  We introduce and demonstrate a scheme for eliminating the inhomogeneous
dephasing of a collective quantum state. The scheme employs off-resonant fields
that continuously dress the collective state with an auxiliary sensor state,
which has an enhanced and opposite sensitivity to the same source of
inhomogeneity. We derive the optimal conditions under which the dressed state
is fully protected from dephasing, when using either one or two dressing
fields. The latter provides better protection, circumvents qubit phase
rotation, and suppresses the sensitivity to drive noise. We further derive
expressions for all residual, higher-order, sensitivities. We experimentally
study the scheme by protecting a collective excitation of an atomic ensemble,
where inhomogeneous dephasing originates from thermal motion. Using photon
storage and retrieval, we demonstrate complete suppression of inhomogeneous
dephasing and consequently a prolonged memory time. Our scheme may be applied
to eliminate motional dephasing in other systems, improving the performance of
quantum gates and memories with neutral atoms. It is also generally applicable
to various gas, solid, and engineered systems, where sensitivity to variations
in time, space, or other domains limits possible scale-up of the system.
