Ivan Iakoupov

A thesis submitted December 14, 2017 for the degree of Doctor of Philosophy and defended January 2018.

The PhD School of Science, Theoretical Quantum Optics, Faculty of Science, Niels Bohr Institute, University of Copenhagen

Academic supervisor:
Anders S. Sørensen

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Enhancement of optical nonlinearities with stationary light

The topic of this thesis is understanding and application of the phenomenon of stationarylight. Stationary light arises in atomic ensembles with certain energy level configurations,when two counter-propagating classical drives (lasers) are applied. Probe light coupledto a different energy level transition than the classical drives can be completely stopped,while still retaining its light character. This is very different from a related phenomenonof slow light or electromagnetically induced transparency (EIT), where stopping propa-gation of light completely converts it into an atomic excitation instead. More generally,we will be interested in the regime of stationary light, where the probe light still prop-agates through the atomic ensemble, but extremely slowly. In other words, probe fieldhas a very low group velocity, which increases its interaction time with any optical non-linearity. Group velocity can be obtained from the dispersion relation. Therefore, thedispersion relations for various stationary light schemes are studied in detail. The studyof the dispersion relations is carried out both in the continuum approximation of atomicensembles and the discrete model where each atom is assumed to be a linear scatterer.The enhancement of the effective nonlinear strength by stationary light is then usedto propose a two-qubit (controlled-phase) quantum gate for the optical photons, whichcan in principle work deterministically. We do find, however, that a heralded operationof the proposed gate achieves much higher conditional fidelity (overlap of the ideal statewith the actual one), since most of the error in the unconditional fidelity is due to lossof photons, which can be detected. We also find that the gate can approach the ideallimit (both in the deterministic and heralded operation) by increasing the total number ofatoms in the atomic ensemble to compensate for a limited single-atom coupling strength.Before discussing stationary light and its application, we also analyse the differentfidelity measures that could be applied to the proposed gate (and related proposals).We show that all of the considered fidelity measures are (approximately) equal due toparticular features of the considered physical system. This result allows one to reducethe number of expressions to be evaluated if the performance of the gate is to be analyzedfor different applications at the same time.

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