Memory-induced weak dissipation in fractional-time-derivative quantum Lindblad-based model

Modeling the interaction between a quantum system and its environment is crucial for practical quantum technologies. The Lindblad master equation is the simplest equation to understand this interaction. In this paper, we have extended the traditional Lindblad equation by fractionalizing its time derivative to account for the memory-induced dissipation. Using this approach, we show weak dissipation of selected quantum systems can be reproduced by this proposed time-fractional Lindblad equation without introducing any specific dissipation terms in the model. By varying the order of the time-fractional Lindblad equation without dissipation terms, we can reproduce the results with good agreements to three tested cases: (a) dissipative Rabi oscillation, (b) dissipative Ising model, and (c) collapse and revival in the Jaynes–Cumming model. We believe this proposed time-fractional Lindblad equation may be a useful modeling tool to characterize weakly dissipative quantum systems in practical quantum technologies, especially if the complex dissipation mechanism is not completely known from the traditional approaches.