Suppression of Bragg Scattering by Collective Interference of Spatially Ordered Atoms with a High-$Q$ Cavity Mode

When $N$ driven atoms emit in phase into a high-$Q$ cavity mode, the intracavity field generated by collective scattering interferes destructively with the pump driving the atoms. Hence atomic fluorescence is suppressed and cavity loss becomes the dominant decay channel for the whole ensemble. Microscopically, 3D light-intensity minima are formed in the vicinity of the atoms that prevent atomic excitation and form a regular lattice. The effect gets more pronounced for large atom numbers, when the sum of the atomic decay rates exceeds the rate of cavity losses and one would expect the opposite behavior. These results provide new insight into recent experiments on collective atomic dynamics in cavities.

Figure 1

$N$ atoms are inside a 1D optical resonator and homogeneously driven by a laser propagating in the transverse direction. The atoms are localized according to a spatial pattern such that they emit in phase into the cavity mode (see 5).

Figure 2

Intensity of the signal at the cavity mirror ($I_{\mathrm{c}\mathrm{a}\mathrm{v}}$, dashed lines) and total atomic fluorescence intensity ($I_{\mathrm{a}\mathrm{t}}$, solid lines) as a function of $N$ for $\Omega =g=10\gamma$, $\kappa =10\gamma$, $\Delta =-1000\gamma$, and (a) ${\delta }_c=0$, (b) ${\delta }_c=-5\gamma$.

Figure 3

Intensity of the signal at the cavity mirror ($I_{\mathrm{c}\mathrm{a}\mathrm{v}}$, dashed line) and of the atomic fluorescence signal ($I_{\mathrm{a}\mathrm{t}}$, solid line) as a function of ${\kappa }^{-1}$ for a single atom. Here $\Omega =\gamma$, $\Delta ={\delta }_c=0$, and (a) $g=\gamma$, (b) $g=10\gamma$. The dash-dotted line corresponds to the free space fluorescence rate.

Figure 4

(a) Mean number of cavity photon and (b) second-order correlation function $g^{(2)}(0)$ as a function of ${\kappa }^{-1}$ for $\Delta ={\delta }_c=0$, $\Omega =\gamma$, and $g=\gamma$ (dashed line), $g=10\gamma$ (solid line).

Figure 5

(a) Ratio $\Gamma =I_{\mathrm{c}\mathrm{a}\mathrm{v}}/I_{\mathrm{a}\mathrm{t}}$ for two atoms as a function of their position $x_1$ and $x_2$ inside the cavity. Here, $g_0=10\gamma$, $\Delta =100\gamma$, ${\delta }_c=0$, $\Omega =\gamma$ for both atoms, and $\kappa =0.2\gamma$. (b) Ratio as in (a) as a function of $x_2$ for $x_1=0$. The dashed line shows $\Gamma$ for the same parameters, but $\kappa =\gamma$. Note that $x_1,x_2$ are plotted modulus $\lambda$, and $x_1\ne x_2$.