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Molecular electronics is a rapidly developing field focused on using molecules as the structural basis for electronic components. It is common in such devices for the system of interest to couple simultaneously to multiple environments. Here we consider a model comprised of a double quantum dot (or molecule) coupled strongly to vibrations and weakly to two electronic leads held at arbitrary bias voltage. The strong vibrational coupling invalidates treating the bosonic and electronic environments simply as acting additively, as would be the case in the weak coupling regime or for flat leads at infinite bias. Instead, making use of the reaction coordinate framework we incorporate the dominant vibrational coupling effects within an enlarged system Hamiltonian. This allows us to derive a non-additive form for the lead couplings that accounts properly for the influence of strong and non-Markovian coupling between the double dot system and the vibrations. Applying counting statistics techniques we track electron flow between the double dot and the electronic leads, revealing both strong-coupling and non-additive effects in the electron current, noise and Fano factor.
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The complete characterisation of the charge transport in a mesoscopic device is provided by the Full Counting Statistics (FCS) $P_t(m)$, describing the amount of charge $Q = me$ transmitted during the time $t$. Although numerous systems have been theoretically characterized by their FCS, the experimental measurement of the distribution function $P_t(m)$ or its moments $langle Q^n rangle$ are rare and often plagued by strong back-action. Here, we present a strategy for the measurement of the FCS, more specifically its characteristic function $chi(lambda)$ and moments $langle Q^n rangle$, by a qubit with a set of different couplings $lambda_j$, $j = 1,dots,k,dots k+p$, $k = lceil n/2 rceil$, $p geq 0$, to the mesoscopic conductor. The scheme involves multiple readings of Ramsey sequences at the different coupling strengths $lambda_j$ and we find the optimal distribution for these couplings $lambda_j$ as well as the optimal distribution $N_j$ of $N = sum N_j$ measurements among the different couplings $lambda_j$. We determine the precision scaling for the moments $langle Q^n rangle$ with the number $N$ of invested resources and show that the standard quantum limit can be approached when many additional couplings $pgg 1$ are included in the measurement scheme.
In a recent experiment [A. Donarini et al., Nat Comms 10, 381 (2019)], electronic transport through a carbon nanotube quantum dot was observed to be suppressed by the formation of a quantum-coherent ``dark state. In this paper we consider theoretically the counting statistics and waiting-time distribution of this dark-state-limited transport. We show that the statistics are characterised by giant super-Poissonian Fano factors and long-tailed waiting-time distributions, both of which are signatures of the bistability and extreme electron bunching caused by the dark state.
In condensed matter physics, non-Abelian statistics for Majorana zero modes (or Majorana Fermions) is very important, really exotic, and completely robust. The race for searching Majorana zero modes and verifying the corresponding non-Abelian statistics becomes an important frontier in condensed matter physics. In this letter, we generalize the Majorana zero modes to non-Hermitian (NH) topological systems that show universal but quite different properties from their Hermitian counterparts. Based on the NH Majorana zero modes, the orthogonal and nonlocal Majorana qubits are well defined. In particular, the non-Abelian statistics for these NH Majorana zero modes become anomalous, which is different from the usual non-Abelian statistics. The usual Ivanovs braiding operator for two Majorana modes is generalized to a non-Hermitian Ivanovs braiding perator. The one-dimensional NH Kitaev model is taken as an example to numerically verify the anomalous non-Abelian statistics for two NH Majorana zero modes. The numerical results are exactly consistent with the theoretical prediction. With the help of braiding these two zero modes, the $pi/8$ gate can be reached and thus universal topological quantum computation becomes possible.
We theoretically study the conditional counting statistics of electron transport through a system consisting of a single quantum dot (SQD) or coherently coupled double quantum dots (DQDs) monitored by a nearby quantum point contact (QPC) using the generating functional approach with the maximum eigenvalue of the evolution equation matrix method, the quantum trajectory theory method (Monte Carlo method), and an efficient method we develop. The conditional current cumulants that are significantly different from their unconditional counterparts can provide additional information and insight into the electron transport properties of mesoscopic nanostructure systems. The efficient method we develop for calculating the conditional counting statistics is numerically stable, and is capable of calculating the conditional counting statistics for a more complex system than the maximum eigenvalue method and for a wider range of parameters than the quantum trajectory method. We apply our method to investigate how the QPC shot noise affects the conditional counting statistics of the SQD system, going beyond the treatment and parameter regime studied in the literature. We also investigate the case when the interdot coherent coupling is comparable to the dephasing rate caused by the back action of the QPC in the DQD system, in which there is considerable discrepancy in the calculated conditional current cumulants between the population rate (master-) equation approach of sequential tunneling and the full quantum master-equation approach of coherent tunneling.
We study analytically the full counting statistics of charge transport through single molecules, strongly coupled to a weakly damped vibrational mode. The specifics of transport in this regime - a hierarchical sequence of avalanches of transferred charges, interrupted by quiet periods - make the counting statistics strongly non-Gaussian. We support our findings for the counting statistics as well as for the frequency-dependent noise power by numerical simulations, finding excellent agreement.
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