The measurement-result-conditioned evolution of a system (e.g. an atom) with spontaneous emissions of photons is well described by the quantum trajectory (QT) theory. In this work we generalize the associated QT theory from infinitely wide bandwidth
Markovian environment to the case of finite bandwidth non-Markovian environment. In particular, we generalize the treatment for arbitrary spectrum, which is not restricted by the specific Lorentzian case. We rigorously prove a general existence of a perfect scaling behavior jointly defined by the bandwidth of environment and the time interval between successive photon detections. For a couple of examples, we obtain analytic results to facilitate QT simulations based on the Monte-Carlo algorithm. For the case where analytical result is not available, numerical scheme is proposed for practical simulations.
In this work we present a large-deviation analysis for the counting statistics of atomic spontaneous emissions continuously detected in finite-bandwidth non-Markovian environment. We show that the statistics of the spontaneous emissions depends on th
e response time of the detector, which can result in big differences such as dynamical phase transition. This feature excludes the idea of regarding the spontaneous emissions as detection-free objective events. Possible experiment is briefly discussed in connection with the state-of-the-art optical cavity set-up.
The Josephson supercurrent through the hybrid Majorana--quantum dot--Majorana junction is investigated. We particularly analyze the effect of spin-selective coupling between the Majorana and quantum dot states, which emerges only in the topological p
hase and will influence the current through bent junctions and/or in the presence of magnetic fields in the quantum dot. We find that the characteristic behaviors of the supercurrent through this system are quite counterintuitive, remarkably differing from the resonant tunneling, e.g., through the similar (normal phase) superconductor--quantum dot--superconductor junction. Our analysis is carried out under the influence of full set-up parameters and for both the $2pi$ and $4pi$ periodic currents. The present study is expected to be relevant to future exploration of applications of the Majorana-nanowire circuits.
In addition to the well-known Landauer-Buttiker scattering theory and the nonequilibrium Greens function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the
particle-number (n)-resolved master equation (n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.
We show that the Coulomb blockade in parallel dots pierced by magnetic flux $Phi$ completely blocks the resonant current for any value of $Phi$ except for integer multiples of the flux quantum $Phi_0$. This non-analytic (switching) dependence of the
current on $Phi$ arises only when the dot states that carry the current are of the same energy. The time needed to reach the steady state, however, diverges when $Phito nPhi_0$.
