Beyond the Spin Model Approximation for Ramsey Spectroscopy

Ramsey spectroscopy has become a powerful technique for probing non-equilibrium dynamics of internal (pseudospin) degrees of freedom of interacting systems. In many theoretical treatments, the key to understanding the dynamics has been to assume the external (motional) degrees of freedom are decoupled from the pseudospin degrees of freedom. Determining the validity of this approximation -- known as the spin model approximation -- is complicated, and has not been addressed in detail. Here we shed light in this direction by calculating Ramsey dynamics exactly for two interacting spin-1/2 particles in a harmonic trap. We focus on $s$-wave-interacting fermions in quasi-one and two-dimensional geometries. We find that in 1D the spin model assumption works well over a wide range of experimentally-relevant conditions, but can fail at time scales longer than those set by the mean interaction energy. Surprisingly, in 2D a modified version of the spin model is exact to first order in the interaction strength. This analysis is important for a correct interpretation of Ramsey spectroscopy and has broad applications ranging from precision measurements to quantum information and to fundamental probes of many-body systems

Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms

We show that $n$ thermal fermionic alkaline-earth atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the $S_n$ symmetry that permutes atoms occupying different vibrational levels of the trap and the SU($N$) symmetry associated with $N$ nuclear spin states. The high symmetry makes the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU($N$) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary non-thermal distribution.Comment: 12 pages, 5 figures (including supplemental materials

Flavor-singlet light-cone amplitudes and radiative Upsilon decays in SCET

We study the evolution of flavor-singlet, light-cone amplitudes in the soft-collinear effective theory (SCET), and reproduce results previously obtained by a different approach. We apply our calculation to the color-singlet contribution to the photon endpoint in radiative Upsilon decay. In a previous paper, we studied the color-singlet contributions to the endpoint, but neglected operator mixing, arguing that it should be a numerically small effect. Nevertheless the mixing needs to be included in a consistent calculation, and we do just that in this work. We find that the effects of mixing are indeed numerically small. This result combined with previous work on the color-octet contribution and the photon fragmentation contribution provides a consistent theoretical treatment of the photon spectrum in radiative Upsilon decay.Comment: 19 pages with 8 figure