Inseparability of light and matter

We study the partial transpose of the density operator to investigate entanglement between a continuous-variable and a finite quantum system. In the framework of the soluble Jaynes-Cummings model we show that the thermal state of a coupled atomic two-level system (a qubit) and a field mode is never separable. We give a more quantitative characterization by computing the temperature and coupling strength dependence of the negativity.