when photons can be trapped in a cavity and manipulated. How they can be observed without being destroyed? An observer is anything that can cause a wave function to collapse. That is an interpretation of wave function collapse (usually referred to as the measurement problem).  Now, 


*

*when can photons be trapped in a cavity and manipulated? 

*How they can be observed without being destroyed!? 

*Through interactions with atoms in cleverly designed experiments!? 
 A: There is a difference between wave function collapse and destroying a photon. Normally, when you detect a photon, you let it hit a device, where the photon is absorbed and its energy is transferred to an electron that creates a photocurrent you can measure. So, after the measurement, the photon is no more, you only know that you had one but cannot do anything with it now.
The thing that Serge Haroche does is that he measures photons without destroying them. In this way, he knows how many photons there are in the cavity, and can perform other operations on them later. But of course, when he starts with a coherent state and measures the photon number, the state will collapse into a Fock state.
The basic idea of this measurement is to use dispersive interaction with single atoms. Thus, the photons are not absorbed, but imprint a phase shift on the atom that can be measured provided the atom is initially in superposition of ground and excited state. If you want to know more about the technique, I suggest you look at articles describing these experiments (from Nature and Phys. Rev. A).
Edit: arXiv versions of the mentioned papers: http://arxiv.org/abs/0707.3880, http://arxiv.org/abs/0905.0114.
A: 
"So, after the measurement, the photon is no more,"

I think true word is disappeared not destroyed.
It means they can be observed without being disappeared?
When the wave function of a photon collapses with observation, it means that one of the properties of the photon is being destroyed; they can not be observed without being destroyed but they can be observed without being disappeared.
