Fundamental limits of Spectroscopy with Quantum Light*

Spectroscopy with quantum light is a newly emerging field in which the quantum nature of
light is exploited to reveal information about the properties of matter. Although there is
evidence that spectroscopy with quantum light has advantages compared to classical
spectroscopic methods, this advantage has not been quantified. By using the techniques
of Quantum Estimation Theory (QET) we quantify this advantage for the estimation of
parameters of matter. We obtain the ultimate precision limit for the estimation of the
dipole moment of the atoms when they interact with different states of quantum light,
namely non-classical and entangled light, and we compare their performance. We also
calculate the precision that can be achieved by different measurement techniques and
compare them with the fundamental quantum limit. This allows the identification of the
best current measuring scheme and it motivates the search for better detection systems
that can achieve the ultimate precision.