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The collisional frequency shift of a trapped-ion optical clock
Collisions with background gas can perturb the transition frequency of
trapped ions in an optical atomic clock. We develop a non-perturbative
framework based on a quantum channel description of the scattering process, and
use it to derive a master equation which leads to a simple analytic expression
for the collisional frequency shift. As a demonstration of our method, we
calculate the frequency shift of the Sr optical atomic clock transition due
to elastic collisions with helium
Displacement operators: the classical face of their quantum phase
In quantum mechanics, the operator representing the displacement of a system
in position or momentum is always accompanied by a path-dependent phase factor.
In particular, two non-parallel displacements in phase space do not compose
together in a simple way, and the order of these displacements leads to
different displacement composition phase factors. These phase factors are often
attributed to the nonzero commutator between quantum position and momentum
operators, but such a mathematical explanation might be unsatisfactory to
students who are after more physical insight. We present a couple of simple
demonstrations, using classical wave mechanics and classical particle
mechanics, that provide some physical intuition for the phase associated with
displacement operators.Comment: 14 pages, 4 figures, reorganized and reformatte
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