Multiple-scale analysis of open quantum systems

Bernal-García, D. N.; Rodríguez, Boris A.; Vinck-Posada, Herbert

doi:10.1016/j.physleta.2019.02.044

Cited by 10 publications

(6 citation statements)

References 62 publications

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“…A second source of dissipation and decoherence is the pumping of the TLS, a common situation which is usually neglected. We will address the problem of the description of the dissipation and decoherence processes in a twolevel atom-cavity system at zero temperature considering both dissipative mechanisms through a phenomenological master equation [37]. In Lindblad form, the equation is…”

Section: Non-unitary Evolution Of the Systemmentioning

confidence: 99%

Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness

Viotti,

Lombardo,

Villar

2021

Preprint

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We follow a generalized kinematic approach to compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models, which provide a fully quantum description for a two-level system interacting with a single mode of the (cavity) electromagnetic field, in a perfect or dissipative cavity respectively. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls and the incoherent pumping of the two-level system. Our approach allows to compare the geometric phases acquired in these models, leading to an exhaustive characterization of the corrections introduced by the presence of the environment. We also provide geometric interpretations for the observed behaviours. When the resonance condition is satisfied, we show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution. This fact is supported with a geometrical explanation as well.

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Section: Non-unitary Evolution Of the Systemmentioning

confidence: 99%

Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness

Viotti,

Lombardo,

Villar

2021

Preprint

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“…for the two possible splitting of the argument of the exponential in Eq. (11). The apparently most natural choice is A = L and B = λ(E − 1), leading to…”

Section: J Ementioning

confidence: 99%

“…Various efforts have been done in this direction, leading to partial results both with reference to equations in time-local form [6][7][8][9][10][11][12], as well as to equations in time non local form [13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Quantum renewal processes

Vacchini

2020

Sci Rep

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We introduce a general construction of master equations with memory kernel whose solutions are given by completely positive trace preserving maps. These dynamics going beyond the Lindblad paradigm are obtained with reference to classical renewal processes, so that they are termed quantum renewal processes. They can be described by means of semigroup dynamics interrupted by jumps, separated by independently distributed time intervals, following suitable waiting time distributions. In this framework one can further introduce modified processes, in which the first few events follow different distributions. A crucial role, marking an important difference with respect to the classical case, is played by operator ordering. Indeed, for the same choice of basic quantum transformations different quantum dynamics arise. In particular for the case of modified processes it is natural to consider the time inverted operator ordering, in which the last few events are distributed differently.

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“…Multiplescale perturbation [1], for example, is a highly-developed approximation method that solves complex dynamics in a perturbative way, by introducing trial variables as different timescales which are often of physical importance themselves. It is used in many fields, especially in such quantum optics topics [2] as spontaneous radiation processes [3][4][5] and nonlinear solitons [6,7]. A summary of its applications in quantum optical problems can be found in Ref.…”

Section: Introductionmentioning

confidence: 99%

Multiple-scale perturbation method on integro-differential equations: Application to continuous-time quantum walks on regular networks in non-Markovian reservoirs

Meng

Zhang

et al. 2019

Phys. Rev. Research

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Non-Markovianity may significantly speed up quantum dynamics when the system interacts strongly with an infinite large reservoir, of which the coupling spectrum should be fine-tuned. The potential benefits are evident in many dynamics schemes, especially the continuous-time quantum walk. Difficulty exists, however, in producing closed-form solutions with controllable accuracy against the complexity of memory kernels. Here, we introduce a new multiple-scale perturbation method that works on integro-differential equations for general study of memory effects in dynamical systems. We propose an open-system model in which a continuous-time quantum walk is enclosed in a non-Markovian reservoir, that naturally corresponds to an error correction algorithm scheme. By applying the multiple-scale method we show how emergence of different timescales is related to transition of system dynamics into the non-Markovian regime. We find that up to two long-term modes and two short-term modes exist in regular networks, limited by their intrinsic symmetries. In addition to the effective approximation by our perturbation method on general forms of reservoirs, the speed-up of quantum walks assisted by non-Markovianity is also confirmed, revealing the advantage of reservoir engineering in designing time-sensitive quantum algorithms.

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Multiple-scale analysis of open quantum systems

Cited by 10 publications

References 62 publications

Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness

Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness

Quantum renewal processes

Multiple-scale perturbation method on integro-differential equations: Application to continuous-time quantum walks on regular networks in non-Markovian reservoirs

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