Entanglement harvesting in double-layer graphene by vacuum fluctuations in a microcavity

The aim of this work is to study the entanglement harvesting between two graphene layers inside a planar microcavity. Applying time-dependent perturbation theory it is shown that nonclassical correlations between electrons in different layers are obtained through the exchange of virtual photons. Considering different initial states of the electrons and the vacuum state of the electromagnetic field, the negativity measure that quantifies the entanglement is computed through the photon propagator for time scales smaller than the light-crossing time of the double layer. The results are compared with those obtained for hydrogenic probes and pointlike Unruh-DeWitt detectors, showing that for different initial states, entangled $X$ states and more general entangled reduced matrices are obtained, which enlarge the classification of bipartite quantum states.

Figure 1

The device setup of double-layer graphene inside a planar microcavity.

Figure 2

Photon cavity propagator as a function of space and time.

Figure 3

The function ${\mathcal{F}}_{ij}$ as a function of the relative distance of both graphene sheets with respect to the cavity.

Figure 4

The negativity measure as a function of each graphene layer’s relative distance with respect the cavity.

Figure 5

The negativity as a function of the momentum transfer for different relative distances $d_1/L$ and $d_2/L$.

Figure 6

Initial and final angles of both conduction electrons in each graphene sheet.