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Fred M. Ellis




The major PhD’s research portion of this work consisted of the design and apparatus development of the ultra high frequency driven PT symmetric dimer. Non-Hermitian Hamiltonians H which commute with the PT symmetry operator might have a real spectrum depending on the parameter which controls the degree of Non-Hermiticity. In electronics, a combination of two LC oscillators coupled capacitively or inductively, one with active conductance and the other with negative conductance, creates a circuit version of a PT system. Traditionally, the study and application of PT-symmetric systems have been focused on static (time-independent) potentials. Using periodic driving schemes in PT symmetric systems can allow for the management of the spontaneous PT-symmetry breaking for arbitrary values of the gain and loss parameters. Performing the first time-dependent PT-symmetric experiment (working at frequency of 235 MHz) we found that the UHF driven PT symmetric dimer supports a sequence of spontaneous PT-symmetry broken domains bounded by exceptional points in its spectrum. The position and size of these instability islands can be controlled through the amplitude and frequency of the driving. Driving scheme will give us another degree of freedom to control the instability of the system by changing the amplitude or frequency of the drive.

In the next part of my research, “Lasing Death” phenomenon in electronics framework was investigated. By presenting the experimental system of two 3 MHz coupled RLC circuits with active nonlinear conductances, we demonstrate that amplification action can be tamed via asymmetric pumping. Under specific conditions we observe the counterintuitive phenomenon of stabilization of the system even when the overall gain provided is increased.



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