Indirect driving of a cavity-QED system and its induced nonlinearity

The linear driving for a single-mode optical field in a cavity can result from the external driving of a classical field even when the coupling between the classical field and the cavity is weak. We revisit this well-known effect with a microscopic model where a classical field is applied to a wall of the cavity to excite the atoms in the wall, and recombination of the low excitations of the wall mediates a linear driving for the single-mode field inside the cavity. With such modeling about the indirect driving through the quantum excitations of the wall, we theoretically predict several nonlinear optical effects for the strong-coupling cases, such as photon antibunching and photon squeezing. We propose a greatly simplified nonlinear quantum photonics model.

Figure 1

Schematic of indirect quantum driving model. The wall of the cavity consists of $N$ two-level atoms with the same energy difference ${\omega }_a$. A classical field with frequency ${\omega }_f$ is applied to excite these atoms to generate a linear driving for the single-mode cavity field.

Figure 2

Cavity response vs detuning. Here, ${\omega }_{ac}={\omega }_a-{\omega }_c=5\times {10}^4$, $N=1\times {10}^4$, $\Omega =1$, $g=1$. All parameters are in the units of cavity decay rate, $\kappa$. In this figure the shift amount is $\delta =0.2$.

Figure 3

The second-order correlation function $g^{\left(2\right)}\left(0\right)$, in Eq. $\left(44\right)$ and total intracavity photon number in Eq. (42) vs coupling strength $g$. Here we take the parameters as : ${\Delta }_c=0$, ${\Delta }_b=45$, $N=1\times {10}^4$, $\Omega =0.1$. All the parameters are in the units of $\kappa$.

Figure 4

Intracavity photon number vs the driving strength. Here $N=1\times {10}^4$, $g=0.1$, ${\Delta }_c=1,$${\Delta }_b=60$. All parameters in the unit of the cavity decay rate, $\kappa$. The different colors in this figure represents the different steady-state values under same parameters, and the inset in this figure depicts the solid red and dashed blue curves in the interval $\Omega \in (0,1]$.

Figure 5

The output intensity spectrum of the single-mode cavity field for (a) different $\Omega$ with fixed ${\Delta }_c=1$ and (b) different ${\Delta }_c$ with fixed $\Omega =10$. Here, $N=1\times {10}^4$, $g=0.1$, and ${\Delta }_b=100$. All the parameters are in the units of the cavity decay rate, $\kappa$.