Entanglement of Λ-atom and thermal photons in a double-band photonic crystal

The entanglement of Lambda-type three-level atoms and thermal photons in a nanocavity inside a double-band photonic crystal is studied. The partially transposed density matrix and, consequently, the negativity, as a measure of entanglement, are determined at a temperature T. By analyzing the eigenvalues of the partially transposed density matrix, we show that the thermal atom-field states remain coherent for all temperatures. Furthermore, plots of the negativity indicate that at a definite temperature, which strongly depends upon the location of the photonic band gaps, the entanglement is maximal. How the location of the photonic band gaps, relative to the atomic transition frequencies, affects this temperature is also addressed.