<p>The motions of a wavepacket in the two coupled potentials studied in this thesis can be classified into either bistable or astable motion according to the wavepacket interference at the curve crossing. Bistable motion, in which the wavepacket performs a coupled oscillation but remains in the same adiabatic and diabatic state, can exist both in bound-bound systems and bound-unbound ones with long time stability. Astable motion, in which the wavepacket at the curve crossing switches between the adiabatic and diabatic states and thus alternates between the two possible turning points in the unforked part of the motion, can only exist in bound-bound systems on a limited time scale. The motion of a wavepacket under bistable interference conditions exhibits all of the features expected if the wavepacket moved in a single anharmonic potential. The revival time can be predicted from the revival times in the corresponding diabatic and adiabatic potentials. The phenomenon was observed not only in model molecular systems but also in the system of the harmonically trapped ion pumped by an external laser field with standing wave spatial profile.</p><p>In order to study the bias effect of the detector on pump-probe rotational anisotropy measurements, in a specific direction the fluorescence polarization effect was removed by measuring the rovibrational wavepacket with the help of properly oriented polarizer placed in front of the detector. Our results show clearly the necessity to take polarization effects into account in ultrafast pump-probe rotational anisotropy measurements.</p>

The motions of a wavepacket in the two coupled potentials studied in this thesis can be classified into either bistable or astable motion according to the wavepacket interference at the curve crossing. Bistable motion, in which the wavepacket performs a coupled oscillation but remains in the same adiabatic and diabatic state, can exist both in bound-bound systems and bound-unbound ones with long time stability. Astable motion, in which the wavepacket at the curve crossing switches between the adiabatic and diabatic states and thus alternates between the two possible turning points in the unforked part of the motion, can only exist in bound-bound systems on a limited time scale. The motion of a wavepacket under bistable interference conditions exhibits all of the features expected if the wavepacket moved in a single anharmonic potential. The revival time can be predicted from the revival times in the corresponding diabatic and adiabatic potentials. The phenomenon was observed not only in model molecular systems but also in the system of the harmonically trapped ion pumped by an external laser field with standing wave spatial profile. In order to study the bias effect of the detector on pump-probe rotational anisotropy measurements, in a specific direction the fluorescence polarization effect was removed by measuring the rovibrational wavepacket with the help of properly oriented polarizer placed in front of the detector. Our results show clearly the necessity to take polarization effects into account in ultrafast pump-probe rotational anisotropy measurements.

In any quantum dynamics method that approximates wave functions as a linearly combined basis set, non-orthogonality can be is a problem. It has been proven in previous studies that, by using the most standard form of Matching Pursuit in combination with a Gaussian wave packet ansatz, exact quantum-mechanical correspondence can be obtained for particle tunneling in one and two dimensions. This study is an attempt to prove that this approach can be generally applicable to systems of arbitrary dimension propagating with an an-harmonic potential, and that adaptive initial state sampling can be used to make the method even more computationally efficient.

Sound generation and radiation properties are studied of full-scale tactical jet engine noise. This is motivated by the high sound exposure levels from jet noise, particularly for tactical engines. Acoustic source reconstruction methods are implemented computationally on existing jet noise data. A comparative study is performed using numerical simulations to understand the capabilities of more advanced beamforming methods to successfully estimate the source properties of a distributed, partially correlated source distribution. The properties and limitations of each beamforming method are described. Having validated the methods, beamforming with regularization—via the Hybrid Method—is implemented on linear array measurements near an installed tactical engine. A detailed analysis of the correlation and coherence properties associated with the phased array measurements guides the implementation of the beamforming. When the measurements are used as inputs to the beamforming, they produce partially correlated, distributed sources in a full-order model representation. A processing technique is also implemented that increases the usable bandwidth of the array measurements to almost an order of magnitude above the array design frequency. To more appropriately study the equivalent sources, a decomposition technique is designed and implemented to create a reduced-order wavepacket model of the jet noise. The wavepacket model is modular and scalable to allow for the efficient characterization of similar jet noise measurements. It is also appropriate for its physical significance, as wavepackets are attributed to the turbulent flow as well as the hydrodynamic and acoustic properties of the radiation. The reduced order model can estimate the levels and coherence properties of the acoustic radiation and represents a significant step towards a complete jet noise prediction model.

Sound generation and radiation properties are studied of full-scale tactical jet engine noise. This is motivated by the high sound exposure levels from jet noise, particularly for tactical engines. Acoustic source reconstruction methods are implemented computationally on existing jet noise data. A comparative study is performed using numerical simulations to understand the capabilities of more advanced beamforming methods to successfully estimate the source properties of a distributed, partially correlated source distribution. The properties and limitations of each beamforming method are described. Having validated the methods, beamforming with regularization”via the Hybrid Method”is implemented on linear array measurements near an installed tactical engine. A detailed analysis of the correlation and coherence properties associated with the phased array measurements guides the implementation of the beamforming. When the measurements are used as inputs to the beamforming, they produce partially correlated, distributed sources in a full-order model representation. A processing technique is also implemented that increases the usable bandwidth of the array measurements to almost an order of magnitude above the array design frequency. To more appropriately study the equivalent sources, a decomposition technique is designed and implemented to create a reduced-order wavepacket model of the jet noise. The wavepacket model is modular and scalable to allow for the efficient characterization of similar jet noise measurements. It is also appropriate for its physical significance, as wavepackets are attributed to the turbulent flow as well as the hydrodynamic and acoustic properties of the radiation. The reduced order model can estimate the levels and coherence properties of the acoustic radiation and represents a significant step towards a complete jet noise prediction model.

The main theme covered in this thesis is experimentalstudies of quantum dynamics and coherent control in homonuclearalkali diatomic molecules by ultrafast laser spectroscopy iththe implementation of pump-probe techniques. A series of experiments have been performed on the Rb2molecules in a molecular beam as well as in a thermal oven. Thereal-time molecular quantum dynamics of the predissociatingelectronically excited D(3)1Πu state of Rb2, which couples to/intersects several otherneighbouring states, is investigated using wavepackets. Thepredissociation of the D state, explored by this wavepacketmethod, arises from two independent states, the (4)3Σu+and (1)3∆u, for which the second corresponds to a much fasterdecay channel above a sharp energy threshold around 430 nm. Thelifetime of the D state above the energy threshold is obtained,τ ≈ 5 ps, by measuring the decay time of thewavepacket in a thermal oven. Further experimentalinvestigation performed in a molecular beam together withquantum calculations of wavepacket dynamics on the D state haveexplored new probe channels of wavepacket evolution: theD′(3)1Σu+ channel, which exhibits vibrational motionin a shelf state and the (4)3Σu+ channel, where direct build-up of thewavefunction is observed due to its spin-orbit oupling to the Dstate. The real-time quantum dynamics of wavepackets confined totwo bound states, A1Σu+(0u+) and b3Πu(0u+), have been studied by experiment andcalculations. It is shown that these two states are fullycoupled by spin-orbit interaction, characterised by itsintermediate strength. The intermediate character of thedynamics is established by complicated wavepacket oscillationatterns and a value of 75 cm-1is estimated for the coupling strength at thestate crossing. The experiments on the Li2molecule are performed by coherent control ofrovibrational molecular wavepackets. First, the Deutsch-Jozsaalgorithm is experimentally demonstrated for three-qubitfunctions using a pure coherent superposition of Li2rovibrational eigenstates. The function’scharacter, either constant or balanced, is evaluated by firstimprinting the function, using a phase-tailored femtosecond(fs) pulse, on a coherent superposition of the molecularstates, and then projecting the superposition onto an ionicfinal state using a second fs pulse at a specific delay time.Furthermore, an amplitude-tailored fs pulse is used to exciteselected rovibrational eigenstates and collision induceddephasing of the wavepacket signal, due to Li2-Ar collisions, is studied experimentally. Theintensities of quantum beats decaying with the delay time aremeasured under various pressures and the collisional crosssections are calculated for each well-defined rovibrationalquantum beat, which set the upper limitsfor ure dephasingcross sections. <b>Keywords:</b>Ultrafast laser spectroscopy, pump-probetechnique, predissociation, wavepacket, pin-orbit interaction,coherent control, (pure) dephasing

<p>The main theme covered in this thesis is experimentalstudies of quantum dynamics and coherent control in homonuclearalkali diatomic molecules by ultrafast laser spectroscopy iththe implementation of pump-probe techniques.</p><p>A series of experiments have been performed on the Rb2molecules in a molecular beam as well as in a thermal oven. Thereal-time molecular quantum dynamics of the predissociatingelectronically excited D(3)¹Πu state of Rb₂, which couples to/intersects several otherneighbouring states, is investigated using wavepackets. Thepredissociation of the D state, explored by this wavepacketmethod, arises from two independent states, the (4)³Σ_u⁺and (1)³∆_u, for which the second corresponds to a much fasterdecay channel above a sharp energy threshold around 430 nm. Thelifetime of the D state above the energy threshold is obtained,τ ≈ 5 ps, by measuring the decay time of thewavepacket in a thermal oven. Further experimentalinvestigation performed in a molecular beam together withquantum calculations of wavepacket dynamics on the D state haveexplored new probe channels of wavepacket evolution: theD′(3)1Σu+ channel, which exhibits vibrational motionin a shelf state and the (4)³Σu+ channel, where direct build-up of thewavefunction is observed due to its spin-orbit oupling to the Dstate.</p><p>The real-time quantum dynamics of wavepackets confined totwo bound states, A¹Σ_u⁺(0_u⁺) and b³Π_u(0_u⁺), have been studied by experiment andcalculations. It is shown that these two states are fullycoupled by spin-orbit interaction, characterised by itsintermediate strength. The intermediate character of thedynamics is established by complicated wavepacket oscillationatterns and a value of 75 cm^-1is estimated for the coupling strength at thestate crossing.</p><p>The experiments on the Li₂molecule are performed by coherent control ofrovibrational molecular wavepackets. First, the Deutsch-Jozsaalgorithm is experimentally demonstrated for three-qubitfunctions using a pure coherent superposition of Li₂rovibrational eigenstates. The function’scharacter, either constant or balanced, is evaluated by firstimprinting the function, using a phase-tailored femtosecond(fs) pulse, on a coherent superposition of the molecularstates, and then projecting the superposition onto an ionicfinal state using a second fs pulse at a specific delay time.Furthermore, an amplitude-tailored fs pulse is used to exciteselected rovibrational eigenstates and collision induceddephasing of the wavepacket signal, due to Li₂-Ar collisions, is studied experimentally. Theintensities of quantum beats decaying with the delay time aremeasured under various pressures and the collisional crosssections are calculated for each well-defined rovibrationalquantum beat, which set the upper limitsfor ure dephasingcross sections.</p><p><b>Keywords:</b>Ultrafast laser spectroscopy, pump-probetechnique, predissociation, wavepacket, pin-orbit interaction,coherent control, (pure) dephasing</p>

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This dissertation details the development and applications of two innovative types of optical filament-based impulsive Raman spectroscopy: filament-assisted Raman spectroscopy (FAIRS) and spectral-to-temporal amplitude mapping polarization spectroscopy (STAMPS). These techniques provide complimentary vibrational and rotational information on molecular systems of interest. Both are powerful due to their impulsive nature which allows for rapid measurement of entire Raman spectra. However, each type of spectroscopy utilizes the filament in a different manner. The recently reported vibrational technique, referred to as filament-assisted impulsive Raman spectroscopy, employs the pulse shortening and continuum generation of filamentation to impulsively excite a massive vibrational coherence in a molecular system for simultaneous measurement of all the Raman-active modes. In the first half of this dissertation, FAIRS is further developed and applied to a plethora of signature molecules. Radioactive decay signature molecules, including nitrogen oxides, ozone, and ions are detected via FAIR spectroscopy. Concurrent generation and detection of ozone, ionic, and excited-state molecules through filamentation is reported for the first time. Production of these species through the strong field chemistry of filamentation and their subsequent filament-driven excitation is a mark of sensitivity of FAIRS. Spatial studies of combustion species in a natural gas flame are also presented. FAIRS monitors the Raman signal intensities of known reactants and products as a function of vertical flame position. The appearance of combustion products as a function of flame height is also tracked. Spectral fringes overlapping the Raman-active modes are present in all measurements and enable more sensitive detection of low signal intensity species. The results described illustrate the potential of FAIRS for threat sensing applications. The rotational technique, referred to as spectral-to-temporal amplitude mapping polarization spectroscopy, temporally chirps the spectral content of the white-light continuum generated during filamentation to map the transient rotational rivals that are impulsively excited by a short pump pulse. In the second half of this dissertation, the initial development and testing, followed by the applications of STAMPS are described. STAMPS proves successful in mapping the rotational wavepacket rephasing of simple linear molecules, including nitrogen, oxygen, and carbon dioxide, as well as the more complicated asymmetric top molecules, ethylene and methanol. The application of STAMPS to the detection of nitrogen oxides and nitrous oxide, which are considered signatures of multiple threat substances and events, is demonstrated. A pressure study of nitrous oxide reveals dephasing effects as a function of time and pressure. These preliminary results also indicate the potential of STAMPS for hazard sensing applications. / Chemistry

This work presents a new implementation of the QP algorithm, a computer method to diagonalize the extremely large matrices arising in multimode vibronic problems. Benchmark calculations are included, showing the accuracy of the program. The QP algorithm is extended to treat multiple electronic surfaces for competitive control and this is demonstrated with an Hamiltonian including three electronic states, a model of the benzene radical cation. Finally, the evolution of zeroth-order states in a simple two electronic states, two dimensional model with a conical intersection is explored, towards building a time-dependent view of overlapping resonances coherent control.