Master's Defense: Bjarke Geza Solyom Høgdall

Coupling microwave resonators to a double quantum dot chain

Superconducting resonators used to build quantum devices can emulate harmonic oscillators. Their energies match the energies in semi-conducting Double Quantum Dots (DQDs), that can emulate atoms. Motivated by energy transport through systems of atoms and oscillators  theoretical systems of double quantum dots and superconducting resonators are studied. A setup with a chain of DQDs and resonators was derived and transformed into a Transverse Field Ising model and further into a 1D spin-less p-wave superconductor using a Jordan-Wigner transformation. With a Bogoliubov transformation a classical solution to a single resonator field is found that minimizes the classical potential. Going to the imaginary time path integral formalism it was possible to study many resonators and their collective excitations. A classical solution to the resonator field was found for a single resonator and many DQD’s. In the imaginary time path integral formalism, a saddle point equation is found for many resonators and DQD’s and an approximate solution found in the fine tuned regime with weak coupling. It is shown that a uniform solution solution could always minimize the action. Fluctuations around the uniform resonator field are then studied and the spectrum and spectral function was found. From the spectrum the group velocity could be estimated.