Quantum synchronization in a cavity

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Quantum synchronization involves two ensembles of atoms within a cavity, requiring specific conditions such as frequency differences, dissipative coupling, and optical pumping. The term "dissipative coupling generated by emission of photons into the same cavity mode" refers to how photons emitted by excited atoms interact within the cavity, influencing synchronization. The imperfect nature of the cavity leads to photon escape, creating a decay channel for excited atoms. Understanding this coupling is crucial for grasping the dynamics of quantum synchronization in such systems. Further literature on cavity quantum electrodynamics may provide additional insights into these processes.
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I am currently studying quantum synchronization. I am reviewing a https://www.researchgate.net/publication/251232415_Quantum_Synchronization_of_Two_Ensembles_of_Atoms which describes quantum synchronization of two ensembles in a cavity. As such, I have a query regarding a cavity physics related concept. At the bottom of page 2 it states the following:

With this system we naturally provide the three necessary ingredients for quantum synchronization: a controllable difference between the oscillation frequencies of two mesoscopic ensembles, a dissipative coupling generated by the emission of photons into the same cavity mode, and a driving force produced by optical pumping

I am particular interested in understanding what exactly is meant by "dissipative coupling generated by emission of photons into the same cavity mode". I'm having difficulty sourcing a basic description of this cavity process. Can anyone provide some insight into this or a good basic reference in literature? Thanks for your time and assistance.
 
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Since the cavity is not perfect, it has a natural decay as photons can escape the cavity. Therefore, an excited atom also has a decay channel through its coupling to the cavity modes.
 
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Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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