Flexible scheme to truncate the hierarchy of pure states

Zhang, P. P.; Bentley, Christopher; Eisfeld, Alexander

doi:10.1063/1.5022225

Cited by 19 publications

(11 citation statements)

References 51 publications

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“…Albeit the vast amount of publications in this field, sophisticated results for the microscopic model of a system and its environment are rare, even for the simple case of two qubits coupled to a common (sub-) Ohmic environment. Therefore we investigate the two-qubit entanglement by means of the numerically exact hierarchy of pure states (HOPS) method [23][24][25][26][27] with two major objectives in mind. First, we draw conclusions about the general applicability of various perturbative approaches.…”

Section: Introductionmentioning

confidence: 99%

Environmentally Induced Entanglement – Anomalous Behavior in the Adiabatic Regime

Hartmann

Strunz

2020

Quantum

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Considering two non-interacting qubits in the context of open quantum systems, it is well known that their common environment may act as an entangling agent. In a perturbative regime the influence of the environment on the system dynamics can effectively be described by a unitary and a dissipative contribution. For the two-spin Boson model with (sub-) Ohmic spectral density considered here, the particular unitary contribution (Lamb shift) easily explains the buildup of entanglement between the two qubits. Furthermore it has been argued that in the adiabatic limit, adding the so-called counterterm to the microscopic model compensates the unitary influence of the environment and, thus, inhibits the generation of entanglement. Investigating this assertion is one of the main objectives of the work presented here. Using the hierarchy of pure states (HOPS) method to numerically calculate the exact reduced dynamics, we find and explain that the degree of inhibition crucially depends on the parameter s determining the low frequency power law behavior of the spectral density J(ω)∼ωse−ω/ωc. Remarkably, we find that for resonant qubits, even in the adiabatic regime (arbitrarily large ωc), the entanglement dynamics is still influenced by an environmentally induced Hamiltonian interaction. Further, we study the model in detail and present the exact entanglement dynamics for a wide range of coupling strengths, distinguish between resonant and detuned qubits, as well as Ohmic and deep sub-Ohmic environments. Notably, we find that in all cases the asymptotic entanglement does not vanish and conjecture a linear relation between the coupling strength and the asymptotic entanglement measured by means of concurrence. Further we discuss the suitability of various perturbative master equations for obtaining approximate entanglement dynamics.

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Section: Introductionmentioning

confidence: 99%

Environmentally Induced Entanglement – Anomalous Behavior in the Adiabatic Regime

Hartmann

Strunz

2020

Quantum

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“…To find the evolution equation for all auxiliary states we can simply take the corresponding z * λ derivatives of (38). Then, the following commutations can be used to move the derivatives to the right hand side…”

Section: Hierarchy Expansionmentioning

confidence: 99%

Non-Markovian Quantum State Diffusion for Spin Environments

Link¹,

Luoma²,

Strunz³

2022

Preprint

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We introduce a theory of non-Markovian quantum state diffusion (NMQSD) for quantum systems coupled to a class of non-Gaussian environments consisting of spins. This allows us to express the time evolved reduced state of the system as the average of an ensemble of stochastically evolving pure states. We develop the theory for arbitrary linear spin environments at zero and also at finite temperature. Moreover, we introduce a hierarchical expansion which constitutes a method to numerically compute the time evolution of the stochastic pure states, and thus to solve the open system problem.

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“…In this work, we use a simple triangular truncation condition for the hierarchy: |k| ≤ K. More advanced truncation schemes are discussed in Ref. 36. It is also possible to use an adaptive algorithm to reduce the size of the hierarchy 29 or use a matrix product state representation.…”

Section: E Hops For Solving the Nmqsd Propagationmentioning

confidence: 99%

Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion

Chen,

Bennett,

Eisfeld

2022

Preprint

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Flexible scheme to truncate the hierarchy of pure states

Cited by 19 publications

References 51 publications

Environmentally Induced Entanglement – Anomalous Behavior in the Adiabatic Regime

Environmentally Induced Entanglement – Anomalous Behavior in the Adiabatic Regime

Non-Markovian Quantum State Diffusion for Spin Environments

Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion

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