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

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>l</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> -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.