# Photon Counting Statistics of a Microwave Cavity Coupled with Double Quantum Dots
## 3 Discussion
If \(\overline{n}_{c}>\overline{n}\), a large emission current is more likely than that of a cavity without DQDs; otherwise, it is less likely. Comparing the cyan line and red line, we find that the probability of small and large emission currents of \(\Delta=5\Gamma\) are higher than those of DQDs replaced with a thermal reservoir with \(\overline{n}_{h}=10\), although \(\overline{n}_{c}=3\) for \(\Delta=5\Gamma\) while \(\overline{n}_{c}=5.5\) for DQDs replaced with a thermal reservoir. This reflects the fact that large-deviation statistics are not only dependent on the parameter \(A_{+}\), but also dependent on the parameters \(A_{-}\) and \(W\). Figure 6 exhibits large-deviation statistics of the net photon emission current as a function of the net photon emission current \(J\) from the cavity to reservoir. From the black line, we see that the probability of the photon emission energy current moving from the cavity to the thermal reservoir is the same as that of the photon emission current from the thermal reservoir to the cavity because the system is in steady state. The blue line and green line show that, if average photon number of the cavity satisfies the condition \(\overline{n}_{c}>\overline{n}\), the photon emission energy current will flow from the thermal reservoir to the system of the DQDs; otherwise, the photon emission energy current will flow in the opposite direction. As for the red line (\(\Delta=5\Gamma\), \(W<0\)) and the magenta line (\(\Delta=0,\ W=0\)), the photon emission current from the thermal reservoir to the cavity are suppressed, which is quite different from that of the other cases. In particular, the most probable photon emission current is shifted from zero to a positive photon emission current \(J\) for the red line (\(\Delta=5\Gamma\), \(W<0\)). From all of the above discussion, we find that the statistical properties of the photon emission counting of a cavity coupled with DQDs are similar to those of a cavity coupled with another thermal reservoir instead of DQDs when \(W>0\); otherwise, these statistical properties are quite different. This is because the effect of the DQDs on the photon emission counting statistical properties is the same as that of a thermal reservoir with \(\gamma_{h}=W,\overline{n}_{h}=A_{+}/W\) when \(W>0\). If the parameters satisfy the  
Figure 5: Large-deviation statistics of the photon emission current. Analytic results for the distribution of the photon emission current \(J\) from a cavity to reservoir with \(\Delta=-5\Gamma\) (blue line); \(\Delta=5\Gamma\) (red line), cavity without DQDs (black line); DQDs replaced by thermal reservoir \(\gamma_{h}=0.02,\overline{n}_{h}=1\) (green line), thermal bath \(\gamma_{h}=0.02,\overline{n}_{h}=10\) (cyan); \(\gamma=0.02,\overline{n}=1,\Gamma=1,\omega_{m}=10\Gamma,\)\(\eta=0.05,\)\(\Omega_{0}=7\Gamma\). Figure 6: Large-deviation statistics of the net photon emission current. Numeric results for the distribution of the net photon emission current \(J\) from a cavity to reservoir with \(\Delta=-5\Gamma\) (blue line); \(\Delta=5\Gamma\) (red line); \(\Delta=0\) (magenta line); DQDs replaced by thermal reservoir \(\gamma_{h}=0.02,\overline{n}_{h}=1\) (black line), thermal bath \(\gamma_{h}=0.02,\overline{n}_{h}=10\) (green); \(\gamma=0.02,\overline{n}=1,\Gamma=1,\omega_{m}=10\Gamma,\)\(\eta=0.05,\)\(\Omega_{0}=7\Gamma\). condition \(W\leq 0\), the effect of the DQDs cannot be replaced by that of a thermal reservoir. This is the essential characteristic of the system presented in this paper.