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arXiv:2109.08442 · PRX Quantum

Exact Dynamics of Nonadditive Environments in Non-Markovian Open Quantum Systems

Dominic Gribben, Dominic M. Rouse, Jake Iles-Smith, Aidan Strathearn, Henry Maguire, Peter Kirton, Ahsan Nazir, Erik M. Gauger, Brendon W. Lovett

Published Feb 7, 2022• 74 citations
arXivHTMLPDF

Abstract

When a quantum system couples strongly to multiple baths, then it is generally no longer possible to describe the resulting system dynamics by simply adding the individual effects of each bath.However, capturing such multibath system dynamics typically requires approximations that can obscure some of the nonadditive effects.Here we present a numerically exact and efficient technique for tackling this problem that builds on the time-evolving matrix product operator (TEMPO) representation.We test the method by applying it to a simple model system that exhibits nonadditive behavior: a two-level dipole coupled to both a vibrational and an optical bath.Although not directly coupled, there is an effective interaction between the baths mediated by the system that can lead to population inversion in the matter system when the vibrational coupling is strong.We benchmark and validate multibath TEMPO against two approximate methods-one based on a polaron transformation, the other on an identification of a reaction coordinate-before exploring the regime of simultaneously strong vibrational and optical coupling where the approximate techniques break down.Here we uncover a new regime where the quantum Zeno effect leads to a fully mixed state of the electronic system.

DOI
10.1103/prxquantum.3.010321

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When a quantum system couples strongly to multiple baths, then it is generally no longer possible to describe the resulting system dynamics by simply adding the individual effects of each bath.However, capturing such multibath system dynamics typically requires approximations that can obscure some of the nonadditive effects.Here we present a numerically exact and efficient technique for tackling this problem that builds on the time-evolving matrix product operator (TEMPO) representation.We test the method by applying it to a simple model system that exhibits nonadditive behavior: a two-level dipole coupled to both a vibrational and an optical bath.Although not directly coupled, there is an effective interaction between the baths mediated by the system that can lead to population inversion in the matter system when the vibrational coupling is strong.We benchmark and validate multibath TEMPO against two approximate methods-one based on a polaron transformation, the other on an identification of a reaction coordinate-before exploring the regime of simultaneously strong vibrational and optical coupling where the approximate techniques break down.Here we uncover a new regime where the quantum Zeno effect leads to a fully mixed state of the electronic system.
In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings or to special cases where specific numerical techniques become effective. Here we present a general and yet exact numerical approach that efficiently describes the time evolution of a quantum system coupled to a non-Markovian harmonic environment. Our method relies on expressing the system state and its propagator as a matrix product state and operator, respectively, and using a singular value decomposition to compress the description of the state as time evolves. We demonstrate the power and flexibility of our approach by numerically identifying the localisation transition of the Ohmic spin-boson model, and considering a model with widely separated environmental timescales arising for a pair of spins embedded in a common environment.
The time-evolving matrix product operator (TEMPO) method is a powerful tool for simulating open system quantum dynamics. Typically, it is used in problems with diagonal system-bath coupling, where analytical expressions for discretized influence functional are available. In this work, we aim to address issues related to off-diagonal coupling by extending the TEMPO algorithm to accommodate arbitrary basis sets. The proposed approach is based on computing the derivative of the discretized path integral expression of a generalized influence functional when increasing one time step, which yields an equation of motion valid for non-diagonal basis set and arbitrary number of non-commuting baths. The generalized influence functional is then obtained by integrating the resulting differential equation. Applicability of the the new method is then tested by simulating one- and two- qubit systems coupled to both Z- and X-type baths.
Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.
It is challenging to simulate open quantum systems that are connected to a reservoir through multiple channels. For example, vibrations may induce fluctuations in both energy gaps and electronic couplings, which represent two independent channels of system-bath couplings. Systems of this kind are ubiquitous in the processes of excited state radiationless decay. Combined with density matrix renormalization group (DMRG) and matrix product states (MPS) methods, we develop an interaction-picture chain mapping strategy for vibrational reservoirs to simulate the dynamics of these open systems, resulting in time-dependent spatially local system-bath couplings in the chain-mapped Hamiltonian. This transformation causes the entanglement generated by the system-bath interactions to be restricted within a narrow frequency window of vibrational modes, enabling efficient DMRG/MPS dynamical simulations. We demonstrate the utility of this approach by simulating singlet fission dynamics using a generalized spin-boson Hamiltonian with both diagonal and off-diagonal system-bath couplings. This approach generalizes an earlier interaction-picture chain mapping scheme, allowing for efficient and exact simulation of systems with multi-channel system-bath couplings using matrix product states, which may further our understanding of nonlocal exciton-phonon couplings in exciton transport and the non-Condon effect in energy and electron transfer.
Non-Markovian open quantum networks are among the most challenging problems in quantum theory, as they suffer from both, the exponentially scaling many-body state space as well as long memory times when the sites are strongly coupled to structured environments. Recent efforts to address them by combining tensor networks with real-time path integrals, such as TEMPO and process tensors, were however limited to systems with rather weak system-environment couplings because strong couplings lead to large bond dimensions. Here, we devise a tensor network scheme (CTEMPO) resulting in particularly small bond dimensions for single-site problems. We then extend this to a practical scheme to simulate non-Markovian quantum networks by time-evolving a corresponding comb tensor network. Benchmarking the single-site algorithm on the spin-boson model we find orders-of-magnitude improvement over established methods. The multi-site algorithm is shown to solve the notoriously difficult problem of the 7-site Fenna-Matthews-Olson photosynthetic complex, whose spectral density contains 62 peaks. We then apply our approach to explore the scaling behavior of the superradiance of up to N=20N=20N=20 quantum dots individually coupled to super-Ohmic phonon baths. Our approach provides a turnkey solution to non-Markovian quantum networks and is compatible with more general tensor network topologies.
We present a numerically exact method to compute the full counting statistics of heat transfer in non-Markovian open quantum systems, which is based on the time-evolving matrix product operator (TEMPO) algorithm. This approach is applied to the paradigmatic spin-boson model in order to calculate the mean and fluctuations of the heat transferred to the environment during thermal equilibration. We show that system-reservoir correlations make a significant contribution to the heat statistics at low temperature and present a variational theory that quantitatively explains our numerical results. We also demonstrate a fluctuation-dissipation relation connecting the mean and variance of the heat distribution at high temperature. Our results reveal that system-bath interactions make a significant contribution to heat dissipation even when the dynamics of the open system is effectively Markovian. The method presented here provides a flexible and general tool to predict the fluctuations of heat transfer in open quantum systems in non-perturbative regimes.