Light is capable of directly manipulating and probing molecular dynamics at its most fundamental level. One versatile
approach to influencing such dynamics exploits temporally shaped femtosecond laser pulses. Oftentimes the control
mechanisms necessary to induce a desired reaction cannot be determined theoretically a priori. However under certain
circumstances these mechanisms can be extracted experimentally through trial and error. This can be implemented
systematically by using an evolutionary learning algorithm (LA) with closed loop feedback. Most frequently, pulse
shaping algorithms operate within either the time or frequency domain, however seldom both. This may influence the
physical insight gained due to dependence on the search basis, as well as influence the speed the algorithm takes to
converge. As an alternative to the Fourier domain basis, we make use of a combined time-frequency representation
known as the von Neumann basis where we observe temporal and spectral effects at the same time.
We report on the numerical and experimental results obtained using the Fourier, as well as the von Neumann basis to
maximize the second harmonic generation (SHG) output in a non-linear crystal. We show that the von Neumann
representation converges faster than the Fourier domain when compared to searches in the Fourier domain. We also
show a reduced parameter space is required for the Fourier domain to converge efficiently, but not for von Neumann
domain. Finally we show the highest SHG signal is not only a consequence of the shortest pulse, but that the pulse
central frequency also plays a key role.
Taken together these results suggest that the von Neumann basis can be used as a viable alternative to the Fourier domain
with improved convergence time and potentially deeper physical insight.
Simulating coherent control with femtosecond pulses on a polyatomic molecule with anharmonic splitting was
demonstrated. The simulation mimicked pulse shaping of a Spatial Light Modulator (SLM) and the interaction was
described with the Von Neumann equation. A transform limited pulse with a fluence of 600 J/m<sup>2</sup> produced 18% of the
population in an arbitrarily chosen upper vibrational state, n =2. Phase only and amplitude only shaped pulse produced
optimum values of 60% and 40% respectively, of the population in the vibrational state, n=2, after interaction with the
ultra short pulse. The combination of phase and amplitude shaping produced the best results, 80% of the population was
in the targeted vibrational state, n=2, after interaction. These simulations were carried out with all the population initially
in the ground vibrational level. It was found that even at room temperatures (300 Kelvin) that the population in the
selected level is comparable with the case where all population is initially in the ground vibrational state. With a 10%
noise added to the amplitude and phase masks, selective excitation of the targeted vibrational state is still possible.
We present a study of dynamical decoupling schemes for the suppression of phase errors from various noise
environments using ions in a Penning trap as a model ensemble of qubits. By injecting frequency noise we
demonstrate that in an ohmic noise spectrum with a sharp, high-frequency cutoff the recently proposed UDD
decoupling sequence gives noise suppression superior to the traditional CPMG technique. Under only the influence
of ambient magnetic field fluctuations with a 1/ω<sup>4</sup> power spectrum, we find little benefit from using the
UDD sequence, consistent with theoretical predictions for dynamical decoupling performance in the presence of
noise spectra with soft cutoffs. Finally, we implement an optimization algorithm using measurement feedback,
demonstrating that local optimization of dynamical decoupling can further lead to significant gains in error
suppression over known sequences.