Abstract
We consider the estimation of a Hamiltonian parameter of a set of highly photosensitive samples, which are damaged after a few photons Nabs are absorbed, for a total time T. The samples are modelled as a two mode photonic system, where photons simultaneously acquire information on the unknown parameter and are absorbed at a fixed rate. We show that arbitrarily intense coherent states can obtain information at a rate that scales at most linearly with Nabs and T, whereas quantum states with finite intensity can overcome this bound. We characterise the quantum advantage as a function of Nabs and T, as well as its robustness to imperfections (non-ideal detectors, finite preparation and measurement rates for quantum photonic states). We discuss an implementation in cavity QED, where Fock states are both prepared and measured by coupling atomic ensembles to the cavities. We show that superradiance, arising due to a collective coupling between the cavities and the atoms, can be exploited for improving the speed and efficiency of the measurement.
Highlights
One exciting prospect of quantum technologies are more precise photonic measurements through the use of quantum correlations [1,2,3,4,5]
Given a fixed photon number N, a variety of quantum states surpasses the shot-noise limit imposed by coherent states, notably squeezed, NOON or twin Fock states [6,7,8]
The FC has been considered for more realistic photon number-resolved measurements (NRM) [68, 70,71,72], and we study it in the Poisson limit in Sec
Summary
One exciting prospect of quantum technologies are more precise photonic measurements through the use of quantum correlations [1,2,3,4,5]. We will show that constraining Nabs instead of N leads to qualitatively new results In frequency measurements, both the probe size (e.g. the number of photons N ) and the total time T are resources for quantum metrology [8, 20,21,22], and interesting interplays between both appear when the probe is subject to noise or decoherence [20,21,22,23,24,25,26,27]. In contrast to previous works (see, for example, [28]), we shall not put the constraint on N , but on the energy that the system can absorb (Nabs) This subtle difference turns out to have important consequences: quantum metrological protocols involving a small amount N ≈ 5 − 10 of photons and a finite amount of samples, can overcome classical strategies using coherent states of (potentially) arbitrary intensity and an arbitrarily large number of samples. We explore similar applications in the context of cavity or circuit QED, and we argue that the collective coupling can be exploited to increase the efficiency and speed of both the measurement and preparation of Fock states
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