We consider an experimentally feasible setup to demonstrate the existence and coherent dynamics of Majorana fermion. The transport setup consists of a quantum dot and a tunnel-coupled semiconductor nanowire which is anticipated to generate Majorana excitations under some conditions. For transport under finite bias voltage, we find that a subtraction of the source and drain currents can expose the essential feature of the Majorana fermion, including the zero-energy nature by gate-voltage modulating the dot level. Moreover, coherent oscillating dynamics of the Majorana fermion between the nanowire and the quantum dot is reflected in the shot noise, via a spectral dip together with a pronounced zero-frequency noise enhancement effect. Important parameters, e.g., for the Majorana's mutual interaction and its coupling to the quantum dot, can be extracted out in experiment using the derived analytic results.

We consider the parallel transport through two quantum dots correlated by a semiconductor nanowire which may support a pair of Majorana bound states at the ends. In addition to transient dynamics, via modulating the quantum dot levels, we reveal a characteristic feature of symmetry and antisymmetry in the spectral density of cross correlation mediated by Majorana fermion. We also find an intriguing behavior of vanished cross correlation when one of the dot levels is in resonance with the Majorana zero mode. PACS numbers: 71.10.Pm,74.78.Na,74.45.+c It has attracted considerable attention in the past years to search for Majorana fermion [1,2] in solid states, such as the 5/2 fractional quantum Hall system[3] and the pwave superconductor and superfluid [4,5]. In particular, it was predicted that a semiconductor nanowire, with strong spin-orbit coupling and subject to external magnetic field, may support zero-energy Majorana bound state (MBS) when the nanowire is in proximity to an s-wave superconductor [6][7][8]. This proposal has the major advantage of requiring only the most conventional materials, being thus easier to implement in experiments. Indeed, in some recent experiments [9][10][11][12], evidences of the MBSs were spotted in this sort of hybrid nanowire systems.The realization and manipulation of Majorana fermion in solid-states may pave a way for the desirable faulttolerant topological quantum computation [13][14][15][16]. In pure physics, the Majorana study in solid states is intriguing because of many unusual effects, such as the nonAbelian statistics [? ], the sharp jump in conductance peak [17], the peculiar noise behaviors [18][19][20][21][22], and the 4π periodic Majorana-Josephson currents [4,6,23,24], etc. Remarkably, most of these effects are associated with the nonlocal nature of the Majorana fermion [25][26][27]. The novel nonlocality feature can be most surprisingly elaborated by the example of its nanowire realization. In this case, the emerged pair of MBSs at the ends of the nanowire constitutes, respectively, the real and imaginary parts of an ordinary fermion. This means that, if an electron with energy smaller than the energy gap between the Majorana zero mode and other exited states is injected into the nanowire, the electron would split into two Majorana bound states which are essentially correlated but spatially separated. In some sense the Majorana's nonlocality can be related to a nonlocal cross Andreev reflection (CAR) process [19,25], because of the presence of superconductivity. However, as described above, the concept of nonlocality of Majorana fermion itself has richer information and is more intriguing than the CAR phenomenon. In Ref.[28] the nonlocal CAR process has been exploited for quantum teleportation, following the same idea of the pio- * Electronic address: skylark.gong@gmail.com † Electronic address: lixinqi@bnu.edu.cn neering work by Bennett et al. [29]. In such teleportation scheme, what is teleportated is the "state information", but not a "matter" as possibly m...

In a solid-state circuit QED system, we extend the previous study of generating and stabilizing a two-qubit Bell state [Phys. Rev. A 82, 032335 (2010)] to a three-qubit GHZ state. In a dispersive regime, we employ the homodyne joint readout for multiple qubits to infer the state for further processing, and in particular we use it to stabilize the state directly by means of an alternate-flip-interrupted Zeno (AFIZ) scheme. Moreover, the stateof-the-art feedback action based on the filtered current enables not only a deterministic generation of the pre-GHZ state in the initial stage, but also a fast recovery from occasional error in the later stabilization process. We show that the proposed scheme can maintain the state with high fidelity if the efficient quantum measurement and rapid single-qubit rotations are available.

Compared with the quantum trajectory equation (QTE), the quantum Bayesian approach has the advantage of being more efficient to infer quantum state under monitoring, based on the integrated output of measurement. For weak measurement of qubits in circuit quantum electrodynamics (cQED), properly accounting for the measurement backaction effects within the Bayesian framework is an important problem of current interest. Elegant work towards this task was carried out by Korotkov in "bad-cavity" and weak-response limits (arXiv:1111.4016). In the present work, based on insights from the cavity-field states (dynamics) and the help of an effective QTE, we generalize the results of arXiv:1111.4016 to more general system parameters. The obtained Bayesian rule is in full agreement with Korotkov's result in limiting cases and as well holds satisfactory accuracy in non-limiting cases in comparison with the QTE simulations. We expect the proposed Bayesian rule to be useful for future cQED measurement and control experiments.

We noted an error in the integrand in equation (18). That is, the phase factor Φ t ( ) m 2