Kraus Mapping for atom-cavity and reservoir system

TL;DR

This paper introduces a discrete operator-based approach to model the evolution of open quantum systems, providing a fundamental perspective that aligns with continuous dynamics and applies to atom-cavity-reservoir systems.

Contribution

It develops a method to derive time-dependent Kraus operators and demonstrates their application to a three-level atom-cavity system, bridging discrete and continuous quantum evolution.

Findings

Successfully reproduces continuous evolution using small discrete operators.

Provides a computational method for time-dependent Kraus operators.

Analyzes the relationship between discrete steps and physical variables.

Abstract

We propose a way to understand the evolution of an open quantum system using a description that dispenses a continuous evolution in time, by discrete operators entangled states, in its most direct and fundamental way. We show that the successive application of these operators in very small time intervals reproduce continuous evolution. It describes and compares the temporal evolution of an open quantum system of three levels, for which the Lindblad equation is solved to obtain the density matrix function of time, a method is developed to find Kraus operators time dependent and also finds constant Kraus operators differentials operate computationally $ n $ times evolving in discrete-time $ \Delta t = \tau = t / n $. It is seen in the example of atom cavity inside a reservoir that by calculating the distance and the relative error we define is a relationship with the evolution of discrete steps and physical variables as $ \omega $ which presuppose a natural discretization found time.