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...

The solid-state superconducting circuit-QED (quantum electrodynamics) system is a promising candidate for quantum computing and quantum information processing, which serves also as an ideal platform for quantum measurement and quantum control studies. In this context, a large number of cavity photons may be involved in the quantum dynamics and will degrade the simulation efficiency. To avoid this difficulty, it is helpful to eliminate the degrees of freedom of the cavity photons, and obtain an effective master-equation description which contains only the qubit states. In this work, we examine two such schemes, the adiabatic elimination (AE) and the more recently proposed polaron transformation (PT) approaches, by comparing their results with exact numerical simulations. We find that in the absence of qubit-flip, which is a specific quantum nondemolition (QND) measurement, the PT scheme is superior to the AE method. Actually, in this case the PT scheme catches the measurement dynamics exactly. However, in the presence of qubit-flip such as for qubit oscillation measurement, the PT scheme is no longer better than the AE approach. We conclude that both schemes, in the weak measurement regime, can work almost equally well. This corresponds to strong cavity damping or weak coupling between the qubit and cavity photons. Out of this regime, unfortunately, one has to include the cavity photons into numerical simulations and more advanced methods/techniques are waiting for their exploration in this field.

Solid-state superconducting circuit-quantum electrodynamics (QED) system is a promising candidate for quantum information processing and an ideal platform for quantum measurement and quantum control studies. As an extension to our previous simulation for single qubit circuit-QED, in this work we simulate the quantum measurement and control of multi-qubit system. Particularly, we consider the deterministic generation of a two-qubit Bell state. In this context we examine the validity conditions of two cavity-photon-elimination scheme. On the level of quantum trajectory simulation, we find that, owing to the qubit flip caused by feedback, the advanced polaron-transformation scheme is no longer applicable if the measurement is not weak, which also makes meaningless the elegant effective measurement operator.