In my Master's thesis, I study a certain class of superradiant states theoretical. Matter that is in a superradiant state uses photons to be in a highly coherent and ordered state. It is suspected that a quantum state like this can be used for supercomputing or really any application that requires coherent photons, such as a very, very precise clock. I designed my calculations to be close to an experimental setup. In this schematic setup, a Bose-Einstein condensate is placed in a single mode cavity and driven with a light field. At a critical light-matter coupling strength, the system will undergo a Dicke-type superradiant phase transition and emit coherent photons.
In my study, the atomic branch of the Dicke model is expanded into arbitrary (but finite) modes, i.e. multiple excited states are possible. To perform this extension using a full set of Bloch functions. This allows distinguishing between multiple electronic levels but also a quasi-momentum space, i.e. quantized states in the Brillouin-zone. The main tools in this expansion are a generalized Holstein-Primakoff transformation that simplifies the interaction terms and displacement operators, which are of a mean-field type. With these simplified terms, I am able to diagonalize the Hamiltonian in the particle number N --> infinity limit. The model exhibits a superradiant second-order quantum phase transition and we find that the presence of p quasi-momentum modes lowers the critical point yc around yc / p1/2.We also derive excitation energies for a 'two-band' Dicke model above zero temperature. This investigation shows that the system undergoes also a thermal superradiant phase transition for finite numbers of particles N in the ultrastrong-coupling regime y --> infinity. A discussion of the particle statistics leads to a generalized description of atoms in this environment and it describes a crossover between bosonic and fermionic configurations.
We also derive excitation energies for a 'two-band' Dicke model above zero temperature. This investigation shows that the system undergoes also a thermal superradiant phase transition for finite numbers of particles N in the ultrastrong-coupling regime y --> infinity. A discussion of the particle statistics leads to a generalized description of atoms in this environment and it describes a crossover between bosonic and fermionic configurations.
In my Bachelor's thesis, I started to develop the above described multi-mode expansion of the Dicke model by focusing on multiple electronic levels. The mode expansion is, again, performed by Bloch functions. A generalized Holstein-Primakoff transformation and displacement operators allow studying the model in the thermodynamic limit. We then have an effective multi-mode model that exhibits a Dicke-type superradiant phase transition. The more complex super-radiant phase is treated numerically while we were able to receive analytical expressions in the normal phase. The behavior of the Bose-Einstein condensate electronic level population, as well as the behavior of the photon mode, is calculated.
My Bachelor's and Master's thesis research has been performed at Technische Universität Berlin (TU Berlin) in the group of Prof. Dr. Tobias Brandes and under the supervision of Prof. Dr. Clive Emary.