The effect of exponential variable magnetic field on the entanglement dynamics of a two-qutrit system with Dzyloshinsky–Moriya interaction in a spin environment

Abstract In this study, we investigate the entanglement dynamics of two qutrits under Dzyloshinsky–Moriya (DM) interaction within a spin-qubit environment, influenced by two identical time-dependent external magnetic fields described by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="script">B</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>γ</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> . To quantify the entanglement between the two spin qutrits, we employ the Holstein–Primakoff transformation to compute the negativity measure. Our analysis reveals that the entanglement dynamics are affected by various factors, including the initial states of the spin environment and the qutrits, the system-environment coupling strength, the strength of the DM interaction, and the intensity of the external magnetic field. Notably, we find that increasing the spin coherence amplitude and the intensity of the magnetic field contributes to the stabilization of entanglement. In the weak coupling regime, an increase in the DM interaction enhances entanglement, irrespective of whether a magnetic field is present. Conversely, in the strong coupling regime, an increase in the DM interaction negatively impacts entanglement, regardless of the presence or absence of a magnetic field.