entanglement invariant has been corrected and a correct invariant valid for a much larger set of states have been found, Eq. (25

Time-evolution of entangled bipartite atomic systems in quantized radiation fields

“…Using this model the so called sudden death effect is found as a result of the time-evolution of the system [34] (see also [35]). Although these results were immediately generalized to the case of six pairwise concurrences [36], the constraint of having no more than one photon in the cavities was preserved; similar results can be found in [37]. The case of an imperfect matching of the atoms to the cavity fields has been also analyzed in connection to the entanglement evolution [38].…”

“…In contrast with other approaches already reported (see e.g. [34][35][36][37][38][39]), the present work provides an analysis of the bipartite atomic concurrence when the initial field state in each of the cavities is not longer the vacuum or the single photon state but an arbitrary Fock state. We have found that the entanglement of the atoms depends on the initial number of photons that integrate the radiation baths in the cavities.…”

“…Concurrence is a measure of the degree of entanglement that takes the value 1 for maximal entanglement and 0 for completely unentangled systems. This has been successfully applied in combination of the Jaynes-Cummings (JC) model [33] to the study of the entanglement of a pair of two-level atoms in QED cavities [34][35][36][37][38][39].…”

“…Introduced in 1963, this model has been extended to be applicable in a diversity of situations (see e.g. [34][35][36][37][38][39] and references quoted therein). For instance, a "double JC" model consisting of a pair of two-level atoms, each one in its own perfect one-mode near-resonant cavity and isolated from the other atom and cavity, has been used to investigate the involved entanglement dynamics in [34].…”

Tripartite entanglement sudden death in Yang-Baxter systems

“…Remarkably, they find that even when there is no interaction (either directly or through a correlated environment), there are certain states whose entanglement decays exponentially with time, while for other closely related states, the entanglement vanishes completely in a finite time. This phenomenon, called entanglement sudden death (ESD), has been well explored in the case of bipartite systems and there are a number of studies looking at ESD in multipartite systems [14][15][16][17][18][19][20][21][22][23].…”