The transfer tensor method: An analytical study case

Area of Science:

• Quantum mechanics
• Quantum information theory
• Open quantum systems

Background:

• The transfer tensor method (TTM) is a powerful tool for analyzing non-Markovian quantum systems.
• TTM captures memory effects through dynamical maps and transfer tensors (TTs).
• The Nakajima-Zwanzig equation is a common approach for modeling open quantum systems.

Purpose of the Study:

• To investigate the deviation between the Nakajima-Zwanzig memory kernel and exact transfer tensors in the TTM.
• To analyze the impact of time discretization on the accuracy of the TTM.
• To explore the conditions under which non-Markovian dynamics can appear Markovian within the TTM framework.

Main Methods:

• Derivation of exact expressions for the dynamical map, TTs, and memory kernel.
• Analysis of an analytically solvable model: a two-level atom coupled to a lossy cavity (Jaynes-Cummings limit).
• Examination of atomic dynamics in coherence and population difference subspaces.

Main Results:

• The memory kernel of the Nakajima-Zwanzig equation deviates from exact TTs for finite time discretizations.
• Both methods converge in the continuous-time limit.
• Regions of enhanced non-Markovianity were identified where TTM time-step choices can induce apparent Markovian dynamics.

Conclusions:

• The choice of time step in the TTM is crucial for accurately representing non-Markovian dynamics.
• Deviations between the Nakajima-Zwanzig kernel and TTs highlight the importance of careful discretization.
• The study provides insights into controlling the apparent Markovianity of open quantum systems using the TTM.