  We introduce a Ramsey pulse scheme which extracts the non-Hermitian
Hamiltonian associated to an arbitrary Lindblad dynamics. We propose a realted
protocol to measure via interferometry a generalised Loschmidt echo of a
generic state evolving in time with the non-Hermitian Hamiltonian itself, and
we apply the scheme to a one-dimensional weakly interacting Bose gas coupled to
a stochastic atomic impurity. The Loschmidt echo is mapped into a functional
integral from which we calculate the long-time decohering dynamics at arbitrary
impurity strengths. For strong dissipation we uncover the phenomenology of a
quantum many-body Zeno effect: corrections to the decoherence exponent
resulting from the impurity self-energy becomes purely imaginary, in contrast
to the regime of small dissipation where they instead enhance the decay of
quantum coherences. Our results illustrate the prospects for experiments
employing Ramsey interferometry to study dissipative quantum impurities in
condensed matter and cold atoms systems.
