Quantum metrology for relativistic quantum fields

In quantum metrology quantum properties such as squeezing and entanglement are exploited in the design of a new generation of clocks, sensors and other measurement devices that can outperform their classical counterparts. Applications of great technological relevance lie in the precise measurement of parameters which play a central role in relativity, such as proper accelerations, relative distances, time and gravitational field strengths. In this paper we generalize recently introduced techniques to estimate physical quantities within quantum field theory in flat and curved space-time. We consider a bosonic quantum field that undergoes a generic transformation, which encodes the parameter to be estimated. We present analytical formulas for optimal precision bounds on the estimation of small parameters in terms of Bogoliubov coefficients for single-mode and two-mode Gaussian channels.

Figure 1

Quantum Fisher information vs $u=\frac{h\tau }{4L\mathrm{arctanh}(h/2)}$ for modes $k=1$ and $k^{\prime }=2$ when the initial state is only squeezed $x=0$, only displaced $x=1$ and with an equal amount of energy associated to squeezing and displacement $x=0.5$.

Figure 2

Quantum Fisher information vs $u=\frac{h\tau }{4L\mathrm{arctanh}(h/2)}$ for three different initial states of the cavity with the same average energy. A single-mode squeezed state in mode $k=1$ (solid black line), two single-mode squeezed states in a product form in modes $k=1$ and $k^{\prime }=2$ (dotted red line) and a two-mode squeezed state in modes $k=1$ and $k^{\prime }=2$ (dashed blue line).