Error-corrected quantum metrology of microwaves with a Rydberg sensor*

Rydberg atoms are execellent sensors in the microwave to mm-wave domain, reaching levels of sensitivity that are of great interest both from fundamental and practical reasons. In a typical configuration, they act as indidual sensors and interaction between atoms usually degrade the performance of the sensor. On the other hand, Rydberg interactions are now widely used in quantum computing and simulations.

We present a metrology protocol in which we exploit the interactions between atoms to correct errors that inevitably occur between sensing and detection of light emitted by the atomic ensemble. We prepare Rydberg atoms in a D orbital state and use a microwave field at 20 GHz to perform a Rabi rotation by a small angle θ to a P orbital state. We aim to estimate the angle of this rotation, which in turn is proportional to the intensity of the incident electromagnetic field. We read-out coherent Rydberg excitations from the atomic ensemble, such that the number of read-out photons is proportional to the number of atoms in the D state. However, losses between the ensemble and the photon detector induce errors which limit the achievable Fisher information F_θ to ηF_θ^Q, i.e. the quantum Fisher information multiplied by system efficiency. We show that by allowing interaction between atoms before the read-out, we are able to beat this quasi-fundamental bound.

The interaction that we use is a lossy many-body interaction which removes P-D pairs of excitations from the system via the Rydberg dipole exchange with the rate of C₃/r³ . This loss, surprisingly, increases the Fisher information by reducing the extent of quantum space the original state decays to. In the experiment, we were able to show more than a twofold increase in the information gained about the paramter θ. Our work shows a very practical application of a feasible quantum error correction protocol applied in quantum metrology.