Quantum metrology and estimation of Unruh effect

Abstract

We study the quantum metrology for a pair of entangled Unruh-Dewitt detectors when one of them is accelerated and coupled to a massless scalar field. Comparing with previous schemes, our model requires only local interaction and avoids the use of cavities in the probe state preparation process. We show that the probe state preparation and the interaction between the accelerated detector and the external field have significant effects on the value of quantum Fisher information, correspondingly pose variable ultimate limit of precision in the estimation of Unruh effect. We find that the precision of the estimation can be improved by a larger effective coupling strength and a longer interaction time. Alternatively, the energy gap of the detector has a range that can provide us a better precision. Thus we may adjust those parameters and attain a higher precision in the estimation. We also find that an extremely high acceleration is not required in the quantum metrology process.I t is well known that a uniformly accelerated detector which interacts with external fields becomes excited in the Minkowski vacuum. This effect is named as Unruh effect 1,2 , which indicates the fact that quantum properties of fields is observer dependent 3-9 . However, despite its crucial role in modern theoretical physics, the experimental detection of the Unruh radiation remains an open research program on date. The main technical obstacle is that the Unruh temperature for the current experimental realizable acceleration lies far below the observable threshold of temperature. More specifically, the Unruh temperature is smaller than 1 Kelvin even for accelerations up to 10 21 m/s 2 2,10,11 . On the other hand, quantum metrology 12 aims to study the bounds of the estimation precision and the quantum strategies that can attain them. The estimation is based on measurements made on a probe system that undergoes an evolution depending on the estimated parameters. For a classical metrology scheme, the effect of statistical errors can be reduced by repeating the measurements and averaging the outcomes. Furthermore, by using some quantum resources and taking into account laws of quantum mechanics, the precision can be enhanced. More specifically, the mean variance of the errors for a given measurement on the parameter h is bounded by the Cramér-Rao inequality 13 Var h ð Þ § nF j h ð Þ ½ {1 , where n is the number of identical measurements repeated and F j h ð Þ is the Fisher information (FI) for a given measurement scheme. Moreover, by optimizing over all the possible set of quantum measurements, the ultimate limit on the variance is set by the quantum Cramér-Rao bound Var h ð Þ § nF Q h ð Þ ½ {1 , where F Q h ð Þ §F j h ð Þ is the quantum Fisher information (QFI). Recently, the adaptation of quantum metrology to improve probing technologies of relativistic effects has been preceded by several pioneering works in different contexts, see for example [14][15][16][17][18][19][20][21][22] . These studies are of great importance for the observation of ...

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