Using the Environment to Understand non-Markovian Open Quantum Systems

Gribben, Dominic; Strathearn, Aidan; Fux, Gerald E.; Kirton, Peter; Lovett, Brendon W.

doi:10.48550/arxiv.2106.04212

Cited by 3 publications

(4 citation statements)

References 55 publications

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“…Further work will study the bath states and seek to quantify the entanglement between the system and the bath, to learn how and when it forms, and how this is all quantitatively related to the negative eigenvalues of the system's Kossakowski matrix. Path integral formulation TEMPO can determine the exact bath dynamics [61]. Since the TCL and the path integrals are equivalent [68], the irrelevant part of the density matrix in the former can potentially be determined using this technique, suggesting that the full density matrix can be determined.…”

Section: Discussionmentioning

confidence: 99%

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Systematic Gorini, Kossakowski, Sudarshan and Lindblad Equation for Open Quantum Systems

Davidović¹

2021

Preprint

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In complex, open quantum systems, with many degrees of freedom, it is difficult to start a Markovian dynamics, let alone prepare a factorized system-environment state. Rather, the Markovian dynamics is an intertwining map of a completely positive (CP) non-Markovian dynamics. The Markovian master equation is usually not CP as such, and should be left alone if it works adequately well. Here we study how the intertwining Markovian dynamics can still be well approximated by a CP map. A coherent quantum dynamics can be systematically approximated by the CP, Geometric Arithmetic Master Equation (GAME), but this is not the case for an incoherent dynamics. This dichotomy is responsible for disagreeing claims if a CP Markovian master equation cannot have systematic accuracy. As an example, we show how the dynamical decoupling of a qubit breaks the perturbative, intertwining map, while fixing the accuracy of the GAME to near-exactness.

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Section: Discussionmentioning

confidence: 99%

“…The TEMPO algorithm can also be modified to calculate the process tensor [59]. This alternative formulation has been used in both optimizing quantum control procedures [60] and in calculating exact bath dynamics [61]. An open source python package [62] improves the performance and includes new approaches.…”

Section: Example: Dynamical Decouplingmentioning

confidence: 99%

Systematic Gorini, Kossakowski, Sudarshan and Lindblad Equation for Open Quantum Systems

Davidović¹

2021

Preprint

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“…The TEMPO algorithm can also be modified to calculate the process tensor [68]. This alternative formulation has been used in both optimizing quantum control procedures [69] and in calculating exact bath dynamics [70]. An open source python package [71] improves the performance and includes new approaches.…”

Section: Path-integral Solutionmentioning

confidence: 99%

Geometric-arithmetic master equation in large and fast open quantum systems

Davidović¹

2022

J. Phys. A: Math. Theor.

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Understanding nonsecular dynamics in open quantum systems is addressed here, with emphasis on systems with large numbers of Bohr frequencies, zero temperature, and fast driving. We employ the master equation, which replaces arithmetic averages of the decay rates in the open system, with their geometric averages, and find that it can improve the second order perturbation theory, known as the Redfield equation, while enforcing complete positivity on quantum dynamics. The characteristic frequency scale that governs the approximation is the minimax frequency: the minimum of the maximum system oscillation frequency and the bath relaxation rate; this needs to be larger than the dissipation rate for it to be valid. The concepts are illustrated on the Heisenberg ferromagnetic spin-chain model. To study the accuracy of the approximation, a Hamiltonian is drawn from the Gaussian unitary ensemble, for which we calculate the fourth order time-convolutionless master equation, in the Ohmic bath at zero temperature. Enforcing the geometric average, decreases the trace distance to the exact solution. Dynamical decoupling of a qubit is examined by applying the Redfield and the geometric-arithmetic master equations, in the interaction picture of the time dependent system Hamiltonian, and the results are compared to the exact path integral solution. The geometric-arithmetic approach is significantly simpler and can be super-exponentially faster compared to the Redfield approach.

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“…Therefore not only can (22) be used to calculate the dynamical map for the system but also all of its correlation functions [44,48]. Recently it has been shown that this further allows the calculation of all correlation functions of the baths as well [49]. Thus, the tensor representation for the influence functional introduced here provides a way to completely characterise the full system-baths dynamics.…”

Section: B Time-ordering Using Tensor Contractionsmentioning

confidence: 99%

Exact dynamics of non-additive environments in non-Markovian open quantum systems

Gribben,

Rouse,

Iles-Smith

et al. 2021

Preprint

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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 multi-bath system dynamics has up to now required approximations that can obscure some of the non-additive 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 behaviour: 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 multi-bath 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.

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Using the Environment to Understand non-Markovian Open Quantum Systems

Cited by 3 publications

References 55 publications

Systematic Gorini, Kossakowski, Sudarshan and Lindblad Equation for Open Quantum Systems

Systematic Gorini, Kossakowski, Sudarshan and Lindblad Equation for Open Quantum Systems

Geometric-arithmetic master equation in large and fast open quantum systems

Exact dynamics of non-additive environments in non-Markovian open quantum systems

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