Entangled states of spin and clock oscillators

Measurements of one quadrature of an oscillator with precision beyond its vacuum state uncertainty have occupied a central place in quantum physics for decades. We have recently reported the first experimental implementation of such measurement with a magnetic oscillator [1]. However, a much more intriguing goal is to trace an oscillator trajectory with the precision beyond the vacuum state uncertainty in \textit{both} position and momentum, a feat naively assumed not possible due to the Heisenberg uncertainty principle. We have demonstrated that such measurement is possible if the oscillator is entangled with a quantum reference oscillator with an effective negative mass [2,3]. The key element is the cancellation of the back action of the measurement on the composite system of two oscillators. Applications include measurements of e.-m. fields, accelleration, force and time [4] with practically unlimited accuracy. In a more general sense, this approach leads to trajectories without quantum uncertainties and to achieving new fundamental bounds on the measurement precision. \begin{enumerate} \item G. Vasilakis et al. \textit{Nature} \quad \textit{Phys}$.$, ~(2015) doi:10.1038/nphys3280. \item K. Hammerer et al. \textit{Phys. Rev. Lett.} 102, 020501 (2009). \item E.S. Polzik and K.Hammerer. \textit{Annalen der Physyk}. 527, No. 1--2, A15--A20 (2015). \item E. S. Polzik and J. Ye. doi: 10.1103/PhysRevA.93.021404 (2016). \end{enumerate}