Fingerprint and universal Markovian closure of structured bosonic environments

TL;DR

This paper introduces a universal Markovian closure for structured bosonic environments that simplifies simulations by replacing infinite residual modes with a small, parametrized set of damped modes, enabling efficient computation of spectra.

Contribution

It presents a novel Markovian closure method that captures environment fingerprints and significantly speeds up simulations while reducing memory requirements.

Findings

Quadratic speed-up over standard methods

Memory use independent of simulation time

Effective for both linear and non-linear spectral calculations

Abstract

We exploit the properties of chain mapping transformations of bosonic environments to identify a finite collection of modes able to capture the characteristic features, or fingerprint, of the environment. Moreover we show that the countable infinity of residual bath modes can be replaced by a universal Markovian closure, namely a small collection of damped modes undergoing a Lindblad-type dynamics whose parametrization is independent of the spectral density under consideration. We show that the Markovian closure provides a quadratic speed-up with respect to standard chain mapping techniques and makes the memory requirement independent of the simulation time, while preserving all the information on the fingerprint modes. We illustrate the application of the Markovian closure to the computation of linear spectra but also to non-linear spectral response, a relevant experimentally accessible many body coherence witness for which efficient numerically exact calculations in realistic environments are currently lacking.