Detection of light-matter interaction in the weak-coupling regime by quantum light

“Mollow spectroscopy” is a photon statistics spectroscopy, obtained by scanning the quantum light scattered from a source system. Here, we apply this technique to detect the weak light-matter interaction between the cavity and atom (or a mechanical oscillator) when the strong system dissipation is included. We find that the weak interaction can be measured with high accuracy when exciting the target cavity by quantum light scattered from the source halfway between the central peak and each side peak. This originally comes from the strong correlation of the injected quantum photons. In principle, our proposal can be applied into the normal cavity quantum electrodynamics system described by the Jaynes-Cummings model and an optomechanical system. Furthermore, it is state of the art for experiment even when the interaction strength is reduced to a very small value.

Figure 1

Cavity mean photon number $n_a$ versus cavity-field detuning $\mathrm{\Delta }$ when the JC model is driven by classical field. The blue circles, black solid line, and red dashed line in panels correspond to the atom-cavity coupling strength $g=0, g=0.01\kappa$, and $g=3\kappa$, respectively. The system parameters used here are $\gamma =0.001\kappa$ and $\mathrm{\Omega }=0.6\kappa$.

Figure 2

Schematics of the studied systems. (a) The cavity QED system consisting of a two-level atom coupled to a single-mode cavity driven by the emission of a quantum source; (b) the optomechanical system is excited by the emission of the same quantum source. Here, the quantum source is made of a two-level atom driven by classical light fields, $f_1^{\mathrm{in}}\left(t\right)$ and $g_1^{\mathrm{in}}\left(t\right)$ are two input channels for exciting the source two-level atom, $f_1^{\mathrm{out}}\left(t\right)$ and $g_1^{\mathrm{out}}\left(t\right)$ are the output channels of the source system, and $a^{\mathrm{in}}\left(t\right)$ is the input channel of the target.

Figure 3

Plot of the photon emission spectrum (a) and photon statistics spectrum (b) when the Mollow triplet is scanned into the JC model. The black solid line and red dashed line in panels correspond to the atom-cavity coupling strength $g=0$ and $g=0.1\kappa$, respectively. (c) Enlarged view of the spectral region of the middle peak delimited by square in (a). Insets: enlarged view the regions of the left and right emission peaks in (a). These spectrum lines show the splittings in the three emission peaks. (d) Enlarged view of the spectral regions of peaks delimited by squares in (b); here the left peak is enlarged in the inset. $\delta$ represents the shift of statistics peak when $g=0.1\kappa$, and ${\delta }_{g^{\left(2\right)}}$ is the difference of the peak with $g=0.1\kappa$ and $g=0$. The system parameters used here are ${\gamma }_s=0.02\kappa , \gamma =0.001\kappa , \mathrm{\Omega }=8\kappa , {\mu }_1=0.5$, and ${\mu }_2=0.5$.

Figure 4

Plot of the photon emission spectrum $n_a$ of steady state for $g=0$ obtained from Eq. (10) (blue circles) and exact numerical calculation (black solid curve). The other system parameters used here are the same as in Fig. 3.

Figure 5

Equal-time second-order photon correlation function $g^{\left(2\right)}$ (the first row), and the norms $\parallel \mathrm{\Delta }{n}_a\parallel$ (the second row) and $\parallel \mathrm{\Delta }{g}^{\left(2\right)}\parallel$ (the third row) of the target cavity versus $g/\kappa$ for different input types of quantum lights. The first, second, and third columns correspond to quantum lights from the central peak, the emission halfway between the central peak and right peak, and the right peak, respectively. The system parameters used here are ${\gamma }_s=0.02\kappa , \gamma =0.001\kappa , \mathrm{\Omega }=8\kappa , {\mu }_1=0.5$, and ${\mu }_2=0.5$.

Figure 6

(a) Mode $\parallel \mathrm{\Delta }{g}^{\left(2\right)}\parallel$ versus $g$ for ${\overline{n}}_{th}=0$ (black solid curve) and ${\overline{n}}_{th}=0.05$ (red dashed curve); two circles correspond to $g=0.01\kappa$. (b) The mode $\parallel \mathrm{\Delta }{g}^{\left(2\right)}\parallel$ versus the thermal average boson number ${\overline{n}}_{th}$ for $g=0.01\kappa$. The other system parameters used here are the same as in Fig. 5.

Figure 7

Cavity mean photon number $n_a$ versus cavity-field detuning $\mathrm{\Delta }$ when the OMS is driven by classical light field. The blue circles, black solid line, and red dashed line in panels correspond to the coupling strength $g_m=0, g_m=0.05\kappa$, and $g_m=6.5\kappa$, respectively. The system parameters used here are ${\omega }_m=5\kappa , {\gamma }_m=0.001\kappa$, and $\mathrm{\Omega }=0.02\kappa$.

Figure 8

Plot the photon emission spectrum (a) and photon statistics spectrum (b) when the Mollow triplet is scanned into the OMS. The black solid lines and red dashed lines in panels correspond to the coupling strength $g_m=0$ and $g_m=0.3\kappa$, respectively. (c) Enlarged view of the spectral region of the middle peak delimited by square in (a). Insets: enlarged view of the regions of the left and right emission peaks in (a). (d) Enlarged view of the regions delimited by squares in (b), and the left peak is enlarged in the inset. ${\delta }_{g^{\left(2\right)}}$ denotes the difference of the peak with $g_m=0.3\kappa$ and $g_m=0$. The system parameters used here are ${\omega }_m=5\kappa , {\gamma }_s=0.02\kappa , {\gamma }_m=0.001\kappa , \mathrm{\Omega }=8\kappa , {\mu }_1=0.5$, and ${\mu }_2=0.5$.

Figure 9

Equal-time second-order correlation function $g^{\left(2\right)}$ (the first row), and the norms $\parallel \mathrm{\Delta }{n}_a\parallel$ (the second row) and $\parallel \mathrm{\Delta }{g}^{\left(2\right)}\parallel$ (the third row) of transmitted light of the target cavity versus $g_m/\kappa$ for different input types of quantum lights. The first, second, and third columns correspond to quantum lights from the central peak, the emission halfway between the central peak and right peak, and the right peak, respectively. The system parameters used here are ${\omega }_m=5\kappa , {\gamma }_s=0.02\kappa , {\gamma }_m=0.001\kappa , \mathrm{\Omega }=8\kappa , {\mu }_1=0.5$, and ${\mu }_2=0.5$.