Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects

Flindt, Christian; Novotný, Tomáš; Braggio, Alessandro; Jauho, Antti–Pekka

doi:10.1103/physrevb.82.155407

Cited by 139 publications

(205 citation statements)

References 132 publications

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“…The calculation of the coefficients entering the cross-correlations is cumbersome, but essentially follows the steps described in Ref. [9] (Sec. IIIA) and the details are not presented here.…”

Section: To Evaluate the Coefficients In The Expansions We Perform Amentioning

confidence: 99%

“…Technically, we employ the recursive perturbation scheme developed in Refs. [8,9]. To calculate the mean current and the average cavity occupation we only need the corrections |0 .…”

Section: To Evaluate the Coefficients In The Expansions We Perform Amentioning

confidence: 99%

“…As a central goal, we examine these photon-mediated processes in the regime of weak couplings between DQDs and cavity, where we employ a recursive perturbation technique [8,9] to calculate the average currents, the mean cavity photon occupation, as well as the cross-correlations between the currents in the DQDs [7,10,11]. This approach, combined with the full numerical simulation, allows us to clearly identify the photon-mediated transport processes order-by-order in the cavity couplings.…”

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confidence: 99%

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Photon-mediated electron transport in hybrid circuit-QED

Lambert

Flindt

Nori

2013

EPL

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-We investigate photon-mediated transport processes in a hybrid circuit-QED structure consisting of two double quantum dots coupled to a common microwave cavity. Under suitable resonance conditions, electron transport in one double quantum dot is facilitated by the transport in the other dot via photon-mediated processes through the cavity. We calculate the average current in the quantum dots, the mean cavity photon occupation, and the current cross-correlations with both a full numerical simulation and a recursive perturbation scheme that allows us to include the influence of the cavity order-by-order in the couplings between the cavity and the quantum dot systems. We can then clearly identify the photon-mediated transport processes.Introduction. -Hybrid structures that combine electronic and photonic degrees of freedom in on-chip circuit-QED architectures are currently undergoing a rapid development [1]. A series of recent experiments [2,3] have shown that controllable coupling between electronic transport in quantum dot structures and a single mode of the electromagnetic field in a microwave cavity is now achievable. Several experiments have realized both a single quantum dot and two tunnel-coupled quantum dots interacting with a microwave resonator [2]. Very recently two quantum dots were successfully coupled to distant parts of a common cavity resonator, and photon-mediated interaction between the spatially separated quantum dot circuits was reported [3].These experimental advances are now fueling an increasing theoretical interest in understanding and predicting the physics of hybrid circuit-QED structures [1,4]. A number of proposals [5] have already considered the coupling of electronic spins in quantum dots to microwave resonators. In parallel, other works [6] have focused on the influence of cavity resonators on the transport properties of nearby quantum dot systems. A very recent work [7] expands theoretically on the experimental setup from Ref.[3] by considering two separated double quantum dots (DQDs) connected to the same cavity mode. With the DQDs weakly coupled to electronic leads at finite voltages, this system displays intriguing Tavis-Cummings physics, non-local charge transport and electronic entan-

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Section: To Evaluate the Coefficients In The Expansions We Perform Amentioning

confidence: 99%

“…Technically, we employ the recursive perturbation scheme developed in Refs. [8,9]. To calculate the mean current and the average cavity occupation we only need the corrections |0 .…”

Section: To Evaluate the Coefficients In The Expansions We Perform Amentioning

confidence: 99%

mentioning

confidence: 99%

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Photon-mediated electron transport in hybrid circuit-QED

Lambert

Flindt

Nori

2013

EPL

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“…However, because of its infinite dimensionality a closed-form expression for the eigenvalue is not feasible to obtain 70 . The cumulants can however be calculated numerically following the Rayleigh-Schrdinger perturbation scheme as described in 66,67 . An analytical expression for the current can be recovered from Eq.…”

Section: B Qme Approachmentioning

confidence: 99%

Reconciling perturbative approaches in phonon-assisted transport junctions

Agarwalla

Segal

2016

The Journal of Chemical Physics

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We present consistent results for molecular conduction using two central-complementary approaches: the non-equilibrium Green's function technique and the quantum master equation method. Our model describes electronic conduction in a donor-acceptor junction in which electron transfer is coupled to nuclear motion, modeled by a harmonic vibrational mode. This primary mode is further coupled to secondary phonon modes, a thermal bath. Assuming weak electron-phonon coupling but arbitrary large molecule-metal hybridization, we compute several non-equilibrium transport quantities: the mean phonon number of the primary mode, charge current statistics. We further present scaling relations for the cumulants valid in the large voltage regime. Our analysis illustrates that the non-equilibrium Green's function technique and the quantum master equation method can be worked out consistently, when taking into account corresponding scattering processes.

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“…Particularly, associated with the peculiar DCD setup, we will discuss and uncover other features in relation with the coherence-mediated transfer and electron accumulation (floating) in the continuum, basing both on an exact treatment for the non-Markovian transport. The issue of non-Markovian transport through quantum dots has received considerable attention in the past years [6][7][8][9][10][11][12][13], * Electronic address: lixinqi@bnu.edu.cn where the non-Markovian transient dynamics are usually manifested in the current noise spectrum or in terms of full counting statistics. Moreover, exploiting the nature of non-Markovianity in broader contexts has been a subject of great interest in recent years, which stimulated novel means such as information-theoretic approach to recognize that non-Markovian dynamics is a reversed flow of information from the environment back to the open system [14,15].…”

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confidence: 99%

Non-Markovian transmission through two quantum dots connected by a continuum

Cao¹,

Xu²,

Jian-Yu³

et al. 2012

Physics Letters A

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We consider a transport setup containing a double-dot connected by a continuum. Via an exact solution of the time-dependent Schrödinger equation, we demonstrate a highly non-Markovian quantum-coherence-mediated transport through this dot-continuum-dot (DCD) system, which is in contrast with the common premise since in typical case a quantum particle does not reenter the system of interest once it irreversibly decayed into a continuum (such as the spontaneous emission of a photon). We also find that this DCD system supports an unusual steady state with unequal source and drain currents, owing to electrons irreversibly entering the continuum and floating there.PACS numbers: 03.65. Yz, Coupling of a finite-size system to a reservoir with continuum energy spectrum is relevant to many fundamental issues of physics, e.g., the emergence of classicality from a quantum world [1], and the origin of irreversibility in statistical physics. Simple example of such type of coupling can be a small system, with discrete states, coupled to a continuum in terms of quantum tunneling.In most cases, coupling with a continuum would result in an irreversible decay of the discrete state, with the particle never coming back, such as the spontaneous emission of photon from an atom. However, in a recent study [2], where a double-dot connected by a continuum was considered, it was found that the second dot can affect the decay from the first dot via quantum interference, and finally lead to a formation of stationary bound state embedded in the continuum. In subsequent related studies [3,4], also concerning this dot-continuum-dot (DCD) system, it was demonstrated that the electron's motion through the continuum is very unusual, say, revealing an undetectable feature in the transfer process, and the information lost into the continuum can be retrieved without generating more disturbance.In the present work we consider inserting the DCD system into a transport configuration, as schematically shown by Fig. 1, which allows for an investigation for the behavior of continuous current through the DCD setup. Moreover, beyond the above DCD studies [2][3][4], where a wideband-limit (WBL) model was assumed for the central continuum, we will generalize our study to a finite-bandwidth Lorentzian spectrum (FBLS) for both the leads and the continuum. As a consequence, the transient transport process is highly non-Markovian, much stronger than in the WBL [5]. Particularly, associated with the peculiar DCD setup, we will discuss and uncover other features in relation with the coherence-mediated transfer and electron accumulation (floating) in the continuum, basing both on an exact treatment for the non-Markovian transport. The issue of non-Markovian transport through quantum dots has received considerable attention in the past years [6-13], * Electronic address: lixinqi@bnu.edu.cn where the non-Markovian transient dynamics are usually manifested in the current noise spectrum or in terms of full counting statistics. Moreover, exploiting the nature of non-Mark...

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Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects

Cited by 139 publications

References 132 publications

Photon-mediated electron transport in hybrid circuit-QED

Photon-mediated electron transport in hybrid circuit-QED

Reconciling perturbative approaches in phonon-assisted transport junctions

Non-Markovian transmission through two quantum dots connected by a continuum

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