Atom-field entanglement in cavity QED: Nonlinearity and saturation

We investigate the degree of entanglement between an atom and a driven cavity mode in the presence of dissipation. Previous work has shown that in the limit of weak driving fields, the steady-state entanglement is proportional to the square of the driving intensity. This quadratic dependence is due to the generation of entanglement by the creation of pairs of photons or excitations. In this work we investigate the entanglement between an atom and a cavity in the presence of multiple photons. Nonlinearity of the atomic response is needed to generate entanglement, but as that nonlinearity saturates the entanglement vanishes. We posit that this is due to spontaneous emission, which puts the atom in the ground state and the atom-field state into a direct product state. An intermediate value of the driving field, near the field that saturates the atomic response, optimizes the atom-field entanglement. In a parameter regime for which multiphoton resonances occur, we find that entanglement recurs at those resonances. In this regime, we find that the entanglement decreases with increasing photon number. We also investigate, in the bimodal regime, the entanglement as a function of atom and/or cavity detuning. Here we find that there is evidence of a phase transition in the entanglement, which occurs at $2\epsilon /g\ge 1$.

Figure 1

Single atom in a driven optical cavity with dipole coupling $g$, cavity field loss rate $\kappa$, and atomic spontaneous emission rate $\gamma$.

Figure 2

Comparison of the wave function to that obtained analytically in the weak-field limit via two measures, the fidelity and impurity, both defined in the text.

Figure 3

Average intracavity photon number and atomic population inversion as a function of driving field for $\kappa =\gamma =g=1.0$.

Figure 4

(a) Log negativity (base 2) as a function of time for various driving-field strengths. (b) Log negativity as a function of driving-field strength for $\gamma t=1.0$, 2.0, and 5.0.

Figure 5

Maximum and steady-state value of the log negativity (base 2) as a function of field strength.

Figure 6

The log-negativity with (a) $\theta =0$ and (b) $\theta =0.5$. Parameters used are $\kappa ,\gamma$, and $g=1$. 100 states of the cavity are kept.

Figure 7

The log-negativity with (a) $\theta =-\mathrm{\Delta }$ and (b) $\theta =\mathrm{\Delta }$. Parameters used are $\kappa ,\gamma$, and $g=1$.

Figure 8

Intracavity photon number (a) and log negativity (b) for high driving fields with $\theta =\mathrm{\Delta }$. Parameters used are $\kappa =1, \gamma =2$, and $g=1000$, with 15 states of the cavity kept. The number of states is still large compared to the intracavity photon number. For large coupling the dressed state splitting is large enough that the drive laser is off resonance, as in a photon blockade. On resonance for weak driving the mean photon number goes as $Y^2$, and is hence small. Increasing coupling detunes the dressed states, and increasing drive intensity saturates the atom.

Figure 9

Log negativity as a function of driving-field and atom-field coupling for $\kappa =1$ and $\gamma =0.1$.