We investigate the ultimate estimation precision, characterized by the quantum Fisher information, of a two-level atom as a detector which is coupled to massless scalar field in the Minkowski vacuum. It has been shown that for an inertial detector moving with a constant velocity, its quantum Fisher information is completely unaffected by the velocity, however, it still decays over time due to the decoherence caused by the interaction between the atom and the field. In addition, for a uniformly accelerated detector ( $w=0$ ) moving along spatially straight line, the accelerated motion will reduce the quantum Fisher information in the estimation of state parameters. However, when the detector trajectory is generated by a combination of the linear accelerated motion and a component of the four-velocity $w=dy/d\ensuremath{\tau}$, we find quite unlike the previous results that, for the nonrelativistic case ($w\ensuremath{\ll}1$), the acceleration could degrade the quantum Fisher information, while the four-velocity component will suppress the degradation of the quantum Fisher information, and thus could enhance the precision of parameters estimation. Furthermore, in the case for ultrarelativistic velocities $(w\ensuremath{\rightarrow}\ensuremath{\infty})$, although the detector still interacts with the environment, it behaves as if it were a closed system as a consequence of relativity correction associated to the velocity, and the quantum Fisher information in this case can be shielded from the effect of the external environment, and thus from the relativistic motion.We investigate the ultimate estimation precision, characterized by the quantum Fisher information, of a two-level atom as a detector which is coupled to massless scalar field in the Minkowski vacuum. It has been shown that for an inertial detector moving with a constant velocity, its quantum Fisher information is completely unaffected by the velocity, however, it still decays over time due to the decoherence caused by the interaction between the atom and the field. In addition, for a uniformly accelerated detector ($w=0$) moving along spatially straight line, the accelerated motion will reduce the quantum Fisher information in the estimation of state parameters. However, when the detector trajectory is generated by a combination of the linear accelerated motion and a component of the four-velocity $w=dy/d\ensuremath{\tau}$, we find quite unlike the previous results that, for the nonrelativistic case ($w\ensuremath{\ll}1$), the acceleration could degrade the quantum Fisher information, while the four-velocity component will suppress the degradation of the quantum Fisher information, and thus could enhance the precision of parameters estimation. Furthermore, in the case for ultrarelativistic velocities $(w\ensuremath{\rightarrow}\ensuremath{\infty})$, although the detector still interacts with the environment, it behaves as if it were a closed system as a consequence of relativity correction associated to the velocity, and the quantum Fisher information in this case can be shielded from the effect of the external environment, and thus from the relativistic motion.

arXiv:2205.08725Physical review. D/Physical review. D.Jun 24, 202122 citations

Quantum Fisher Information and Uncertainty Relations

Shunlong Luo

Letters in Mathematical PhysicsAug 1, 200094 citations

Quantum Fisher Information and Atom-EnvironmentEntanglement in a Moving Four-Level Atom Coupled to a KerrOptomechanical Cavity under a Magnetic Field

Syed Jamal Anwar, S. Abdul Khali S. Abdul Khali, M. Khalid Khan M. Khalid Khan +1 more

Abstract We study phase-sensitive quantum dynamics in a hybrid cavity system consisting of a mov-ing four-level ladder atom, a quantized optical mode, and a mechanical oscillator. The atomicTransitions interact with the cavity field through a motion-dependent Jaynes-Cummings coupling.while radiation pressure couples the intracavity photons to the mechanical mode. A Kerr mediumprovides photon-number-dependent phase shifts, and an external magnetic field generates Zeeman-shifted atomic sublevels. The quantum Fisher information and the von Neumann entropy of thereduced atomic states are used to follow the redistribution of phase information and the generationof atomenvironment correlations. The results show that stronger hybrid coupling generally trans-fers locally accessible phase information away from the atom while increasing the mixedness of theatomic subsystem. Since the full state evolves unitarily, the reduced atomic entropy also quantifiesthe entanglement between the atom and the combined field mechanics sector. Kerr nonlinearityreorganizes this information flow and can produce delayed loss of phase sensitivity or partial recoveryseries at selected times. The work highlights why quantum Fisher information and von NeumannEntropy must be interpreted together when metrological usefulness and entanglement are studied.in hybrid light-matter systems.Abstract We study phase-sensitive quantum dynamics in a hybrid cavity system consisting of a mov-ing four-level ladder atom, a quantized optical mode, and a mechanical oscillator. The atomicTransitions interact with the cavity field through a motion-dependent Jaynes-Cummings coupling.while radiation pressure couples the intracavity photons to the mechanical mode. A Kerr mediumprovides photon-number-dependent phase shifts, and an external magnetic field generates Zeeman-shifted atomic sublevels. The quantum Fisher information and the von Neumann entropy of thereduced atomic states are used to follow the redistribution of phase information and the generationof atomenvironment correlations. The results show that stronger hybrid coupling generally trans-fers locally accessible phase information away from the atom while increasing the mixedness of theatomic subsystem. Since the full state evolves unitarily, the reduced atomic entropy also quantifiesthe entanglement between the atom and the combined field mechanics sector. Kerr nonlinearityreorganizes this information flow and can produce delayed loss of phase sensitivity or partial recoveryseries at selected times. The work highlights why quantum Fisher information and von NeumannEntropy must be interpreted together when metrological usefulness and entanglement are studied.in hybrid light-matter systems.

Sep 10, 20260 citations

w=0

) moving along spatially straight line, the accelerated motion will reduce the quantum Fisher information in the estimation of state parameters. However, when the detector trajectory is generated by a combination of the linear accelerated motion and a component of the four-velocity $w=dy/d\ensuremath{\tau}$, we find quite unlike the previous results that, for the nonrelativistic case ($w\ensuremath{\ll}1$), the acceleration could degrade the quantum Fisher information, while the four-velocity component will suppress the degradation of the quantum Fisher information, and thus could enhance the precision of parameters estimation. Furthermore, in the case for ultrarelativistic velocities $(w\ensuremath{\rightarrow}\ensuremath{\infty})$, although the detector still interacts with the environment, it behaves as if it were a closed system as a consequence of relativity correction associated to the velocity, and the quantum Fisher information in this case can be shielded from the effect of the external environment, and thus from the relativistic motion.