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Journal of Computational and Theoretical Nanoscience

Microscopic Modeling of Energy Dissipation and Decoherence in Open Quantum Systems: Application to Semiconductor Nanodevices

David Taj, Rita Claudia Iotti, Fausto Rossi

Published Aug 1, 2009• 0 citations
Publisher

Abstract

A general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems is presented. More specifically, contrary to the conventional single-particle correlation expansion, we shall investigate the effect of the adiabatic or Markov limit, before considering/performing any reduction procedure. Our fully operatorial approach allows us to better identify the general properties of the scattering superoperators entering our effective quantum-transport theory at various description levels. In particular, we shall show that—contrary to the semiclassical case—the conventional Markov limit does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative and more general adiabatic procedure, which (i) in the semiclassical limit reduces to the standard Fermi's golden rule, and (ii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in semiconductor quantum devices

DOI
10.1166/jctn.2009.1251

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A general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems is presented. More specifically, contrary to the conventional single-particle correlation expansion, we shall investigate the effect of the adiabatic or Markov limit, before considering/performing any reduction procedure. Our fully operatorial approach allows us to better identify the general properties of the scattering superoperators entering our effective quantum-transport theory at various description levels. In particular, we shall show that—contrary to the semiclassical case—the conventional Markov limit does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative and more general adiabatic procedure, which (i) in the semiclassical limit reduces to the standard Fermi's golden rule, and (ii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in semiconductor quantum devices
We shall revisit the conventional adiabatic or Markov approximation, which — contrary to the semiclassical case– does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally addressed by Davies and co-workers almost three decades ago, we shall propose an alternative more general adiabatic procedure, able to provide a reliable/robust treatment of energy-dissipation and dephasing processes in electronic quantum devices. Unlike standard master-equation formulations, our procedure guarantees a positive evolution for a variety of physical subsystem (including the common partial trace), and quantum scattering rates are well defined even for subsystems with internal structure/ continuous energy spectrum. We shall compare the proposed Markov dissipation model with the conventional one also through basic simulations of energy-relaxation versus decoherence channels in prototypical semiconductor nanodevices.
We shall revisit the conventional adiabatic or Markov approximation, which --contrary to the semiclassical case-- does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative more general adiabatic procedure, which (i) is physically justified under the same validity restrictions of the conventional Markov approach, (ii) in the semiclassical limit reduces to the standard Fermi's golden rule, and (iii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in electronic quantum devices. Unlike standard master-equation formulations, the dependence of our approximation on the specific choice of the subsystem (that include the common partial trace reduction) does not threaten positivity, and quantum scattering rates are well defined even in case the subsystem is infinitely extended/has continuous spectrum.
Abstract We shall revisit the conventional adiabatic or Markov approximation, stressing its intrinsic failure in describing the proper quantum‐mechanical evolution of a generic subsystem interacting with its environment. In particular, we shall show that – contrary to the semiclassical case – the Markov limit does not preserve the positivedefinite character of the corresponding density matrix, thus leading to highly non‐physical results. To overcome this problem, we shall propose an alternative adiabatic procedure which (i) in the semiclassical limit reduces to the standard Fermi's golden rule, and (ii) describes a genuine Limblad evolution, thus providing a reliable/robust treatment of energy‐dissipation and dephasing processes in electronic quantum devices. Compared to standard master‐equation formulations, the proposed approach does not involve/require any reduction or average procedure, exactly as for the derivation of the well known Fermi's golden rule. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We shall revisit the conventional adiabatic or Markov approximation, showing its intrinsic failure in describing the proper quantum-mechanical evolution of a generic subsystem interacting with its environment. In particular, we shall show that -contrary to the semiclassical case- the Markov limit does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this problem, we shall propose an alternative adiabatic procedure which (i) in the semiclassical limit reduces to the standard Fermi's golden rule, and (ii) describes a genuine Limblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes.
The design and optimization of new-generation solid-state quantum hardware absolutely requires reliable dissipation versus decoherence models. Depending on the device operational condition, the latter may range from Markov-type schemes (both phenomenological- and microscopic- like) to quantum-kinetic approaches. The primary goal of this paper is to review in a cohesive way virtues versus limitations of the most popular approaches, focussing on a few critical issues recently pointed out (see, e.g., Phys. Rev. B 90, 125140 (2014); Eur. Phys. J. B 90, 250 (2017)) and linking them within a common framework. By means of properly designed simulated experiments of a prototypical quantum-dot nanostructure (described via a two-level electronic system coupled to a phonon bath), we shall show that both conventional (i.e., non-Lindblad) Markov models and density-matrix-based non-Markov approaches (i.e., quantum-kinetic treatments) may lead to significant positivity violations. While for the former case the problem is easily avoidable by choosing genuine Lindblad-type dissipation models, for the latter, a general strategy is still missing.
Starting from a recent reformulation of the Markov limit, we apply the mean- field approximation to the resulting Lindblad-type many-electron dynamics, and derive a closed equation of motion for the electronic single-particle density matrix in the presence of one- and two-body scattering mechanisms. The proposed formulation preserves the positive- definite character of the single-particle density matrix. This result is in striking contrast with conventional Markov approaches, where the single-particle mean-field equations can lead to positivity violations and therefore to unphysical results.