Eric Sorte University of Utah Department of Physics

1. Generic Long-Time Relaxation Behavior of A Nuclear Spin Lattice Eric Sorte University of Utah Department of Physics

2. B0 V Polarization (I = ½): H= -• B= -ħIzBz N – N  P = = μB0 N + N  kBT E= ħLwhereL=  Bz Nuclear Magnetic Resonance (NMR)

3. NMR of Frozen Xenon Why Study Transverse Decay? • Details of transverse-decay spectrum can yield important information about the microscopic nature of these interactions. • The theoretical shape is non-trivial and exceedingly difficult to calculate, particularly in the long-time regime (t > T2). INTERESTING PHYSICS. NOTE • Beats present in FID • Local fields causing periodic oscillations in the long-time regime. (?!) Signal Magnitude Oscillating voltage

4. Appeals to chaos theory yield predictions for the long-time behavior of the NMR free-induction decay and solid echo: …and any and all initial spin configurations should approach this shape. *B. V. Fine, Phys. Rev. Lett. 94, 247601 (2005). A Prediction based on Chaos If spins in a given lattice are measured starting from different spin configurations, they will all approach this late time behavior after sufficient time has passed (a few times T2). WHAT DO WE NEED TO TEST THIS THEORY? • Quantum spin system (S=1/2) • Signals large enough that sufficient signal remains after a few times T2 • Ability to give the spins different initial spin configurations

5. T2 Extreme SNR NMR • Quantum system • With special techniques (SEOP) we produce 100,000x higher signal than you’d normally expect. • Isotopically enriched Xe (86% 129Xe) • Freeze it as polycrystalline solid at 77 K. (Hyperpolarization survives phase transition!) • Apply a 90 pulse. Long-time regime BIG Signals!

6. Spin Echoes in Solids Showing the decay envelopes. • Solid echoes (Powles and Mansfield 1962): 90ºx - τ - 90ºy - detect • Solid echoes only PARTIALLY refocus spins that are dephased by dipole-dipole interactions and do not generally peak at time 2τ. • Degree of refocusing depends on τ.

7. Multiple-spin correlations in FID & echoes • Solid echo works “perfectly” for spins 1/2 taken as pairs. • In a real system, 3-spin, 4-spin, etc. interactions affect the evolution of coherence for longer and longer times τ. Growth of multiple-spin correlations in CaF2 FID. H. Cho, et al., Phys. Rev. B 72, 054427 (2005). Solid echoes with different delay times give different initial spin conditions

8. Liquid hyperpolarized 129Xe Produced by phase exchange in a convection cell. Acquire FID and several solid echoes with different interpulse delay times τ and compare the behavior of the transverse NMR decays at times > T2. *T. Su, G.L. Samuelson, S.W. Morgan, G. Laicher, and B. Saam, App. Phys. Lett. 85, 2429 (2004).

9. Results in enriched solid 129Xe* • Echoes shown starting at delay time τau from start of FID. • Each echo represents a distinct initial transverse spin state.

10. Generic Long-Time Behavior Data are fit (red line) to: • Generic long-time behavior: γ and ωhave same value for all 4 initial spin configurations. Compare to initial behavior.

11. Similar Results for Other Lattices Natural Xenon (26% 129Xe, 21% 131Xe) Isotopic Mix of Xenon (30% 129Xe, 70% 131Xe) • Only one echo (with relatively short τ) could be acquired to compare to FID; SNR issues for larger τ. • Work is progressing on other lattices

12. T2 An Interesting Time Scale • Conventional long-time exponential behavior requires that “long times” be much larger (orders of magnitude) than 1/T2. • Here, γandω are both on the order of 1/T2. Behavior appears to be outside the realm of conventional statistical physics.

13. FacultyBrian SaamDavid AilionGernot Laicher Graduate StudentsEric SorteZayd Ma UndergraduatesLaurel HalesHaleigh Van Eerden Summary Chaos-based theory provides compelling explanation for behavior that is beyond the scope of conventional statistical physics.