Photon emission by an atom in a lossy cavity

The dynamics of an initially excited two-level atom in a lossy cavity is studied by using the quantum trajectory method. Unwanted losses are included, such as photon absorption and scattering by the cavity mirrors and spontaneous emission of the atom. Based on the obtained analytical solutions, it is shown that the shape of the extracted spatiotemporal radiation mode sensitively depends on the atom-field interaction. In the case of a short-term atom-field interaction we show how different pulse shapes for the field extracted from the cavity can be controlled by the interaction time.

Figure 1

The cavity mode of frequency ${\omega }_{\text{c}}$ is detuned by $\Delta$ from the two-level atomic transition frequency ${\omega }_{\text{a}}={\omega }_{\text{c}}+\Delta$. ${\kappa }_1$ and ${\kappa }_2$ are the photon escape rate of the cavity and the cavity mirrors’ absorption and scattering rate, respectively. $\Gamma$ is the dipole relaxation rate from level $|2⟩$ to $|1⟩$.

Figure 2

The probabilities ${\left|\alpha \left(t\right)\right|}^2$ (dashed line), ${\left|\beta \left(t\right)\right|}^2$ (dotted line), $p_{\text{ext}}\left(t\right)$ (full line), and $p_{\text{abs}}\left(t\right)$, $p_{\text{spo}}\left(t\right)$ (dot-dashed lines) are shown for $2g/\kappa =10$, $\Delta /\kappa =0.1$, ${\kappa }_1/\kappa =0.9$, and $\Gamma /\kappa =0.5$.

Figure 3

Plot of the amplitude envelope ${ϵ}_i\left(z,t\right)\sqrt{p_{\text{ext}}\left(\infty \right)/{\kappa }_1}$ for the spatiotemporal mode of the cavity output field, with parameters $2g/\kappa =10$, $\Delta /\kappa =0.1$, ${\kappa }_1/\kappa =0.9$, $\Gamma /\kappa =0.5$, and $\kappa t=7$.

Figure 4

The probabilities $p_{\text{in}}\left(t\right)$ (dotted line) and ${\overline{p}}_{\text{ext}}\left(t\right)$ (full line) are shown for $\tau =\pi /\left|\Omega \right|$, $2g/\kappa =10$, $\Delta /\kappa =0.1$, ${\kappa }_1/\kappa =0.9$, and $\Gamma /\kappa =0.5$.

Figure 5

The probabilities $p_{\text{in}}\left(t\right)$ (dotted line) and ${\overline{p}}_{\text{ext}}\left(t\right)$ (full line) are shown for $\tau =2\pi /\left|\Omega \right|$, $2g/\kappa =10$, $\Delta /\kappa =0.1$, ${\kappa }_1/\kappa =0.9$, and $\Gamma /\kappa =0.5$.

Figure 6

Plot of the amplitude envelope ${ϵ}_i\left(z,t\right)\sqrt{{\overline{p}}_{\text{ext}}\left(\infty \right)/{\kappa }_1}$ for the spatiotemporal mode of the cavity output field, for $\tau =\pi /\left|\Omega \right|$, $\kappa t=7$, $2g/\kappa =10$, $\Delta /\kappa =0.1$, ${\kappa }_1/\kappa =0.9$, and $\Gamma /\kappa =0.5$.

Figure 7

Plot of the amplitude envelope ${ϵ}_i\left(z,t\right)\sqrt{{\overline{p}}_{\text{ext}}\left(\infty \right)/{\kappa }_1}$ for the spatiotemporal mode of the cavity output field, for $\tau =2\pi /\left|\Omega \right|$, $\kappa t=7$, $2g/\kappa =10$ and $\Delta /\kappa =0.1$, ${\kappa }_1/\kappa =0.9$, and $\Gamma /\kappa =0.5$.

Figure 8

Plot of the amplitude envelope ${ϵ}_i\left(z,t\right)\sqrt{{\overline{p}}_{\text{ext}}\left(\infty \right)/{\kappa }_1}$ for the spatiotemporal mode of the cavity output field in the region $17\le \kappa z/c\le 20$, for $\kappa \tau =2.2$, $\kappa t=20$, $2g/\kappa =10$, $\Delta /\kappa =0.1$, ${\kappa }_1/\kappa =0.9$, and for $\Gamma =0$ (full line), or $\Gamma /\kappa =0.5$ (dashed line).