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Spectroscopy methods with quantum sensors


  Tuvia Gefen [1]  ,  Amit Rotem [1]  ,  Simon Schmitt [2]  ,  Liam P. McGuinness [2]  ,  Fedor Jelezko [2]  ,  Alex Retzker [1]  
 [1] Racah Institute of Physics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel
[2] Institute of Quantum Optics, Ulm University, 89081 Ulm, Germany

We consider the problem of quantum spectroscopy, namely reconstruction of the frequency components of a time dependent Hamiltonian. This task is of great interest to
 chemical analysis, nano-scale NMR and frequency standards. We examine theoretically and experimentally the following question: Given an oscillating Hamiltonian, 
what is the best achievable precision in detecting the frequencies of this Hamiltonian. It turns out that some misconceptions have led to suboptimal techniques and 
a considerable improvement can be introduced. This observation was demonstrated experimentally with a new technique. We find that the precision of the frequency
tracking scales as 1/T1.5, while for long enough probe coherence time an optimal scaling of 1/T2 is achievable (with a suitable control). We  show that these control methods 
basically give rise to an accelerated phase accumulation, which results in an enhanced precision. Relevance to nano-scale NMR and future challenges will be discussed.