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Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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Graduate

This work examines the use of higher order multiphoton resonances in higher harmonic generation together with judicious exploitation of coherent interaction properties to achieve efficient harmonic generation. A detailed experimental study on third harmonic generation in two photon resonant coherent interaction and a theoretical study on four photon resonant coherent interaction have been conducted. Two photon resonant coheren propagation in lithium vapor (2S-4S and 2S-3D interaction) has been studied in detail as a function of phase and delay of the interacting pulse sequence. Under coherent lossless propagation of 90 phase shifted pulse pair, third harmonic generation is enhanced. A maximum energy conversion efficiency of 1% was measured experimentally. This experiment shows that phase correlated pulse sequence can be used to control multiphoton coherent resonant effects. A larger two photon resonant enhancement does not result in more efficient harmonic generation, in agreement with the theoretical prediction. An accurate (to at least 0.5 A°) measurement of intensity dependent Stark shift has been done with the newly developed "interferometric wavemeter." Stark shifts as big as several pulse bandwidths (of picosecond pulses) result in a poor tuning of multiphoton resonance and become a limiting factor of resonant harmonic generation. A complete theory has been developed for harmonic generation in a four photon resonant coherent interaction. A numerical application of the theory to the Hg atom successfully interprets the experimental observations in terms of the phase dependent stimulated Raman scattering. With the intensity required for four photon resonant transition, the calculation predicts a dramatic Stark shift effect which completely destroys the resonance condition. This model provides a basis for the development of future schemes for efficient higher order coherent upconversion.

本論文包括對 Jaynes-Cummings-Hubbard (JCH) 系統的研究。在這個系統中，每個耦合光學腔之內都放置了一顆雙態原子，偶極相互作用導致系統有激發光子和原子的自由度。對量子電動力學系統的研究，使我們對光子與原子間的相互作用以及量子相變有更深的認識。 / 我們研究了一維JCH系統中有兩個激發子的本徵態。我們發現當真空拉比頻率與腔間穿隧率之比超過某一臨界值，兩個激發子的束縛態就會出現。 / 我們還為兩個腔的JCH系統之演化作出研究，並指出系統的量子態在一定條件下可演變成薛丁格貓態。從相干態演化到薛丁格貓態所需的時間亦被估計。 / 最後，我們使用主方程來探討驅動JCH系統的去相干。在這篇論文中，我們提出了一些低激發量的穩態的例子。許多不同的穩態系統的光子統計將被討論。 / This thesis comprises of an investigation of the Jaynes-Cummings-Hubbard (JCH) system. In such a system, single two-level atoms are embedded in each coupled optical cavity, and the dipole interaction leads to dynamics involving photonic and atomic degrees of freedom. The investigation of quantum electrodynamics in the system provides insight about the behaviour of strongly interacting photons and atoms and quantum phase transition. / We examine the eigenstates of the one-dimensional JCH system in the two-excitation subspace. We discover that two-excitation bound states emerge when the ratio of vacuum Rabi frequency to the tunnelling rate between cavities exceeds a critical value. / We also study for the time evolution of a two-cavity JCH system, and indicate that the evolved state can be a Schrödinger's cat state under certain conditions. The time required for evolving a coherent state into a Schrödinger's cat state is also estimated. / Finally, we investigate the decoherence of a driven JCH system by using the master equation. In this thesis we present several examples of steady state when the total number of excitation is low. The photon statistics of the steady state of the system will be discussed. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wong, Tsz Ching Max = Jaynes-Cummings-Hubbard模型的課題 / 黃子澄. / "November 2012." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 79-84). / Abstracts also in Chinese. / Wong, Tsz Ching Max = Jaynes-Cummings-Hubbard mo xing de ke ti / Huang Zicheng. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Basic Description of the Jaynes-Cummings-Hubbard Model --- p.4 / Chapter 2.1 --- Jaynes-Cummings Model --- p.4 / Chapter 2.1.1 --- Hamiltonian --- p.5 / Chapter 2.1.2 --- Energy Eigenstates --- p.6 / Chapter 2.2 --- Coupled-cavity System without Atoms --- p.8 / Chapter 2.2.1 --- A One-dimensional Coupled-cavity Chain --- p.8 / Chapter 2.2.2 --- Normal Modes --- p.9 / Chapter 2.3 --- Jaynes-Cummings-Hubbard Model --- p.10 / Chapter 2.3.1 --- Eigenstates of Single Excitation --- p.11 / Chapter 2.3.2 --- Dynamics of Single Excitation --- p.12 / Chapter 2.3.3 --- Single Excitation in the Weak Coupling Limit --- p.15 / Chapter 2.3.4 --- Single Excitation in the Strong Coupling Limit --- p.16 / Chapter 3 --- Solution of the JCH Model with Two Excitations --- p.17 / Chapter 3.1 --- Two-particle Bound States in the Bose-Hubbard Model --- p.17 / Chapter 3.2 --- Two-polariton Bound States in the JCH Model --- p.19 / Chapter 3.2.1 --- Bound State Eigenvectors --- p.24 / Chapter 3.2.2 --- Bound State Eigenvalues --- p.26 / Chapter 3.2.3 --- Critical Coupling --- p.28 / Chapter 3.2.4 --- Analytic Approximations in Strong Coupling Regime n≫k --- p.30 / Chapter 3.3 --- Dynamics of Two Excitations in Strong Coupling Regime --- p.33 / Chapter 3.3.1 --- Initial Condition: --- p.33 / Chapter 3.3.2 --- Initial Condition: Superposition of j2; gin in Gaussian Distribution --- p.34 / Chapter 3.3.3 --- Initial Condition: Superposition of j1; gin j1; gim in Gaussian Distribution --- p.39 / Chapter 3.3.4 --- Initial Condition: Superposition of j1;+in j1; ¡im in Gaussian Distribution --- p.39 / Chapter 4 --- JCH Model in a Two-cavity Con¯guration --- p.41 / Chapter 4.1 --- Generation of SchrÄodinger's Cat State: Numerical Simulation --- p.41 / Chapter 4.2 --- Generation of SchrÄodinger's Cat States: Analytic Solution --- p.45 / Chapter 4.2.1 --- Estimation of Optimum Parameters --- p.53 / Chapter 4.3 --- Coherent States as Initial Conditions --- p.55 / Chapter 5 --- Decoherence of a Weakly Driven JCH Model --- p.60 / Chapter 5.1 --- Master Equation --- p.60 / Chapter 5.2 --- Driven JCH Model: N-cavity Configuration --- p.61 / Chapter 5.2.1 --- One-excitation Approximation --- p.63 / Chapter 5.2.2 --- Simple Harmonic Oscillator Limit --- p.66 / Chapter 5.3 --- Driven JCH Model: Two-cavity Configuration --- p.69 / Chapter 6 --- Conclusion --- p.76 / Bibliography --- p.79

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