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arXiv:2105.02518

High-precision estimation of the parameters in the reservoir via the two-level system

Mengmeng Luo, Wenxiao Liu, Yuetao Chen, Shaoyan Gao

Published May 6, 2021• 0 citations
arXivHTMLPDF

Abstract

A scheme is proposed to estimate the system and environmental parameter, the detuning, temperature and the squeezing strength with a high precision by the two-level atom system. It hasn't been reported that the squeezing strength estimation through quantum Fisher information. We find entangled state and optimal superposition state are beneficial for parameter estimation with one-qubit probe by calculating quantum Fisher information and fidelity. And the fidelity between initial and final states of the atom can be improved via the two-qubit probe. Moreover, the phenomenon of quantum Fisher information return occurs when the detuning or the temperature is estimated. Our work provides a basis for precision measurement technology and quantum information processing.

DOI
10.48550/arxiv.2105.02518

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A scheme is proposed to estimate the system and environmental parameter, the detuning, temperature and the squeezing strength with a high precision by the two-level atom system. It hasn't been reported that the squeezing strength estimation through quantum Fisher information. We find entangled state and optimal superposition state are beneficial for parameter estimation with one-qubit probe by calculating quantum Fisher information and fidelity. And the fidelity between initial and final states of the atom can be improved via the two-qubit probe. Moreover, the phenomenon of quantum Fisher information return occurs when the detuning or the temperature is estimated. Our work provides a basis for precision measurement technology and quantum information processing.
A novel scheme is proposed to estimate three environmental parameters, the detuning, the temperature and the squeezing strength with one-qubit or two-qubit probes. Quantum Fisher information and the fidelity of the atom probes are calculated. When the detuning between the frequency of cavity field and the atomic transition frequency is estimated, the dynamics of quantum Fisher information shows oscillatory and rising behaviors. To estimate the temperature of the thermal reservoir, the one-qubit probe with the superposition initial state is more favorable than the two-qubit probe with the entangled initial state. When the squeezing strength of the squeezed vacuum reservoir is estimated, we find that the estimation precision is significantly improved by utilizing the two-qubit probe with the maximal entangled initial state. Our work provides a potential application in the open quantum system and quantum information processing.
The quantum Fisher information (QFI) of a two-level atom in an anisotropic and isotropic photonic band-gap (PBG) crystal has been studied without Born or Markovian approximation. We show that the precision of the parameter estimation for the two-level atom in the photonic crystal is greatly different from that of a two-level atom in vacuum or that subjected to the usual non-Markovian reservoir. The phenomenon shows that the QFI, namely, the precision of estimation, changes dramatically with the environment structure. The results also show that, for PBG materials, environmentally high values of QFI trapping can be achieved and thus prevention of QFI sudden drop occurs, which greatly enhances the coherence and increases the precision of estimation. Moreover, the QFI in the isotropic PBG is more easily preserved than that of the anisotropic PBG under the same condition. These features make the atom system in PBG materials a good candidate for implementation of different schemes of quantum optics and information with high precision.
Abstract We study the impact of quantum correlations existing within the system-environment thermal equilibrium state while estimating the parameters of the spin reservoir. By employing various physical situations of interest, we present results for the reservoir temperature and its coupling strength with the central two-level system. The central system (probe) interacts with the bunch of randomly oriented spin systems and attains a thermal equilibrium state. We consider a projective measurement which prepares the probe’s initial state, and then the global system (probe and reservoir) evolves unitarily. The reduced density operator encapsulates the information about the spin reservoir which can be extracted by doing measurements on the probe. The precision of such measurement is quantified by quantum Fisher information. We repeat this process if the probe-reservoir initial state is not correlated (product state). We compare the estimation results for both with and without the outturn of initial correlations. In the temperature estimation case, our results are promising as one can significantly improve the accuracy of the estimates by including the effect of initial correlations. A similar trend prevails in the case of coupling strength estimation especially at low temperatures.
Small, controllable quantum systems, known as quantum probes, have been proposed to estimate various parameters characterizing complex systems such as the environments of quantum systems. These probes, prepared in some initial state, are allowed to interact with their environment, and subsequent measurements reveal information about different quantities characterizing the environment, such as the system-environment coupling strength, the cutoff frequency, and the temperature. These estimates have generally been made by considering only the way that the probe undergoes decoherence. However, we show that information about the environment is also imprinted on the probe via the probe and environment correlations that exist before the probe state preparation. This information can then be used to improve our estimates for any environment. We apply this general result to the particular case of a two-level system probe undergoing pure dephasing, due to a harmonic-oscillator environment, to show that a drastic increase in the quantum Fisher information, and hence the precision of our estimates, can indeed be obtained. We also consider applying periodic control pulses to the probe to show that with a combination of the two---the effect of the control pulses as well as the initial correlations---the quantum Fisher information can be increased by orders of magnitude.
Quantum parameter estimation is one of the most important applications in quantum metrology. The basic theory of quantum parameter estimation－quantum Cramer-Rao bound－shows that the precision limit of quantum parameter estimation is directly related to quantum Fisher information. Therefore quantum Fisher information is extremely important in the quantum parameter estimation. In this paper we use quantum parameter estimation theory to estimate the coupling constant of the Jaynes-Cummings model with large detuning. The initial probing state is the direct product state of qubit and radiation field in which Fock state, thermal state and coherent state are taken into account respectively. We calculate the quantum Fisher information of the hybrid system as well as qubit and radiation field for each probing state after the parameter evolution under the Hamiltonian of the Jaynes-Cummings model with large detuning. The results show that the quantum Fisher information increases monotonically with the average photon number increasing. The optimal detection state is that when the qubit system is in the equal weight superposition of the ground and the excited state, at this time the quantum Fisher information always reaches a maximum value, When the radiation field of probing state is Fock state or the thermal state, the information about the estimated parameter is included only in the qubit. The estimation accuracy of the coupling constant with thermal state or coherent state is higher than that with Fock state.
In the present manuscript, we demonstrate the potential to control and enhance the accuracy of parameter estimation (P-E) in a two-level atom (TLA) immersed in a cavity field that interacts with another cavity. We investigate the dynamics of quantum Fisher information (FI), considering the influence of coupling strength between the two cavities and the detuning parameter. Our findings reveal that, in the case of a perfect cavity, a high quantum FI value can be maintained during the dynamics concerning the detuning and coupling strength parameters. The results indicate that with a proper choice of quantum model parameters, long-term protection of the FI can be achieved without being affected by decoherence.