Non-Markovian correlation functions for open quantum systems

Jin, Jinshuang; Karlewski, Christian; Marthaler, Michael

doi:10.1088/1367-2630/18/8/083038

Cited by 5 publications

(6 citation statements)

References 53 publications

(124 reference statements)

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“…In addition to this, we have also assumed that the full density matrix is not separable for all times which is another reason that QRT is no longer valid in the present case. Furthermore, for a non-Markovian equation the irrelevant term is non-zero and usual QRT can not be used to compute the system correlation in this case [36][37][38] . The equation for off-diagonal matrix element, Ω +− , is coupled to both diagonal Ω ++ , Ω −− and off-diagonal Ω −+ elements of the reduced system operator, and can be written in the form…”

Section: Generalized Master Equationmentioning

confidence: 99%

Theory of non-Markovian dynamics in resonance fluorescence spectrum

Kumar¹

2018

Opt Quant Electron

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We present a detailed theoretical study of non-Markovian dynamics in the fluorescence spectrum of a driven semiconductor quantum dot (QD), embedded in a cavity and coupled to a three-dimensional (3D) acoustic phonon reservoir. In particular, we investigate the effect of pure dephasing on one of the side-peaks of the Mollow-triplet spectrum, expressed in terms of the off-diagonal element of the reduced system operator. The QD is modeled as a two-level system with an excited state representing a single exciton, and ground state represents the absence of an exciton. Coupling to the radiative modes of the cavity is treated within usual Born-Markov approximation, whereas dot-phonon coupling is discussed within non-Markovian regime beyond Born approximation. Using an equation-of-motion technique, the dot-phonon coupling is solved exactly and found that the exact result coincides with that of obtained within Born approximation. Furthermore, a Markov approximation is carried out with respect to the phonon interaction and compared with the non-Markovian lineshape for different values of the phonon bath temperature. We have found that coupling to the phonons vanishes for a resonant pump laser. For a non-resonant pump, we have characterzied the effect of dot-laser detuning and temperature of the phonon bath on the lineshape. The sideband undergoes a distinct narrowing and aquires an asymmetric shape with increasing phonon bath temperature. We have explained this behavior using a dressed-state picture of the QD levels.

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Section: Generalized Master Equationmentioning

confidence: 99%

Theory of non-Markovian dynamics in resonance fluorescence spectrum

Kumar¹

2018

Opt Quant Electron

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“…This converts TNL-ME into a set of three time-local equation-of-motion (TL-EOM) formalism. The latter has the advantage in such as the initial value problems and nonequilibrium non-Markovian correlation functions [28]. The underlying algebra here is closely related to the DEOM theory [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Memory effect preserved time-local approach to noise spectrum of transport current

Xu¹,

Jin²,

Wang³

et al. 2022

Preprint

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Within the second-order non-Markovian master equation description, we develop an efficient method for calculating the noise spectrum of transport current through interacting mesoscopic systems. By introducing proper current-related density operators, we propose a practical and very efficient time-local approach to compute the noise spectrum, including the asymmetric spectrum, which contains the full information of energy emission and absorption. We obtain an analytical formula of the current noise spectrum to characterize the nonequilibrium transport including electron-electron Coulomb interaction and the memory effect. We demonstrate the proposed method in transport through interacting-quantum-dots system, and find good agreement with the exact results under broad range of parameters.

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“…derived time-local equations of motion for the two-time non-Markovian correlation function of arbitrary system operators in open quantum systems and used them to demonstrate that they could account for the typical non-Markovian effects in current fluctuation spectra of single and double quantum dots. [23]. Cosacchi et.…”

Section: Introductionmentioning

confidence: 99%

“…Many different approaches to calculate the TTCFs have been developed over the years [12][13][14][15][16][17][18][19][20][21][22][23]. Quantum regression theorem (QRT) provides a direct relation between the dynamics of single-time expectation values of system operators and their two-time correlation functions in Markovian systems and is used extensively in the earlier modelling attempts [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…Quantum regression theorem (QRT) provides a direct relation between the dynamics of single-time expectation values of system operators and their two-time correlation functions in Markovian systems and is used extensively in the earlier modelling attempts [12,13]. Validity of QRT in formulation of TTCFs for non-Markovian systems was questioned by various groups [24][25][26][27] which lead to various proposals to amend it to account for the memory effects [14][15][16][17][18][19][20][21][22][23]. de Vega and Alonso [22] used the stochastic Schrödinger equation approach to derive time evolution equations for single and two-time correlation functions of arbitrary system operators and used it to calculate the spectral properties of a two level atom weakly interacting with a highly non-Markovian electromagnetic environment.…”

Section: Introductionmentioning

confidence: 99%

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Two-time correlation functions beyond quantum regression theorem: Effect of external noise

Kurt

2021

Preprint

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We present the results of a study of the two-time correlation functions of a dichotomously driven two-level system in contact with a thermal bath by using corrections beyond quantum regression theorem. In the strong system-environment coupling regime, it is found that the noise parameters could be tuned to control the magnitude of corrections at low environmental temperatures. Motional averaging and narrowing effect of the external noise were observed on the absorption and emission spectra of the two-state system. Furthermore, effects similar to the destruction of tunneling and noise enhancement of transport are observed in the dynamics of the two-time correlations.

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Non-Markovian correlation functions for open quantum systems

Cited by 5 publications

References 53 publications

Theory of non-Markovian dynamics in resonance fluorescence spectrum

Theory of non-Markovian dynamics in resonance fluorescence spectrum

Memory effect preserved time-local approach to noise spectrum of transport current

Two-time correlation functions beyond quantum regression theorem: Effect of external noise

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