In this thesis, I present an experimental study of quantum control techniques for transferring population between vibrational states of atoms trapped in an optical lattice. Results from a range of techniques are compared, including techniques tested previously in the same system.
In the study of the Adiabatic Rapid Passage (ARP) technique, control of population transfer is realized through varying the chirp rate and modulation amplitude of a frequency-chirped sinusoidal displacement of the lattice. Meanwhile, dependence of population transfer on the chirp direction is observed, which is explained by a model of ARP in a 3-level system.
In the study of the coherent control technique, interference between a one-phonon transition at 2\omega and a two-phonon transition at omega is experimentally demonstrated. The omega and 2\omega transitions are realized by sinusoidally displacing the optical lattice at omega and sinusoidally modulating the lattice depth at 2\omega, respectively. The branching ratio of transitions to the first excited state and to higher excited states is controlled by varying the relative phase between these two pathways. The highest measured branching ratio of 17\pm2 is achieved among all the experiments using this coherent control scheme.
In the study of the GRadient Ascent Pulse Engineering (GRAPE) technique, a "pulse" involving both displacement and depth-modulation of the lattice is used to transfer population. This pulse is theoretically engineered with the GRAPE algorithm to optimize the fidelity between the first excited state and the final state, when the lattice Hamiltonian without gravity for a specific lattice depth is considered. The experimental result shows that there is almost no excitation into higher excited states during population transfer from the ground to the first excited state, even when this process is affected by gravity and inhomogeneous broadening in reality.
By comparing all the techniques, the GRAPE technique is found to be the best in terms of increasing population transfer into the first excited state while reducing excitation into higher excited states. On the other hand, the ARP technique creates the highest normalized population inversion, a ratio of the difference to the sum of the ground and the first excited state populations.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/43764 |
| Date | 14 January 2014 |
| Creators | Zhuang, Chao |
| Contributors | Steinberg, Aephraim |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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