A thesis submitted February 2, 2015 for the degree of Doctor of Philosophy and defended March 19, 2015.
The PhD School of Science
Faculty of Science, Niels Bohr Institute, Quantum Photonics, University of Copenhagen, Denmark
Professor Peter Lodahl
Quantum electrodynamics with 1D articial atoms: from Purcell enhancement to single-photon nonlinearities
A 1D atom, a single quantum emitter coupled to a single optical mode, exhibits rich quantum electrodynamic (QED) e_ects and is thought to be the key ingredient for many applications in quantuminformation processing. Single quantum dots (QD) in photonic-crystal waveguides (PCW) constitute a robust platform for realizing a 1D atom, and are the subject of theoretical and experimental investigations in this thesis. We use _nite element method in 3D to calculate the local density of states (LDOS) in photonic-crystal membranes. The detailed spatial maps show strong inhibition of LDOS in the bandgap of the PhC, as large as 160 times. The method is extended to PCWs using a set of active boundary conditions. The extended method allows separating the contribution to the LDOS from the propagating mode and the radiation continuum. The detailed spatial maps of the LDOS show that for a broad spectral range, the contribution from the radiation continuum is much less than the contribution from the guided mode. The coupling e_ciency between an embedded emitter and the PCW is shown to be higher than 90% for a wide range of dipole positions, frequencies and orientaitions, which quali_es the system as a candidate for a 1D atom. One of the signatures and functions of a 1D atom is the nonlinear optical response at the single-photon level. A PCW chip is designed to experimentally study the transmission spectrum of an embedded QD. The transmission spectrum is shown to be modi_ed by 30% around the resonance of the QD. The power dependence of the transmission shows a nonlinearity with a critical power of 1:9 nW, which corresponds to an average number of 0.8 photons per lifetime of the emitter at the position of the QD. The autocorrelation function of the transmitted _eld shows bunching of the transmitted photons as expected from the theory. The value of g(2)(0) is around 1.08. The results con_rm the observation of an on-chip giant optical nonlinearity and the 1D atom behavior. Another direction in this thesis has been to investigate the e_ect of Anderson localization on the electrodynamics of QDs in PCWs. A large data set of the statistics of Purcell-enhancement of QDs in Anderson-localized cavities is presented. The average Purcell-enhancement of 4.5 times, with a peak value of 12 is observed for QDs randomly positioned in Anderson-localized modes of a PCW.