Efficient simulation of non-Markovian system-environment interaction

Rosenbach, R.; Cerrillo, Javier; Huelga, Susana F.; Cao, Jianshu; Plenio, Martin B.

doi:10.1088/1367-2630/18/2/023035

Cited by 77 publications

(62 citation statements)

References 66 publications

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“…The CC mapping has been used to study an Otto cycle stroke type engine [38], stochastic thermodynamics based on coarse-graining [41], continuously coupled but not periodically driven engines [37], a fermionic autonomous Maxwell demon [39] and a fermionic electronic Maxwell demon [40], all in the strong coupling and non-Markovian regime. It has offered an accurate method for the study of open quantum systems apart from the thermodynamic applications [53][54][55] and is closely related to the method of time evolving density matrix using orthogonal polynomials algorithm [50,[56][57][58]. It was, however, not applied to the study of periodically driven systems so far.…”

Section: Collective Coordinate Mappingmentioning

confidence: 99%

From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

et al. 2018

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We combine the formalisms of Floquet theory and full counting statistics with a Markovian embedding strategy to access the dynamics and thermodynamics of a periodically driven thermal machine beyond the conventional Born-Markov approximation. The working medium is a two-level system and we drive the tunneling as well as the coupling to one bath with the same period. We identify four different operating regimes of our machine which include a heat engine and a refrigerator. As the coupling strength with one bath is increased, the refrigerator regime disappears, the heat engine regime narrows and their efficiency and coefficient of performance decrease. Furthermore, our model can reproduce the setup of laser cooling of trapped ions in a specific parameter limit. [35,36], redefined system-reservoir partitions (collective coordinate (CC) mappings) [37-41], a quantum absorption refrigerator [42], quenched thermodynamic protocols [43,44] and the derivation of an exact expression for the entropy production of a finite arbitrary system in contact with one or several thermal reservoirs [45], but none of which were applied to periodically driven machines so far. Exceptions are [46] and [47]. In [46] a polaron transformation and Floquet theory were used to include arbitrary strong coupling effects but only as long as the rotating wave approximation for the system Hamiltonian and the Markovian approximation for the reservoir hold. In [47] a periodically driven three-level heat engine was studied using the numerical method of hierarchy of equations of motion, an approach that is based in a decomposition of the bath correlation function rather than an explicit representation of the bath. For this reason, access to more general, thermodynamically relevant thermal transport properties requires a tailored solution [48].However, none of the aforementioned methods was successfully applied to the combinations of problems we want to tackle: a driven system coupled to multiple heat reservoirs with a possibly strong, driven and non-Markovian coupling. To achieve this we combine three methods: a CC mapping [49,50], Floquet theory for open systems [14,21] and full counting statistics [51]. This novel and unique combination provides access to steady state thermodynamics lifting the restriction of common assumptions such as a very fast driving, Markovian and weakly coupled reservoirs, and the secular approximation. First, in the CC mapping, we identify a collective degree of freedom in the reservoir, sometimes referred to as reaction coordinate [52] that is responsible for the strong coupling and non-Markovian effects. Second, using Floquet theory, we derive a master equation for the original system plus CC and apply full counting statistics methods to obtain the change in energy of the reservoirs unambiguously. This strategy allows us to perform a consistent thermodynamic analysis of periodically driven thermal machines. Furthermore, it also allows us to accurately treat periodic time dependencies in the interaction between system and res...

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Section: Collective Coordinate Mappingmentioning

confidence: 99%

From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

et al. 2018

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“…25,37,39,40 A multitude of powerful computational methods have been developed to deal with the difficulties faced in modelling strongly dissipative quantum systems. Examples include the hierarchical equations of motion (HEOM), [41][42][43][44][45][46] density matrix renormalisation group (and related) techniques, 25,36,47,48 and those based on the path integral formalism. [49][50][51][52] All can converge to numerically exact results in specific circumstances.…”

Section: Introductionmentioning

confidence: 99%

Energy transfer in structured and unstructured environments: Master equations beyond the Born-Markov approximations

Iles-Smith

Dijkstra

Lambert

et al. 2016

The Journal of Chemical Physics

128

164

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Criteria for the accuracy of small polaron quantum master equation in simulating excitation energy transfer dynamics J. Chem. Phys. 139, 224112 (2013) (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no longer hold. Finally, we apply the reaction coordinate formalism to the case of a structured environment comprising of both underdamped (i.e., sharply peaked) and overdamped (broad) components simultaneously. We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions. C 2016 AIP Publishing LLC. [http://dx

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“…By construction, T-TEDOPA can be implemented as a plug-in procedure by the already existing and highly optimized TEDOPA codes, which can now be used to efficiently simulate open quantum system dynamics across the entire temperature range. Our approach is particularly relevant whenever one wants to provide a quantitative description of open-system dynamics in the presence of structured and non-perturbative environments, such as those commonly encountered in quantum biology [5], nanoscale thermodynamics [57] or condensed-matter systems [38], as well as situations where the effect of environmental noise has to be identified accurately to discriminate it from possible fundamental decoherence in high-precision tests of the quantum superposition principle [58,59], or be exploited as building block in other methods, such as the Transfer Tensor scheme [60,61]. Future research will be devoted to the extension of the T-TEDOPA method to more general types of system-bath interactions.…”

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confidence: 99%

Efficient Simulation of Finite-Temperature Open Quantum Systems

et al. 2019

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Chain-mapping techniques in combination with the time-dependent density matrix renormalization group are a powerful tool for the simulation of open-system quantum dynamics. For finite-temperature environments, however, this approach suffers from an unfavorable algorithmic scaling with increasing temperature. We prove that the system dynamics under thermal environments can be non-perturbatively described by temperature-dependent system-environmental couplings with the initial environment state being in its pure vacuum state, instead of a mixed thermal state. As a consequence, as long as the initial system state is pure, the global system-environment state remains pure at all times. The resulting speedup and relaxed memory requirements of this approach enable the efficient simulation of open quantum systems interacting with highly structured environments in any temperature range, with applications extending from quantum thermodynamics to quantum effects in mesoscopic systems.

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Efficient simulation of non-Markovian system-environment interaction

Cited by 77 publications

References 66 publications

From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

Energy transfer in structured and unstructured environments: Master equations beyond the Born-Markov approximations

Efficient Simulation of Finite-Temperature Open Quantum Systems

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