Quantum Fisher information of two atoms with dipole\u2013dipole interaction under the environment of phase noise lasers

Yu Chen,Zhi He,Zheng-Wen Long,Shen-Tong Ji

doi:10.1038/s41598-021-99449-9

Abstract

We investigate the parameter estimation problems of two-atom system driven by the phase noise lasers (PNLs) environment. And we give a general method of numeric solution to handle the problems of atom system under the PNLs environment. The calculation results of this method on Quantum Fisher Information (QFI) are consistent with our former results. Moreover, we consider the dipole–dipole (d–d) interaction between the atoms under PNLs environment with the collective decay, and the results show that larger d–d interaction and smaller collective decay rate lead to larger QFI of the two-atom system. So the collective decay will destroy the QFI while the d–d interaction will preserve the QFI, these results can be used to protect the QFI of two-atom system driven by the PNLs environment.

Highlights

We investigate the parameter estimation problems of two-atom system driven by the phase noise lasers (PNLs) environment
This is quantum Cramér–Rao theorem, and it is an important theorem of quantum m etrology[4,5,6,7,13]. It can be seen from this theorem that, under the quantum framework, the accuracy of parameter estimation is determined by the Quantum Fisher Information (QFI), and the larger the value is, the smaller the variance of the estimator will be Eq (1) is logically consistent with the Cramér–Rao theorem[42]:
We have studied the dynamical characters of parament estimation of two atoms driven by PNLs

Summary

Introduction

We investigate the parameter estimation problems of two-atom system driven by the phase noise lasers (PNLs) environment. In 1976, G.S.Agarwal provided the phase diffusion model of the P NL20, and he discussed the analytical solution of one atom under the driven of PNL and in considering the spontaneous emission He gave us the spectrum, the master equation still includes a random variable, which make us hard to use for some physical problems. There are some researchers studied the physical problems on PNLs with this J.D.Cresser’s master equation, such as Q FI1,32, the discord of two-qubit X state[33], and the discord and the entanglement of three-qubit GHZ state and W state[34] They investigated multi-atom PNLs problems by using this master equation, their calculations are with no interactions between atoms and no spontaneous emissions, and do not focus on more complicated problems with d–d interactions and collective decay (or cooperative emission) of multiple atoms when the atoms are much closer to each other.

Results

Discussion

Conclusion