Ph.D Thesis

Ph.D StudentElias Yuval
SubjectExperimental Heat-Bath Cooling of Spins
DepartmentDepartment of Chemistry
Supervisors ASSOCIATE PROF. Tal Mor
Full Thesis textFull thesis text - English Version


Heat-bath algorithmic cooling (AC) is a technique to enhance the signal strength in Nuclear Magnetic Resonance (NMR), by generating ensembles of highly polarized spins; spin-half nuclei in a constant magnetic field are considered bits (more precisely, quantum bits), in a known probability distribution, and algorithmic steps on these bits are translated into NMR pulse sequences using common tools of NMR quantum computation.

AC combines entropy-preserving manipulations, borrowed from data compression algorithms, with selective reset that transfers entropy from selected spins to the surrounding heat-bath. In theory,  for large spins systems, this combined set of actions may increase spin polarization far beyond the Shannon entropy-conservation bound.

Experimental realization of AC in liquid NMR requires spin systems with both rapid and slow relaxation. For commercially-available 13C-labeled trichloroethylene (TCE) in organic solvent, we found significantly faster T1 relaxation for the proton, and improved the 13C/1H T1 ratios further by adding a Cr-based paramagnetic reagent. We

implemented two consecutive steps of selective reset, transferring entropy from both labeled carbons to the heat-bath. We performed such heat-bath cooling (HBC) experiments on standard NMR spectrometers and obtained polarizations beyond the Shannon bound.

HBC and AC might be useful for in vivo 13C brain spectroscopy, which follows prolonged metabolic processes where substrates that are hyperpolarized ex-vivo are not effective. We applied HBC to 1,2-13C2-amino acids using the alpha protons to shift entropy from selected carbons to the environment. For glutamate, commonly observed in vivo in

the brain, and glycine, both carbons were cooled by about 2.5-fold. In other experiments, the total entropy of each spin system was shown to decrease. We investigated the effect of adding Magnevist, a gadolinium contrast agent, on HBC of glutamate, after finding that it improved 13C/1H T1 ratios in 13C-labeled glucose by 2-3-fold.

On the road to AC, we evaluated and developed cooling algorithms and studied limitations and prospects. We analyzed optimal AC for improving the signal of nuclear spins, and found that signal averaging is sometimes more efficient. AC and HBC may be safely applied in vivo for spectral editing, whereby 13C signals of particular metabolites are selectively enhanced.

Recently, Yosi Atia (with my guidance) used high fidelity radio-frequency pulses obtained by quantum optimal control to successfully run multiple cycles of AC with TCE. Similar results were obtained earlier in Canada in solid state NMR using malonic acid, where rapid proton repolarization enabled efficient HBC of the three labeled carbons.