Alejandro González-Tudela

**ALEJANDRO GONZÁLEZ-TUDELA**Max-Planck-Institut für Quantenoptik, Garching, GERMANY

Photon counting is one of the most important measurements in the field of quantum optics: the arrival times of photons are correlated, providing useful information on the quantum dynamics of the emitter. Much more information can be accessed if also the energies of the photons are correlated. This practice is becoming increasingly popular experimentally, where it poses no conceptual difficulties (filters can be interposed in front of the detectors). Theoretically, however, such a quantity has remained a challenge due to frequency being a non-commuting observable with time, resulting in cumbersome integral expressions, only manageable for two photons and for simple systems.

We present our recently developed theory of frequency-filtered and time-resolved *N*-photon correlations that solves all the issues related to this problem. Namely, we show how to compute correlations for any *N* photons (rather than previously at most two) for arbitrary systems (rather than previously resonance fluorescence of the two-level system), at all time delays (rather than tau=0 as in most previous cases) and all this without approximations (unlike most previous studies). We present as a result so-called two-photon spectra that measure the correlations between all the frequencies of a quantum system and unravel a rich and unsuspected dynamics, such as *leapfrog processes* whereby transitions between far-off energy levels are linked through virtual photons, resulting in strongly correlated emission by the system. This can be taken advantage of to optimize quantum emitters or to design new classes altogether (like heralded N-photon emitters). We focus on the paradigm of cavity QED, the well-known Jaynes-Cummings dynamics of strong light-matter coupling to illustrate how familiar results fit in a more general picture, as well as the exciting possibilities opened by our formalism and the new quantities that it introduces.

We also apply our theory to fluctuating systems by including in the master equation both the magnitude and speed of fluctuations. We show how spectral filtering can be used to recover the information otherwise blurred by the fluctuations.**
Seminar, July 23, 2013, 15:00. Seminar Room
Hosted by Prof. Darrick Chang**