Computational analysis of photon echo and exceptional points dynamics in lossy quantum systems
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The focus of this thesis is investigating regimes where experimental realisations of theoretical hypothesis is difficult. Mainly we investigated three topics. Firstly, Photon echo in overlapping pulses regime. We showed that for overlapping carrier enveloped pulses the echo peak position is sensitive to the relative phase and depends on delay between the pulses, pulse width, dephasing times etc of the overlapping pulses. We also showed that observing the photon echo in such a regime is easier when the pulses interfere destructively as the echo signal is relatively stronger although echo peak position shifted forward in time more than constructive interference case. Secondly, an experiment of electromagnetically induced transparency in silicon with shallow donors. In this case we explained what went wrong with this experiment and suggested a parameter regime where EIT can be observed experimentally. We also briefly explored a three-level system with losses using non-hermitian quantum mechanics and reproduced some general results(coherent population trapping, effect of loss on different state populations in a three level system) of a hermitian hamiltonian using non-hermitian hamiltonian. Thirdly, we investigated non-hermitian quantum mechanics using two and four level systems. We observed the general properties of exceptional points namely, non-hermitian degeneracy where both the eigenvalues and the eigenvectors coalesce thus leaving the hamiltonian matrix defective, phase rigidity, topological properties and differences between encircling exceptional points quasi-statically and dynamically. We then suggested experiments to observe these exceptional points, investigated exceptional rings, compared symmetric and asymmetric non-hermitian hamiltonians with identical eigenvalues and found a regime where no matter how small the gain it always wins against loss.