2,775 research outputs found
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 -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 thermal fermionic alkaline-earth atoms in a flat-bottom trap
allow one to robustly implement a spin model displaying two symmetries: the
symmetry that permutes atoms occupying different vibrational levels of
the trap and the SU() symmetry associated with 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()
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
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