Beyond The Fermi's Golden Rule: Discrete-Time Decoherence Of Quantum Mesoscopic Devices Due To Bandlimited Quantum Noise

TL;DR

This paper introduces a novel approach to modeling the real-time dynamics of mesoscopic quantum devices by exploiting the bandlimited nature of quantum noise, leading to a discrete-time formalism and efficient simulation methods.

Contribution

It proposes a bandlimited input-output formalism and a discrete-time matrix product state framework for open quantum systems, based on the spectral properties of quantum noise.

Findings

Quantum noise can be modeled as a discrete-time process with elementary steps inversely proportional to its bandwidth.

The approach results in a bounded bond dimension in the matrix product state representation, simplifying simulations.

The method is demonstrated on a spin-boson model, showing its practical applicability.

Abstract

We are at the midst of second quantum revolution where the mesoscopic quantum devies are actively employed for technological purposes. Despite this fact, the description of their real-time dynamics beyond the Fermi's golden rule remains a formiddable theoretical problem. This is due to the rapid spread of entanglement within the degrees of freedom of the surrounding environment. This is accompanied with a quantum noise (QN) acting on the mesoscopic device. In this work we propose a possible way out: to exploit the fact that this QN is usually bandlimited. This is because its spectral density is often contained in peaks of localized modes and resonances, and may be constrained by bandgaps. Inspired by the Kotelnikov sampling theorem from the theory of classical bandlimited signals, we put forward and explore the idea that when the QN spectral density has effective bandwidth $B$, the quantum noise becomes a discrete-time process, with an elementary time step $\tau\propto B^{-1}$. After each time step $\tau$, one new QN degree of freedom (DoF) gets coupled to the device for the first time, and one new QN DoF get irreversibly decoupled. Only a bounded number of QN DoFs are significantly coupled at any time moment. We call these DoFs the \textit{Kotelnikov modes}. As a result, the real-time dissipative quantum motion has a natural structure of a discrete-time matrix product state, with a bounded bond dimension. This yields a microscopically derived collision model. The temporal entanglement entropy appears to be bounded (area-law scaling) in the frame of Kotelnikov modes. The irreversibly decoupled modes can be traced out as soon as they occur during the real-time evolution. This leads to a novel\textit{bandlimited} input-output formalism and to quantum jump Monte Carlo simulation techniques for real-time motion of open quantum systems. We illustrate this idea on a spin-boson model.