Eric Sorte
            Major Research Projects
Manifestations of Chaos in Spin Systems:
Nuclear magnetic resonance (NMR) has yielded valuable information to researchers for over five decades.  Motivations for manipulating the magnetic nuclear states of atoms range widely and cover a vast array of disciplines and applications.  In the many-body systems of interest in NMR, the description of the spin-spin relaxation in the solid state is usually treated in the formulation of infinite temperature spin correlation functions according to the rules of statistical physics.  The disquieting fact is, however, that despite the ubiquitous applications of the methods and results of NMR, and despite its importance as a source of microscopic information in many investigations, the accuracy of first principle calculations of measured quantities continues to be severely limited despite extensive work on the subject.  In fact, many results have been obtained that according to conventional theories seem impossible.  While many theories have been postulated to predict the behavior of the ensemble magnetization of spin-correlated systems under various manipulations, none has ever fully succeeded in providing an accurate formalism for predicting measurements directly from a microscopic treatment of the many-body spin dynamics.  The long-time properties of the spin correlation functions have been particularly resistant to explanations based on conventional statistical methods.
One of my collaborators, Boris Fine, has proposed a theory based on a conjecture of chaotic mixing in quantum spin systems to model these free induction decays.  The theory asserts that a Brownian-like Markovian treatment can be used to describe the long-time behavior of ensemble-averaged quantities on a non-Markovian timescale.  Based on this assertion, the theory makes the specific prediction that a universal behavior, independent of the initial spin configurations, will dominate the long-time behavior of the spin correlation function.  Additionally, the proposed model makes predictions for the amplitude and phases of manipulated spin-coherences relative to the free induction decay of the spin system.
My first peer-reviewed publication on this subject (Phys. Rev. B) was to characterize the free-induction decays (FID’s) and various spin echoes of  CaF2 and 129Xe in solid phase and compare them to the proposed model.  Hyperpolarization of 129Xe affords such enormous signal intensity that precise characterization of the NMR transverse decay is possible over a range of more than 5 orders of magnitude.  Previous results from our group have indeed shown a universal behavior in the long-time tail of the FID and several solid echoes in remarkable agreement with a form predicted by the model proposed by our collaborator.  This work focused on characterizing the decays as a function of the isotopic concentration of 129Xe.  I have been studying seven different systems, distinguishable by the relative concentrations of various isotopes of xenon, and investigating their behavior under various spin manipulations. These systems vary in concentrations of 129Xe from 86% to 26%.  The rest of the lattice is made up of varying concentrations of 131Xe and spinless isotopes.  The transverse decay of the NMR signal is wholly determined by the interactions between nuclear spins, which to first order is magnetic dipole interaction.  Therefore, manipulating the relative abundances of the isotopes systematically allows a full exploration of the universal long time behavior and its underlying causes.  In essence, we can “tune” the distances between magnetically active and magnetically passive isotopes, varying thereby the dipole interaction strength in each sample.  Observation and comparison of the decays in these distinct systems has generated a large body of data for the further development of the theory.  This work extends the body of data to other unique lattices that also exhibit the universal behavior predicted by the new theory, including single crystal calcium fluoride.
We have recently submitted three additional papers on this topic.  Two theoretical papers extend the model and explain additional predictions (including the ability to actually calculate the shapes of echoes based on the theory).   The third is an experimental paper that tests the new predications resulting from the model.
Noble-gas---Alkali metal frequency shifts:
In a different line of experiments, I have made the first accurate measurement of the Knight-shift in Rb-129Xe molecules.  This has been a long sought after measurement in the spin-exchange community because it provides a simple and robust means of measuring noble-gas polarizations unambiguously in a variety of situations, in particular in 129Xe flow-through polarizers.  The frequency shift can also help put quantitative constraints on the poorly understood Rb—noble-gas inter-atomic potentials.  An attempt to make this measurement was made 20 years ago, however, until now a precise measurement has eluded researchers.  Current polarimetry methods compare the intensity of the noble-gas signal to that of a water sample and attempt to thereby extrapolate the magnitude of the noble-gas polarization; such measurements are not very accurate.  With this number, one can make a direct and reliable measurement of noble-gas polarization by measuring a simple frequency.  This work has been submitted to Physical Review Letters.
Xenon polarimetry using moment expansion parameters:
Continuing on the theme of more accurate polarimetry, I am currently performing other experiments that explore the changes in NMR lineshapes away from the high-temperature limit.  As our ability to polarize solid xenon has continued to improve, we have begun  
to explore the  predicted polarization dependence of the first and second moments of the NMR lineshape.  A somewhat complicated acquisition scheme involving two spectrometers running in parallel and triggering one another's acquisitions has been devised to accommodate the experimental constraints of the experiment.  This experiment is designed, built, and preliminary data have been acquired.  This method will provide yet another simple means of noble-gas polarimetry.
Hyperfine effect in Organic Light Emitting Diodes:
Finally, in collaboration with Dr. Valy Vardeny I have been developing the experimental apparatus to measure extremely low spin-density spin-valve samples in an attempt to directly measure the 13C nuclear polarization enhancement due to injected carrier electrons into disordered organic devices.  These devices are manufactured as a 100 nm layer of organic (DOOPPV, MEHPPV, 13C enriched C60 ) sandwiched between ferromagnetic contacts.  Polarized charge carriers are injected into the organic layer, and angular momentum is then thought to be transferred to the nuclei via the hyperfine interaction, polarizing the nuclei above the thermal Boltzmann level.  The low spin-density (~1015 nuclear spins) makes this a challenging experiment for NMR.  We have obtained preliminary data demonstrating the feasibility of the experiment, and have applied for a grant for further work based on those results.