Ramsey interferometry of non-Hermitian quantum impurities

We introduce a Ramsey pulse scheme which extracts the non-Hermitian Hamiltonian associated with an arbitrary Lindblad dynamics. We propose a related protocol to measure via interferometry a generalized 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 become 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-atom systems.