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Physical review. B./Physical review. B

Waiting-time distribution as a sensitive probe of non-Markovian dephasing dynamics in a double-dot Aharonov-Bohm interferometer

RuiQiang Li, Yi Ding, Yiying Yan, Yuguo Su, Yixiao Huang, Zoltán Néda, Elijah Omollo Ayieta, Georg Engelhardt, JunYan Luo

Published Jan 8, 2025• 4 citations
Publisher

Abstract

We investigate electron transport through a double dot Aharonov-Bohm interferometer coupled to a heat bath, which provides not only a dephasing source but also non-Markovian memory effects. The distribution of waiting times between subsequent electron transfers is utilized to analyze the unique non-Markovian dephasing dynamics, especially at short times. We show how the coherent oscillations in the weak system-bath coupling regime are washed out in the strong coupling limit, due to the dephasing during the propagation of the electrons through the double dot interferometer. Intriguingly, we find for an intermediate coupling strength that the non-Markovian properties of the system-bath coupling unambiguously give rise to a revival of the coherent oscillations in the waiting time distribution. By analyzing the corresponding moments, we furthermore demonstrate the unique advantages of the higher-order moments in revealing the non-Markovian characteristics.

DOI
10.1103/physrevb.111.035412

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We investigate electron transport through a double dot Aharonov-Bohm interferometer coupled to a heat bath, which provides not only a dephasing source but also non-Markovian memory effects. The distribution of waiting times between subsequent electron transfers is utilized to analyze the unique non-Markovian dephasing dynamics, especially at short times. We show how the coherent oscillations in the weak system-bath coupling regime are washed out in the strong coupling limit, due to the dephasing during the propagation of the electrons through the double dot interferometer. Intriguingly, we find for an intermediate coupling strength that the non-Markovian properties of the system-bath coupling unambiguously give rise to a revival of the coherent oscillations in the waiting time distribution. By analyzing the corresponding moments, we furthermore demonstrate the unique advantages of the higher-order moments in revealing the non-Markovian characteristics.
We formulate a quantum theory of electron waiting time distributions for charge transport in nanostructures described by non-Markovian generalized master equations. We illustrate our method by calculating the waiting time distribution of electron transport through a dissipative double quantum dot, where memory effects are present due to a strongly coupled heat bath. We consider the influence of non-Markovian dephasing on the distribution of electron waiting times and discuss how spectral properties of the heat bath may be detected through measurements of the electron waiting time.
We study the dynamics of a dressed qubit implemented by a spinless fermion hopping between two lattice sites with each site strongly coupled to a bath of phonons. We employ Lang-Firsov transformation to make the problem tractable perturbatively. Applying time-convolutionless master equation within the polaron frame, we investigate decoherence dynamics of the dressed qubit within the singlet-triplet basis of the system for a wide range of bath spectral densities. It is shown that the coherence persists for longer time scales for large coupling values and shows non-monotonic behaviour reflecting the presence of non-Markovianity in the dynamics. Non-Markovianity, characterized by coherence revivals and non-monotonic decay patterns, emerges distinctly depending on the bath spectrum and coupling strengths. Systems coupled to sub-Ohmic baths, whether both or in combination with another type, display pronounced memory effects at relatively small values of couplings. In contrast, combinations involving Ohmic and super-Ohmic baths exhibit noticeable non-Markovianity only at higher couplings.
The Aharonov-Bohm (AB) effect, which predicts that a magnetic field strongly influences the wave function of an electrically charged particle, is investigated in a three-site system in terms of the quantum control by an additional dephasing source. The AB effect leads to a nonmonotonic dependence of the steady-state current on the gauge phase associated with the molecular ring. This dependence is sensitive to site energy, temperature, and dephasing, and can be explained using the concept of the dark state. Although the phase effect vanishes in the steady-state current for strong dephasing, the phase dependence remains visible in an associated waiting-time distribution, especially at short times. Interestingly, the phase rigidity (i.e., the symmetry of the AB phase) observed in the steady-state current is now broken in the waiting-time statistics, which can be explained by the interference between transfer pathways.
The nonequilibrium real-time dynamics of electron coherence is explored in the quantum transport through the double-dot Aharonov-Bohm interferometers. We solve the exact master equation to find the exact quantum state of the device, from which the changes of the electron coherence through the magnetic flux in the nonequilibrium transport processes is obtained explicitly. We find that the relative phase between the two charge states of the double dot localizes to π2\fracπ{2}2π​ or −π2-\fracπ{2}−2π​ for all different magnetic flux. This nontrivial phase localization process can be manifested in the measurable occupation numbers.
The spin-boson model, describing a two-level system coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong coupling regime. Here, we additionally consider dephasing as a source of Markovian dissipation on top of the non-Markovian dynamics due to an Ohmic bath, and investigate the dynamics of the spin. We show that the characteristic frequency of the spin dynamics, while strongly renormalized by the bosonic bath, changes in a simple fashion (or does not change at all) with dephasing. To obtain these results, we develop an exact nonperturbative method known as the stochastic Schr\"odinger equation, mimicking the Ohmic bath via a stochastic magnetic field combined with the Lindblad quantum master equation due to dephasing, which allows us to numerically compute the dynamics. Furthermore, we derive weak-coupling analytic results utilizing the well-known noninteracting blip approximation. Our findings are relevant to quantum simulation of the spin-boson model in the regime of strong coupling in trapped ions and circuit QED architectures among others.
In this paper, we develop a nonperturbation theory for describing decoherence dynamics of electron charges in a double quantum dot gated by electrodes. We extend the Feynman-Vernon influence functional theory to fermionic environments and derive an exact master equation for the reduced density matrix of electrons in the double dot for a general spectral density at arbitrary temperature and bias. We then investigate the decoherence dynamics of the double-dot charge qubit with backreaction of the reservoirs being fully taken into account. Time-dependent fluctuations and leakage effects induced from the dot-reservoir coupling are explicitly explored. The charge qubit dynamics from the Markovian to non-Markovian regime is systematically studied under various manipulating conditions. The decay behavior of charge qubit coherence and the corresponding relaxation time T1{T}_{1}T1​ and dephasing time T2{T}_{2}T2​ are analyzed in detail.