# Photon Counting Statistics of a Microwave Cavity Coupled with Double Quantum Dots
## 4 Conclusions and Remarks  
In summary, we firstly employed Born-Markov approximation and the projecting operator method to obtain the reduced master equation of a cavity coupled with a system of DQDs which was driven by an external microwave field. Then, we investigated the influences of the parameters of DQDs on the photon emission counting statistical properties, especially the WTDs and large deviation statistics, of the cavity. The results show that the interaction between the DQDs and cavity has an obvious effect on the statistical properties of photon emission counting.  
Firstly, the decay rates of WTDs of the cavity for short and long time limits--the cumulants of waiting time--can be effectively tuned by the driving external field Rabi frequency, the frequency of the cavity photon, the detuning between the microwave driving frequency, and the energy-splitting of the DQDs. Conversely, the state and properties of the DQDs can be extracted from WTDs and the cumulants of waiting time.  
Secondly, the first-order, second-order and third-order cumulants of waiting time vary much more steeply if the rate \(W\), which is the rate difference between a photon absorbed and emitted by DQDs, has larger maximum as the detuning varies.  
Thirdly, the photon emission energy current will flow from the thermal reservoir to the system of the DQDs when the average photon number of the cavity in a steady state is larger than that of the thermal reservoir; otherwise, the photon emission energy current will flow in the opposite direction.  
Finally, the effect of the DQDs and the effect of a thermal reservoir with \(\gamma_{h}=W,\overline{n}_{h}=A_{+}/W\) on the photon emission counting statistical properties is the same when the rate difference of a photon absorbed and emitted by DQDs is larger than zero. If the rate difference between a photon absorbed and emitted by DQDs is less than or equal to zero, the effect of the DQDs cannot be replaced by that of a thermal reservoir.  
On the whole, WTDs and the large-deviation statistics properties of a cavity can be strictly regulated and controlled by the parameters of the DQD system online. The effects of the DQDs on the statistical properties of photon emission counting are irreplaceable in certain parameter regions. Thus, these results deepen our understanding of the statistical properties of photon emission counting, enrich the control techniques for the photon emission of a cavity, and open a new door for the construction of nanostructured devices of photon emission on demand and optoelectronic devices.  
All authors prepared the manuscript and contributed to the concepts and theoretical results exposed in this article. Numerical calculations were run by F.W. All authors have read and approved the final manuscript.  
This work was funded by the National Natural Science Foundation of China (Grant No. 61774062, No. 11674109, and No. 61275059); the Natural Science Foundation of Guangdong Province, China (Grant No. 2016A030313443); the Science and Technology Planning Project of Guangdong Province, China (Grant No. 2017A020219007); and the Research Fund Program of Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices.  
The authors declare no conflict of interest.