Spontaneous emission from a two-level atom in a bisphere microcavity

Dynamics of the spontaneous emission from a two-level atom embedded in a bisphere microcavity is analyzed theoretically. A bisphere supports a morphology-dependent resonance having such a high quality factor with local field enhancement that the strong coupling between the atom and the cavity can be realized. By taking full account of the photon degree of freedom, we derive theoretically the coupling constant between the atom and the cavity as well as the radiation damping constants, which are used in the conventional cavity QED approach. In addition, we show that the power spectrum of the spontaneous emission at a local observation point is strongly affected by the photon Green function.

Figure 1

The normalized LDOS $\rho (\mathbf{x};\omega )∕{\rho }_0\left(\omega \right)$ is plotted as a function of frequency at the marked point (shown in the inset) of a bisphere in contact. The dielectric constant and radius of the bisphere were taken to be ${\epsilon }_a=12$ and $r=0.5a$, respectively. The background medium is air $({\epsilon }_b=1)$.

Figure 2

(Color) The spatial profile of the normalized LDOS $\rho (\mathbf{x};\omega )∕{\rho }_0\left(\omega \right)$ in the $xy$ plane. The frequency was taken to be $\omega a∕2\pi c=1.2669$, which is the peak frequency of the highest $Q$ in Fig. 1. Solid lines stand for the boundary of the bisphere.

Figure 3

(Color) Left panel: the contour map of the emission spectrum $S\left(\omega \right)$ of the two-level atom whose level spacing $\Omega$ is slightly different from the cavity eigenfrequency ${\omega }_c=1.5\mathrm{eV}$. The cavity line $(\omega ={\omega }_c)$ and the atom line $(\omega =\Omega )$ are also shown. The following parameters are used: $g=6.58\times {10}^{-5}\mathrm{eV}$, $\kappa =1.31\times {10}^{-5}\mathrm{eV}$, $\gamma =5.99\times {10}^{-8}\mathrm{eV}$. Right panel: the emission spectrum at the zero detuning $\Omega ={\omega }_c$.

Figure 4

(Color) The contour map of $f(\mathbf{x};\omega )$ in the $xy$ plane $(z=0)$ at a cavity eigenfrequency $\omega a∕2\pi c=1.2669$. The two-level atom is placed at $\mathbf{x}=(0.90a,0,0)$. The color map is given in a logarithmic scale.

Figure 5

(Color) Left panel: $f(\mathbf{x};\omega )$ is plotted at $\mathbf{x}=(0,5a,0)$ around $\omega ={\omega }_c$. Center panel: The contour map of the power spectrum $I(\mathbf{x};\omega )$ at a local observation point $[\mathbf{x}=(0,5a,0)]$ is plotted as a function of detuning $\Omega -{\omega }_c$ and frequency. A similar color map of a logarithmic scale as in Fig. 4 was used. Right panel: The power spectrum at the zero detuning is shown in a logarithmic scale.