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Journal of the Optical Society of America B

Dynamics of quantum Fisher information and quantum coherence of two interacting atoms under time–fractional analysis

K. El Anouz, Chibueze Paul Onyenegecha, Alexander Iheanyichukwu Opara, Ahmed Salah, Abderrahim El Allati

Published Feb 10, 2022• 16 citations
Publisher

Abstract

In this paper, we give an exact general solution to the fractional Schrödinger equation of two interacting atoms. It consists of using the Riemann–Liouville fractional integral operator to examine the interaction between two identical atoms under temporal–fractional evolution. The dynamics of quantum Fisher information with respect to changes in the phase parameter and the quantum coherence by means of the l 1 -norm and relative entropy of coherence are discussed. Moreover, the analytical fractional solution allows us to evaluate the relationship between the estimation precision of the phase parameter and the coherence measures for various atom–atom states. Indeed, the obtained results show a good similarity between these measures for certain critical values of the phase parameter. In addition, it is observed that initially, for such coherent-like fractional states, the amount of quantum Fisher information may be sensitive or insensitive to changes in the phase parameter. Therefore, one can conclude that quantum Fisher information can be considered as an indicator of quantum coherence in a composite quantum state.

DOI
10.1364/josab.444823

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Quantum Fisher information (QFI) quantifies the sensitivity of a quantum state to a parameter change and plays a key role in quantum metrology. Meanwhile, quantum coherence is a crucial resource for quantum information processing. However, despite extensive studies on various aspects of quantum metrology, the interplay between the dynamics of the QFI and quantum coherence remains unexplored. Here, we explore the factorization relationship between the QFI and quantum coherence, both theoretically and experimentally. We prepare pure states in qubit and qutrit systems and apply unitary evolution to investigate this relationship. Our results confirm the factorization law, offering strong evidence for this relationship. Furthermore, we establish a lower bound on the variance of the estimated parameter that does not require the final state information. This approach reveals a deep connection between the QFI and quantum coherence, providing insights into quantum parameter estimation. These findings have potential applications in quantum sensing and quantum metrology.
We study the temporal evolution of quantum coherence and parameter estimation for two-mode coherent-state superposition by using the master equation. Analytic expressions are provided and numerically displayed, which can illustrate the reliance of the coherence and Fisher information during the dynamics. Generally, we find that the amount of the quantum measures has the same behavior during the time variation, and displays a different order that depends on the different strength regimes of the input radiation fields and then disappears at infinite times. We show that these measures start from maximal value at the initial instant and decrease the time goes on. Moreover, we can observe that these measures can be protected resisted from the environment effect during the dynamics, showing an important feature of coherence and Fisher information. The obtained results can be assumed more practical in the characterization of the behavior of the coherence and Fisher information under the effect of the environment. Our observations can provide significant implications in harnessing these phenomena in quantum optics and information.
This paper delves into the exploration of quantum resources within a two-qubit system composed of two 2-level atoms connected to distinct thermal baths. Various quantifiers are employed to evaluate different aspects of the system’s quantum characteristics. Specifically, the [Formula: see text]-norm and relative entropy of coherence ([Formula: see text] and [Formula: see text]) are utilized to gauge quantum coherence, while local quantum Fisher information (LQFI) is used to quantify non-classical correlations within the system. The findings suggest that the amount of quantum correlations and coherence decline as the spontaneous emission rate [Formula: see text] and the mean thermal photon number n increase. However, it is observed that manipulating parameters defining the initial state of the two-level atoms system can enhance non-classical correlations and quantum coherence between the two atoms. Additionally, it is noted that these three key metrics entirely vanish in the asymptotic limit of time. Our research underscores the importance of precisely adjusting the parameters of the initial system state, which is prepared in an extended Werner-like state (EWL), to protect quantum resources shared between the two atoms from environmental influences.
Abstract In this work, we examine the quantum information characteristics of a hydrogen-like system under a Coulomb potential by using previously derived exact solutions of the generalized Schrödinger equation formulated within the conformable fractional framework. The approach introduces a fractional parameter (0<α≤1)(0 < \alpha \le 1)(0<α≤1) ( 0 < α ≤ 1 ) , which permits a continuous transition between standard quantum mechanics and a fractional description. Utilizing these available analytical solutions, we determine the associated energy spectrum and wavefunctions and employ them to quantify the informational structure of the system. In particular, we calculate the Shannon entropy in both position and momentum spaces, along with the Fisher information, as fundamental indicators of uncertainty, spatial spreading, and sensitivity to local variations of the probability density. The results show that the fractional parameter (α)(\alpha )(α) ( α ) produces nontrivial corrections to these quantum information measures, indicating modifications in localization properties and momentum profiles. Also, the formalism recovers the conventional hydrogenic limit when (α→1)(\alpha \rightarrow 1)(α→1) ( α → 1 ) , which validates the consistency of the formulation. In this context, these results show that the conformable fractional framework constitutes a consistent extension for analyzing quantum systems via information-theoretic quantities without modifying the exact solutions, providing a systematic approach to investigate deviations from integer-order dynamics.
Abstract In this work, we investigate quantum Fisher information (QFI) and quantum coherence (QC) of an atom in a dissipative cavity. In a zero-temperature reservoir and with one excitation number, we obtain the analytical solutions of QFI and QC as well as their relationship for Ohmic and Lorentzian reservoirs, respectively. The results show that both the atom–cavity coupling and the cavity–reservoir coupling can effectively protect QFI and QC. In particular, QFI and QC will tend to their stable values when the atom–cavity coupling or cavity–reservoir coupling is larger than a certain value. QC can augment QFI and can effectively improve the quantum metrology. In addition, we give a physical explanation of the dynamic behavior of QFI and QC using the decoherence rate.