Microcavities coupled to multilevel atoms

A three-level atom in the $\Lambda$ configuration coupled to a microcavity is studied. The two transitions of the atom are assumed to couple to different counterpropagating mode pairs in the cavity. We analyze the dynamics both in the strong-coupling and the bad-cavity limits. We find that, compared to a two-level setup, the third atomic state and the additional control field modes crucially modify the system dynamics and enable more advanced control schemes. All results are explained using appropriate dressed-state and eigenmode representations. As potential applications, we discuss optical switching and turnstile operations and detection of particles close to the resonator surface.

Figure 1

Schematic setup. The upper panel shows the resonator coupled to the fiber and an atom. The lower panel shows the internal structure of the $\Lambda$-type atom.

Figure 2

Alternative implementation of our model system based on two microcavities. Without the atom, the resonators do not interact, as they are not in resonance. The atom in the $\Lambda$ configuration acts as a quantum link, with the two transitions each coupling to one of the resonators, respectively.

Figure 3

In (a), the normalized output flux ${\mathcal{T}}_{F_{b_1}}$ of mode $b_{1,\text{out}}$ in dependence of ${\Delta }_1$ and ${\Delta }_2$ is shown. (b) shows a cut of ${\mathcal{T}}_{F_{a_1}}$ and ${\mathcal{T}}_{F_{b_1}}$ at ${\Delta }_2=149\gamma$, which is close to one of the eigenvalues of our system. The parameters are $(g_0,h,{\kappa }_{i,\text{in}})/\gamma =(100,15,1)$.

Figure 4

Dressed-state atomic-level splitting for up to one photonic excitation of the system.

Figure 5

In (a), the population of the atomic state $|1\rangle$ is shown in dependence of both the detunings. The parameters are $(g_0,h,{\kappa }_{i,\text{in}})/\gamma =(100,15,1)$. In (b), the population of state $|3\rangle$ is shown.

Figure 6

Reflection ${\mathcal{T}}_{F_{b_1}}$ for different azimuthal positions $x$ of the atom and fixed ${\Delta }_2=0$. We chose $kx=0$, $\frac{\pi }{4}$, $0.4\pi$, and $\frac{\pi }{2}$.

Figure 7

(a) ${\mathcal{T}}_{F_{a_1}}$ for the bad-cavity regime with $g_0=70\gamma$ and $h=250\gamma$. (b) Cut at ${\Delta }_2=-22\gamma$ for the same parameters.

Figure 8

(a) Second-order correlation function ${\mathbf{g}}_{F_{a_1,a_1}}^{\left(2\right)}$ for the bad-cavity regime with $g_0=70\gamma$ and $h=250\gamma$. (b) Cut at ${\Delta }_2=-22\gamma$ for the same parameters.

Figure 9

(a) Cross correlation ${\mathbf{g}}_{F_{a_1,a_2}}^{\left(2\right)}$ for the bad-cavity regime with $g_0=70\gamma$ and $h=250\gamma$. (b) Cut at ${\Delta }_2=-22\gamma$ for the same parameters.