The relevant theory for this experiment can be found HERE and HERE. In the presence of the first photon, the state of the second photon should acquire a phase, and remain the same if the first photon is not present. Aside from the fact that single photons are pretty cool, CPHASE gates are “universal” for quantum computation (QC). This means that if we can implement a CPHASE gate on two photons and a few others, of which the Hadamard gate is one of the most important ones, we can do any computation of arbitrary size using only these single and two-photon interactions. Of course this assumes that our implementation is robust and faultless, but even with imperfect realization of such gates, we can begin to attempt the construction of a quantum computer.  This implementation of CPASE combines the phenomenon of photon blockade in the intermediate coupling regime with the optical stark shift. The AC Stark shift controls the spectral position of the reflectivity window by detuning the quantum dot (this is the control pulse). By tuning this window, the signal photon is reflected with a particular phase from the cavity. In the absence of the control photon, the signal photon can either transmit or reflect with a different phase.