Quantum state measurement for molecules

Measuring the density operator of a quantum system provides complete state information. This thesis concerns quantum state measurement in diatomic molecules. We have developed techniques to reconstruct the density operator of a vibrational wave packet excited by an ultrafast laser pulse. These techniques can be used to reconstruct the quantum state of a wave packet without making any assumptions about the initial state of the molecule or the amplitude and phase of the excitation pulse.;Molecular emission tomography measures a phase space quasi-probability distribution of a vibrational wave packet. We introduce tomographic state measurement, and we discuss the requirements for successful reconstruction of quantum states with complicated phase space distributions.;Molecular tomographic state reconstruction relies on measurements of the time-dependent spectrum (TDS) of molecular fluorescence. Accurate state measurement requires quality TDS data. We describe the experimental implementation of molecular emission tomography, emphasizing the important parameters for optimization of the TDS signal. We present phase space quasi-probability distributions, reconstructed from experimental data.;We introduce a new state reconstruction technique for directly measuring elements of the density matrix for a wave packet evolving in an anharmonic potential. We establish a direct relationship between elements of the density matrix and the TDS of molecular fluorescence. Taking advantage of this relationship, we analyze three methods for direct density matrix reconstruction from measurements of the TDS.;The initial state of our molecular sample is described by a large mixture of ro-vibrational levels. We consider the effects of molecular rotations and a mixed initial state. We develop simulations to explain the form of the TDS signals measured in the laboratory, and we find that tomographic state reconstruction provides measurements of vibrational quantum states which are relatively insensitive to large distributions of initial rotational levels.;We have measured the TDS of the coherent component of the emission from a vibrational wave packet. We present a model for this emission which is in excellent agreement with the measured data. We examine the effects of both polarization and quantum interference on the coherent signal, and we discuss how this signal can be used for state reconstruction.