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

Nuclear Magnetic Resonance (NMR) B0 V μB 0 H = -  B = -  ħI z B z  E = ħ  L where  L =  B z = kBTkBT P = N  – N  N  + N  Polarization (I = ½):

NMR of Frozen Xenon Oscillating voltage Signal Magnitude  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 > T 2 ). INTERESTING PHYSICS. NOTE  Beats present in FID  Local fields causing periodic oscillations in the long-time regime. (?!) Why Study Transverse Decay?

A Prediction based on Chaos *B. V. Fine, Phys. Rev. Lett. 94, (2005). 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. 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 T 2 ). Signals large enough that sufficient signal remains after a few times T 2 Ability to give the spins different initial spin configurations Quantum spin system (S=1/2) WHAT DO WE NEED TO TEST THIS THEORY?

 Quantum system  With special techniques (SEOP) we produce 100,000x higher signal than you’d normally expect.  Isotopically enriched Xe (86% 129 Xe)  Freeze it as polycrystalline solid at 77 K. (Hyperpolarization survives phase transition!)  Apply a 90  pulse. Extreme SNR NMR T2T2 Long-time regime BIG Signals!

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

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. Solid echoes with different delay times give different initial spin conditions Growth of multiple-spin correlations in CaF 2 FID. H. Cho, et al., Phys. Rev. B 72, (2005).

Produced by phase exchange in a convection cell. Liquid hyperpolarized 129 Xe *T. Su, G.L. Samuelson, S.W. Morgan, G. Laicher, and B. Saam, App. Phys. Lett. 85, 2429 (2004). Acquire FID and several solid echoes with different interpulse delay times τ and compare the behavior of the transverse NMR decays at times > T 2.

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

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

Similar Results for Other Lattices  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 Natural Xenon (26% 129 Xe, 21% 131 Xe) Isotopic Mix of Xenon (30% 129 Xe, 70% 131 Xe)

An Interesting Time Scale  Conventional long-time exponential behavior requires that “long times” be much larger (orders of magnitude) than 1/T 2.  Here, γ and ω are both on the order of 1/T 2. Behavior appears to be outside the realm of conventional statistical physics. T2T2

Summary Chaos-based theory provides compelling explanation for behavior that is beyond the scope of conventional statistical physics. Faculty Brian Saam David Ailion Gernot Laicher Graduate Students Eric Sorte Zayd Ma Undergraduates Laurel Hales Haleigh Van Eerden