In the last years several estimation strategies have been formulated to
determine the value of an unknown parameter in the most precise way, taking
into account the presence of noise. These strategies typically rely on the use
of quantum entanglement between the sensing probes and they have been shown to
be optimal in the asymptotic limit in the number of probes, as long as one
performs measurements on shorter and shorter time scales. Here, we present a
different approach to frequency estimation, which exploits quantum coherence in
the state of each sensing particle in the long time limit and is obtained by
properly engineering the environment. By means of a commonly used master
equation, we show that our strategy can overcome the precision achievable with
entanglement-based strategies for a finite number of probes. We discuss a
possible implementation of the scheme in a realistic setup that uses trapped
ions as quantum sensors.Comment: 11+3 pages, 2 figure
