  The sampled negative energy density seen by inertial observers, in arbitrary
quantum states is limited by quantum inequalities, which take the form of an
inverse relation between the magnitude and duration of the negative energy. The
quantum inequalities severely limit the utilization of negative energy to
produce gross macroscopic effects, such as violations of the second law of
thermodynamics. The restrictions on the sampled energy density along the
worldlines of accelerated observers are much weaker than for inertial
observers. Here we will illustrate this with several explicit examples. We
consider the worldline of a particle undergoing sinusoidal motion in space in
the presence of a single mode squeezed vacuum state of the electromagnetic
field. We show that it is possible for the integrated energy density along such
a worldline to become arbitrarily negative at a constant average rate. Thus the
averaged weak energy condition is violated in these examples.This can be the
case even when the particle moves at non-relativistic speeds. We use the
Raychaudhuri equation to show that there can be net defocussing of a congruence
of these accelerated worldlines. This defocussing is an operational signature
of the negative integrated energy density. These results in no way invalidate
nor undermine either the validity or utility of the quantum inequalities for
inertial observers. In particular, they do not change previous constraints on
the production of macroscopic effects with negative energy, e.g., the
maintenance of traversable wormholes.
