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Classical and Quantum Gravity

Parameter estimation in cosmic string spacetime by using the inertial and accelerated detectors

Ying Hua Yang, Jieci Wang, Mengjie Wang, Jiliang Jing, Zehua Tian

Published Jan 24, 2020• 6 citations
Publisher

Abstract

Abstract Since cosmic string spacetime is locally flat but with nontrivial global topology characterized by a deficit angle, we devote to address the quantum bound to the estimation of the deficit angle parameter by using a two-level atom as a detector which is coupled to a massless scalar field. We show that the initial excited state of the detector is the optimal state, and quantum precision always obtains the maximum value when the detector evolves for a limited time. We find that the sensitivity in the predictions for the deficit angle parameter decreases with the increase of . We also note that a uniform, rectilinear accelerated motion does not improve the estimation accuracy, so we obtain the inertial detector is better than the uniform, rectilinear accelerated detector. Therefore, we provide a possibility for detecting the nontrivial global topology in the spacetime.

DOI
10.1088/1361-6382/ab6f73

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Abstract Since cosmic string spacetime is locally flat but with nontrivial global topology characterized by a deficit angle, we devote to address the quantum bound to the estimation of the deficit angle parameter by using a two-level atom as a detector which is coupled to a massless scalar field. We show that the initial excited state of the detector is the optimal state, and quantum precision always obtains the maximum value when the detector evolves for a limited time. We find that the sensitivity in the predictions for the deficit angle parameter decreases with the increase of . We also note that a uniform, rectilinear accelerated motion does not improve the estimation accuracy, so we obtain the inertial detector is better than the uniform, rectilinear accelerated detector. Therefore, we provide a possibility for detecting the nontrivial global topology in the spacetime.
Abstract Quantum metrology studies the ultimate precision limit of physical quantities by using quantum strategy. In this paper we apply the quantum metrology technologies to the relativistic framework for estimating the deficit angle parameter of cosmic string spacetime. We use a two-level atom coupled to electromagnetic fields as the probe and derive its dynamical evolution by treating it as an open quantum system. We estimate the deficit angle parameter by calculating its quantum Fisher information(QFI). It is found that the quantum Fisher information depends on the deficit angle, evolution time, detector initial state, polarization direction, and its position. We then identify the optimal estimation strategies, i.e., maximize the quantum Fisher information via all the associated parameters, and therefore optimize the precision of estimation. Our results show that for different polarization cases the QFIs have different behaviors and different orders of magnitude, which may shed light on the exploration of cosmic string spacetime.
The presence of a cosmic string modifies vacuum fluctuations, making the evolution of a two-level polarizable atom position-dependent. Such modifications produce effects on the atomic dynamics analogous to those induced by a reflecting boundary. We show that these quantum boundary effects can be estimated by performing a sequence of NNN measurements on a single probe atom. For a fixed total probe time, the precision limit is attained by preparing each probe in its optimal initial state, performing the corresponding optimal measurement, and shortening the probe time of each probe. The optimal measurement is uniquely determined by the probe's initial state, and the precision limit obtained with the atom initially in the excited state is four times higher than that for an equal-weight superposition state. The estimation precision displays damped oscillatory behavior as the atom-boundary or atom-string separation increases. In the boundary case, the optimal polarization is always parallel to that boundary. In cosmic-string spacetime, by contrast, the optimal polarization is along the azimuthal direction around the string. The relative advantage of the other polarization directions depends on both the atom-string separation and the deficit angle. For small deficit angles and sufficiently large separations, radial polarization perpendicular to the string becomes less favorable than the other directions.
Abstract We analyze the quantum Fisher information (QFI) for a particle detector coupled to a thermal electromagnetic field in the cosmic string spacetime. It is found that vacuum fluctuation, temperature, detector polarization and nontrivial spacetime topology affect the QFI. Vacuum fluctuation and temperature degrade QFI. When deficit angle parameter ν = 1 and detector is far away from the string, the results in free Minkowski spacetime are restored. When detector is close to the string, QFI can be effectively enhanced; specially when detector lies in the string and is not polarized along axial direction, the detector seems like a closed system, and QFI completely is not affected by the thermal electromagnetic fluctuation. For nonzero detector–string distance, QFI appears oscillatory behaviors as detector–string distance varies. In addition, this detector eventually evolves to a thermal state, which is not related to the initial state and other various parameters, which implies QFI cannot persist in for long evolution time in the cosmic string spacetime. In principle, the detector polarization, detector–string distance, temperature and deficit angle parameter provide us with more parameters to steer the QFI behaviors, which might be helpful to enhance the precision of sensing the characters of cosmic string spacetime.
We probe the κ\kappa κ -deformation of spacetime using a two-level atom as a detector coupled to a κ\kappa κ -deformed massless scalar field which is invariant under a κ\kappa κ -Poincaré algebra and written in commutative spacetime. To address the quantum bound to the estimability of the deformation parameter κ\kappa κ , we perform measurements on the two-level detector and maximize the value of quantum Fisher information over all possible detector preparations. We prove that the population measurement is the optimal measurement in the estimation of the deformation parameter κ\kappa κ . In particular, we show that the relativistic motion of the detector affects the precision in the estimation of the parameter κ\kappa κ , which can effectively improve this precision comparing to that of the static detector case by many orders of magnitude.
Quantum metrology studies the ultimate limit of precision in estimating a physical quantity if quantum strategies are exploited. Here we investigate the evolution of a two-level atom as a detector which interacts with a massless scalar field using the master equation approach for open quantum system. We employ local quantum estimation theory to estimate the Unruh temperature when probed by a uniformly accelerated detector in the Minkowski vacuum. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over all possible detector preparations and evolution times, and compare its behavior with that of the quantum Fisher information (QFI). We find that the optimal precision of estimation is achieved when the detector evolves for a long enough time. Furthermore, we find that in this case the FI for population measurement is independent of initial preparations of the detector and is exactly equal to the QFI, which means that population measurement is optimal. This result demonstrates that the achievement of the ultimate bound of precision imposed by quantum mechanics is possible. Finally, we note that the same configuration is also available to the maximum of the QFI itself.
Abstract We study the entanglement dynamics of two static atoms coupled with a bath of fluctuating scalar fields in vacuum in the cosmic string spacetime. Three different alignments of atoms, i.e. parallel, vertical, and symmetric alignments with respect to the cosmic string are considered. We focus on how entanglement degradation and generation are influenced by the cosmic string, and find that they are crucially dependent on the atom-string distance r, the interatomic separation L, and the parameter ν\nu ν ν that characterizes the nontrivial topology of the cosmic string. For two atoms initially in a maximally entangled state, the destroyed entanglement can be revived when the atoms are aligned vertically to the string, which cannot happen in the Minkowski spacetime. When the symmetrically aligned two-atom system is initially in the antisymmetric state, the lifetime of entanglement can be significantly enhanced as ν\nu ν ν increases. For two atoms which are initially in the excited state, when the interatomic separation is large compared to the transition wavelength, entanglement generation cannot happen in the Minkowski spacetime, while it can be achieved in the cosmic string spacetime when the position of the two atoms is appropriate with respect to the cosmic string and ν\nu ν ν is large enough.