Cavity-enhanced channeling of emission from an atom into a nanofiber

We study spontaneous emission of an atom near a nanofiber with two fiber-Bragg-grating (FBG) mirrors. We show that the coupling between the atom and the guided modes of the nanofiber can be significantly enhanced by the FBG cavity even when the cavity finesse is moderate. We find that, when the fiber radius is 200 nm and the cavity finesse is about 30, up to 94% of spontaneous emission from the atom can be channeled into the guided modes in the overdamped-cavity regime. We show numerically and analytically that vacuum Rabi oscillations and strong coupling can occur in the FBG cavity even when the cavity finesse is moderate (about 30) and the cavity length is large (on the order of 10 cm to 1 m), unlike the case of planar and curved Fabry-Perot cavities.

Figure 1

(Color online) Spontaneous emission of an atom in the vicinity of a nanofiber with two fiber-Bragg-grating mirrors.

Figure 2

Dependences of the total spontaneous emission rate $\Gamma$ (solid lines) and its two components ${\gamma }_{\text{cavgyd}}$ (dashed lines) and ${\gamma }_{\text{rad}}$ (dotted lines) on (a) the FBG mirror reflectivity ${\left|R\right|}^2$ and (b) the fiber radius $a$ in the case where the dipole of the atom is oriented along one of the spherical basis vectors ${\mathbf{u}}_{\pm 1}$. In (a), the fiber radius is $a=200\text{nm}$. In (b), the reflectivity of the FBG mirrors is ${\left|R\right|}^2=0.9$. In both cases, the atom is located on the fiber surface $\left(r=a\right)$ and at the cavity center $\left(z=0\right)$. The length of the cavity is such as the phase shift per cavity crossing ${\Phi }_0$ is an even multiple of $\pi$. The wavelength of the atomic transition is ${\lambda }_0=852\text{nm}$. The refractive indices of the fiber and the vacuum clad are $n_1=1.45$ and $n_2=1$, respectively. The rates are normalized to the free-space decay rate ${\gamma }_0$.

Figure 3

Dependences of the channeling efficiency $\eta ={\gamma }_{\text{cavgyd}}/\Gamma$ on (a) the FBG mirror reflectivity ${\left|R\right|}^2$ and (b) the fiber radius $a$ for the parameters of Fig. 2.

Figure 4

Dependences of the total spontaneous emission rate $\Gamma$ (solid lines) and its two components ${\gamma }_{\text{cavgyd}}$ (dashed lines) and ${\gamma }_{\text{rad}}$ (dotted lines) on (a) the axial coordinate $z$ and (b) the radial coordinate $r$ of the atom in the case where the dipole of the atom is oriented along one of the spherical basis vectors ${\mathbf{u}}_{\pm 1}$. In (a), the atom is located at $r=a$ (on the fiber surface). In (b), the atom is located at $z=0$ (at the center of the cavity). The fiber radius is $a=200\text{nm}$. The reflectivity of the FBG mirrors is ${\left|R\right|}^2=0.9$. Other parameters are as in Fig. 2.

Figure 5

Dependences of the channeling efficiency $\eta ={\gamma }_{\text{cavgyd}}/\Gamma$ on (a) the axial coordinate $z$ and (b) the radial coordinate $r$ of the atom for the parameters of Fig. 4.

Figure 6

Dependences of the total spontaneous emission rate $\Gamma$ (solid lines) and its two components ${\gamma }_{\text{cavgyd}}$ (dashed lines) and ${\gamma }_{\text{rad}}$ (dotted lines) on (a) the axial coordinate $z$ and (b) the radial coordinate $r$ of the atom in the case where the dipole of the atom is oriented along the fiber axis $z$. In (a), the atom is located at $r=a$ (on the fiber surface). In (b), the atom is located at ${\beta }_{0}z=\pm \pi /2$ (one-fourth of the guided-light wavelength from the cavity center). The fiber radius is $a=200\text{nm}$. The reflectivity of the FBG mirrors is ${\left|R\right|}^2=0.9$. Other parameters are as in Fig. 2.

Figure 7

Dependences of the channeling efficiency $\eta ={\gamma }_{\text{cavgyd}}/\Gamma$ on (a) the axial coordinate $z$ and (b) the radial coordinate $r$ of the atom for the parameters of Fig. 6.

Figure 8

Time evolution of the upper-state population $P_a={\left|C_a\right|}^2$ of the atom in a long FBG cavity. The length of the cavity is $L=20\text{cm}$ and is tuned to resonance with the atomic transition frequency so that the phase shift per cavity crossing ${\Phi }_0$ is an (a) even or (b) odd multiple of $\pi$. The reflectivity of the FBG mirrors is ${\left|R\right|}^2=0.9$. The atom is located on the fiber surface and at the cavity center. Other parameters are as in Fig. 2. For comparison, the exponential decay of the atomic upper-state population in the absence of the cavity is shown by the dashed curves.

Figure 9

Time evolution of the upper-state population $P_a={\left|C_a\right|}^2$ of the atom in a short FBG cavity. The length of the cavity is $L=2\text{mm}$ and is tuned to resonance with the atomic transition frequency so that the phase shift per cavity crossing ${\Phi }_0$ is an (a) even or (b) odd multiple of $\pi$. The reflectivity of the FBG mirrors is ${\left|R\right|}^2=0.9$. The atom is located on the fiber surface and at the cavity center. Other parameters are as in Figs. 2, 8. For comparison, the exponential decay of the atomic upper-state population in the absence of the cavity is shown by the dashed curves.

Figure 10

Time evolution of the upper-state population $P_a={\left|C_a\right|}^2$ of the atom in a FBG cavity with length $L=100\text{m}$ (a), 10 m (b), 1 m (c), 10 cm (d), 1 cm (e), and 1 mm (f). The length of the cavity is tuned to exact resonance with the atomic transition frequency so that the phase shift per cavity crossing ${\Phi }_0$ is an even multiple of $\pi$. The atom is located on the fiber surface and at the cavity center. The reflectivity of the FBG mirrors is ${\left|R\right|}^2=0.9$. Other parameters are as in Fig. 2.

Figure 11

Time evolution of the upper-state population $P_a={\left|C_a\right|}^2$ of the atom at different distances $r-a=0$ (solid line), 50 nm (dashed line), and 100 nm (dotted line) from the fiber surface in a FBG cavity. The cavity length is $L=10\text{cm}$. The atom is located at the center of the cavity. Other parameters are as in Figs. 2, 10.