Steady-state quantum correlations of two driven qubits collectively interacting with a vacuum reservoir

TL;DR

This paper analytically investigates how two driven atoms interacting with a vacuum field develop steady-state quantum correlations, revealing position-dependent effects on entanglement and discord.

Contribution

It provides an analytical study of steady-state quantum correlations in two driven atoms, highlighting the impact of atomic positions and laser intensity.

Findings

Inequivalent atomic positions enable significant steady-state entanglement.

High laser intensities produce X-states suitable for discord comparison.

Position and driving conditions critically influence quantum correlation dynamics.

Abstract

We consider two two-level atoms fixed at different positions, driven by a monochromatic laser field, and interacting collectively with the vacuum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics of the two atoms and their steady-state is obtained analytically for two configurations, one in which the atoms are in equivalent positions and another in which they are not. The steady-state populations of the energy levels of the free atoms, entanglement, quantum discord and degree of mixed-ness are calculated analytically as a function of the laser field intensity and the distance between the two atoms. It is found that driving both atoms with the laser field is inefficient for the generation of steady-state correlations when they are in equivalent positions. On the contrary, inequivalent positions lead to the possibility of considerable steady-state entanglement and left/right quantum discord. It is shown that an X-state can be obtained for high laser field intensities for both configurations. This allows the comparison of two measures of quantum discord. The behaviour and relationships between correlations are studied and several limiting cases are investigated.