Figure 4

Transmission (T, green), reflection (R, red) and scattering (S, brown) spectra of the array of atoms for an incoming probe pulse. The driving field has the Rabi frequency \(\Omega _{d}= 2\pi \times 4.0\text{ MHz}\) and detuning \(\Delta _{d} = - 2\pi \times 20.0\text{ MHz}\) and the cavity mode has the coupling strength \(\eta = 2\pi \times 4.0\text{ MHz}\) and detuning \(\Delta _{c} = - \Delta _{d} - \Delta \simeq 2\pi \times 19.0\text{ MHz}\). All the other parameters are as in Fig. 3. When the cavity mode is empty, \(n_{c}=0\) and \(\Omega _{c} =0\), (long dashed lines), the probe field undergoes nearly perfect reflection from the atomic array at the AC Stark shifted collective resonance frequency \(\Delta _{p} = \Delta ' \equiv \Delta + S_{e}\). When the cavity mode contains a photon, \(n_{c}=1\) and \(\Omega _{c} = \eta \), (solid lines), together with the driving field it results in EIT for the probe field in the vicinity of \(\Delta _{p} = \Delta '\). For reference, we also show the response of two level atoms as in Fig. 1(c) (thin dashed lines). Inset shows the transmission, reflection and scattering of the probe field at frequency \(\Delta _{p} = \Delta '\) vs the atomic position uncertainly \(\sigma _{x} = \sigma _{y}\) while \(\sigma _{z} = 0.01~\mu \text{m}\)