Effects of dipole-dipole interaction on the transmitted spectrum of two-level atoms trapped in an optical cavity

The transmission spectrum of two dipole-coupled atoms interacting with a single-mode optical cavity in the strong coupling regime is investigated theoretically for the lower and higher excitation cases. The dressed states containing the dipole-dipole interaction (DDI) are obtained by transforming the two-atom system into an effective single-atom system. We find that the DDI can enhance the effects resulting from the positive atom-cavity detunings but weakens them for the negative detuning cases for the lower excitation, which causes the spectrum to exhibit two asymmetric peaks with shifted heights and positions. For the higher excitation cases, the DDI augments the atomic saturation and leads to the deforming of the spectrum. Furthermore, the large DDI can cause the atom and the cavity to decouple, producing a singlet of the normal-mode spectrum.

Figure 1

Schematic representation of two two-level atoms with dipole-dipole interaction intensity $J$ interacting with a single-mode high-finesse cavity. The decay rates of atoms and cavity field are $\gamma$ and $\kappa$, respectively. The cavity is pumped by a coherent laser field with strength $\eta$.

Figure 2

The normal-mode spectrums for different DDI intensities is shown. The parameters are $\Delta =0$, $(\eta ,\kappa ,\gamma ,{\gamma }^{\prime })=(0.12,0.12,0.0767,0.05)g$.

Figure 3

The normal modes form an avoided crossing between the resonances of the bare atoms and the bare cavity. Three different cases of $\Delta /g=1$ (dashed-dotted), $\Delta =0$ (solid), and $\Delta /g=-1$ (dotted) are shown. The dipole-dipole interaction strength is taken as $J/g=1$. The parameters are $(\eta ,\kappa ,\gamma ,{\gamma }^{\prime })=(0.12,0.12,0.0767,0.05)g$.

Figure 4

The normal-mode spectrums for different values of $\Delta$ and $J$ are plotted. There is no dipole-dipole interaction between atoms, that is $J=0$, ${\gamma }^{\prime }=0$.

Figure 5

The normal-mode spectrums for different values of $\Delta$ and $J$ are plotted. Both the detuning and the dipole-dipole interaction are considered. The dipole-dipole interaction intensity is taken as $J/g=1$. Other parameters are $(\eta ,\kappa ,\gamma ,{\gamma }^{\prime })=(0.12,0.12,0.0767,0.05)g$.

Figure 6

The normal-mode structure is revealed for different pump intensities. With increase of pump intensities, atoms tend to saturation, and the two peaks bend towards the center. In the limit of the high excitation, the atoms are saturated and the spectrum shows a single peak, as is shown in the inset. $J=0.5g$, $\kappa =\gamma =0.1g$, $\Delta =0$, ${\gamma }^{\prime }=0.01g$.

Figure 7

The effects of the atom-cavity detuning on the normal-mode structure of high excitation. The spectrum deformed and changes to a singlet in the limit of large detuning. ${\eta }^2/{\kappa }^2=4$, $J=0$, $\kappa =\gamma =0.1g$, ${\gamma }^{\prime }=0.1g$.

Figure 8

The effects of dipole-dipole interaction on the normal-mode structure of high excitation. The spectrum deformed and changes to a singlet in the limit of high dipole-dipole interaction intensity. ${\eta }^2/{\kappa }^2=4$, $\Delta =0$, $\kappa =\gamma =0.1g$, ${\gamma }^{\prime }=0.1g$.