title: Spatio-temporal correlations of ensembles of multi-level atoms
Creators: name: Bojer, Manuel
Publisher: name: Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Year: 2024

description: Until 1963, the concept of coherence of optical fields was limited to what is nowadays called first-order coherence. In 1963, Roy J. Glauber generalised the notion of coherence by introducing higher-order correlation functions of the field variables and defining appropriate conditions based on them. A particular class of correlation functions are the so-called photon correlation functions, which can be measured with simple photon detectors. On the one hand, these correlation measurements can be used to characterise the underlying optical system, on the other hand the correlation measurements can be viewed as conditional photon measurements. Thereby, the measurement of the first incoming photons create correlated states whose properties are then detected via the later measured photons. In that way, measurement-induced quantum correlations can be imprinted on a quantum system. Another method to create quantum correlations is via an interaction with the system, such that quantum correlations can build up via the dynamics of the system. In this thesis, we investigate the spatio-temporal correlations of several ensembles of atoms, with quantum correlations generated via dipole-dipole interactions in the course of the dynamics of the atoms as well as via conditional photon measurements. As a first setup, we consider three atoms, where two atoms interact with each other, but the remaining atom is far distant from the two-atom subsystem, such that it does not interact with the other two atoms. We demonstrate that the spontaneous emission behaviour of this system can be engineered via conditional photon measurements allowing to observe strong subradiant and superradiant radiation of photons simultaneously depending solely on the direction of observation. Further, we show that by introducing the remote atom into the system, we can extract information, for instance, the separation and the initial state of the two close-by atoms, which is not accessible in the two-atom system alone. In this way, we demonstrate a potential prospect for quantum sensing, i.e., adding an auxiliary system and using conditional photon measurements to entangle it with the system of interest. We then switch to an atomic ensemble of N mutually far separated atoms, such that interactions between the atoms can be neglected. Again, by conditional photon measurements, used to create quantum correlations between the different atoms, we demonstrate that a temporal Dicke-like superradiant emission behaviour of the consecutively measured photons can be observed in a particular direction. Such an emission behaviour, known as Dicke superradiance, is usually restricted to atoms, which are closer separated than the wavelength of the light, such that they interact with each other via dipole-dipole interactions and become correlated in the course of photon emission. Afterwards, we investigate under which conditions an independent atomic ensemble emits similar to a thermal source in terms of higher-order photon correlation functions. We define two conditions restricting on the one hand the single-atom coherences with respect to the population of the atoms, and on the other hand the correlation order with respect to the number of atoms. We demonstrate the validity of the two conditions and the similarity of the light statistics to the one of thermal sources via several examples, one of them being a dilute atomic cloud driven by a plane wave laser field in the strong driving regime. Finally, we analyse the photon emission of the same atomic ensemble, but weakly driven. Here, the dynamics of the atoms can be essentially described by a classical oscillating dipole model. However, since the atoms can only emit one photon at a time, the radiated light statistics differs drastically from that of classical dipoles. In particular, we find observation directions in which the atoms emit quantum light characterised by a value of the normalised second-order autocorrelation function less than 1.