arXiv:2608.27163

Dynamics and spectra of open quantum systems coupled to anharmonic environments

Kian Damezin, Brendon W. Lovett, Erik M. Gauger, Adam Burgess

quant-phSubmitted Aug 27, 2026• Announced Aug 28, 2026• 0 citations

Abstract

In open quantum systems, the environment is typically modelled as a collection of harmonic oscillators, whereas realistic environments often exhibit unique non-Markovian effects due to the anharmonicity of the environment. Here we present a framework for modelling anharmonic environments in open quantum systems numerically exactly, in which, via a matching criterion, we map the anharmonic environment onto an effective harmonic one. This results in an effective spectral density that is a collection of shifted bare spectra arising from the non-equidistant energy gaps of the anharmonic environment, along with a unique zero-frequency term that effectively acts as static disorder on the system. This is due to the non-zero variance of the diagonal of the bath coupling operator. In tandem, we develop a framework for investigating the effects of environments comprising a few damped anharmonic modes where the matching criterion fails to work due to the non-Gaussianity of the environment. For both continuous and discrete damped anharmonic environments, this work investigates their unique influence on the system's dynamics, including enhanced non-Markovianity compared to a harmonic approximation, novel effects in the absorption spectrum, and the potential for anharmonic environments to enhance energy transport.

Related papers

Optimized auxiliary oscillators for the simulation of general open quantum systems

F. Mascherpa, Andrea Smirne, Alejandro D. Somoza +5 more

A method for the systematic construction of few-body damped harmonic oscillator networks accurately reproducing the effect of general bosonic environments in open quantum systems is presented. Under the sole assumptions of a Gaussian environment and regardless of the system coupled to it, an algorithm to determine the parameters of an equivalent set of interacting damped oscillators obeying a Markovian quantum master equation is introduced. By choosing a suitable coupling to the system and minimizing an appropriate distance between the two-time correlation function of this effective bath and that of the target environment, the error induced in the reduced dynamics of the system is brought under rigorous control. The interactions among the effective modes provide remarkable flexibility in replicating non-Markovian effects on the system even with a small number of oscillators, and the resulting Lindblad equation for the system and the modes may therefore be integrated at a very reasonable computational cost using standard methods for Markovian problems, even in strongly nonperturbative coupling regimes and at arbitrary temperatures including zero. We apply the method to an exactly solvable problem in order to demonstrate its accuracy, and present two studies based on current research in the context of coherent transport in biological aggregates and organic photovoltaics as more realistic examples of its use and potential; performance and versatility are highlighted, and theoretical and numerical advantages over existing methods, as well as possible future improvements, are discussed.

arXiv:1904.04822Physical Review AMay 14, 202098 citations

Pseudomode description of general open quantum system dynamics: non-perturbative master equation for the spin-boson model

Graeme Pleasance, Francesco Petruccione

We outline a non-perturbative approach for simulating the behavior of open quantum systems interacting with a bosonic environment defined by a generalized spectral density function. The method is based on replacing the environment by a set of damped harmonic oscillators - the pseudomodes - thereby forming an enlarged open system whose dynamics is governed by a Markovian master equation. Each pseudomode is connected to one of the poles of the spectral density when analytically continued to the lower-half complex frequency plane. Here, we extend previous results to a completely generic class of open system models, and discuss how our framework can be used as a powerful and versatile tool for analyzing non-Markovian open system dynamics. The effectiveness of the method is demonstrated on the spin-boson model by accurately benchmarking its predictions against numerically exact results.

arXiv:2108.05755Aug 12, 20212 citations

Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes

Graeme Pleasance, Barry M. Garraway, Francesco Petruccione

We develop an exact framework for describing the non-Markovian dynamics of an open quantum system interacting with an environment modeled by a generalized spectral density function.The approach relies on mapping the initial system onto an auxiliary configuration, comprising the original open system coupled to a small number of discrete modes, which in turn are each coupled to an independent Markovian reservoir.Based on the connection between the discrete modes and the poles of the spectral density function, we show how expanding the system using the discrete modes allows for the full inclusion non-Markovian effects within an enlarged open system whose dynamics is governed by an exact Lindblad master equation.Initially we apply this result to obtain a generalization of the pseudomode method [B.M. Garraway, Phys. Rev. A. 55, 2290 (1997)] in cases where the spectral density function has a Lorentzian structure.For many other types of spectral density function, we extend our proof to show that an open system dynamics may be modeled physically using discrete modes which admit a non-Hermitian coupling to the system and for such cases determine the equivalent master equation to no longer be of Lindblad form.For applications involving two discrete modes, we demonstrate how to convert between pathological and Lindblad forms of the master equation using the techniques of the pseudomode method.

arXiv:2002.09739Physical Review ResearchOct 12, 202084 citations

Engineering a Non-Markovian Environment to Enhance Entanglement and To Generate Hidden Quantum Networks

Kenneth Mui, Da-Wei Luo, Duan Wang +1 more

Abstract We contribute further to recent theoretical studies of entanglement dynamics in open quantum systems to include a continuous variable N-harmonic oscillator ring system bathed in Ornstein–Uhlenbeck noise. Despite the fact that harmonic oscillator systems are one of the most studied systems in physics, we believe that our work here is unique and sheds a new perspective in terms of a potential application. We present two sets of differential equations that govern the dynamics of N harmonic oscillators derived from first principles, one for a Markovian environment and the other for non-Markovian one. With these two sets, we are able to compare their entanglement dynamics between environments given an initial state of our oscillators. Across several system and environmental parameters, we show that the entanglement dynamics between oscillator pairs in a non-Markovian environment may be significantly enhanced in both magnitude and duration when compared to its Markovian approximation. We showcase this by numerically simulating a specific solution, i.e., we choose N = 4 oscillators, where two harmonic oscillators are initialized as a two-mode squeezed state while the remaining oscillators are vacuum states. By leveraging our N = 4 results, we consider a slightly larger number of oscillators, i.e., N = 6, and show how we can generate a hidden quantum network, in the absence of direct coupling, that may allow multiple parties to secretly and passively entangle oscillators in their possession. This is accomplished by exploiting the environmental memory effect and maintaining resonance with other oscillators or the central frequency in a shared non-Markovian bath, which may allow for autonomous entanglement distribution over a network of oscillators and aid in future quantum technologies.

Quantum Information and ComputationMar 1, 20260 citations

Non-Markovian effects & decoherence processes in open quantum systems

Graeme Pleasance

This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.

Feb 22, 20180 citations

Convergence of numerical approximations to non-Markovian bosonic gaussian environments

Rahul Trivedi, Daniel Malz, J. I. Cirac

Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. A common approach to the analysis of such systems is to approximate the non-Markovian environment by discrete bosonic modes thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been proposed in previous works [D. Tamascelli et al, PRL (2012), A. W. Chin et al, J. of Math. Phys (2010)], the resulting approximation lacks rigorous convergence guarantees. In this paper, we initiate a rigorous study of the convergence properties of these methods. We show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that, for most physically interesting models of non-Markovian environments, the approximation error falls off polynomially with the number of modes. Our results lend rigor to numerical methods used for approximating non-Markovian quantum dynamics and allow for a quantitative assessment of classical as well as quantum algorithms in simulating non-Markovian quantum systems.

Jul 15, 20211 citation