Non-Markovian dynamics of a nanomechanical resonator measured by a quantum point contact

We study the dynamics of a nanomechanical resonator (NMR) subject to a measurement by a low transparency quantum point contact (QPC) or tunnel junction in the non-Markovian domain. We derive the non-Markovian number-resolved (conditional) and unconditional master equations valid to second order in the tunneling Hamiltonian without making the rotating-wave approximation and the Markovian approximation, generally made for systems in quantum optics. Our non-Markovian master equation reduces, in appropriate limits, to various Markovian versions of master equations in the literature. We find considerable difference in dynamics between the non-Markovian cases and its Markovian counterparts. We also calculate the time-dependent transport current through the QPC which contains information about the measured NMR system. We find an extra transient current term proportional to the expectation value of the symmetrized product of the position and momentum operators of the NMR. This extra current term, with a coefficient coming from the combination of the imaginary parts of the QPC reservoir correlation functions, has a substantial contribution to the total transient current in the non-Markovian case, but was generally ignored in the studies of the same problem in the literature. Considering the contribution of this extra term, we show that a significantly qualitative and quantitative difference in the total transient current between the non-Markovian and the Markovian wide-band-limit cases can be observed. Thus, it may serve as a witness or signature of the non-Markovian features in the coupled NMR-QPC system.Comment: Accepted for publication in Physical Review B (20 pages, 13 figures

Decoherence and the retrieval of lost information

We found that in contrast with the common premise, a measurement on the environment of an open quantum system can {\em reduce} its decoherence rate. We demonstrate it by studying an example of indirect qubit's measurement, where the information on its state is hidden in the environment. This information is extracted by a distant device, coupled with the environment. We also show that the reduction of decoherence generated by this device, is accompanied with diminution of the environmental noise in a vicinity of the qubit. An interpretation of these results in terms of quantum interference on large scales is presented.Comment: 9 pages, 8 figures, additional explanations added, Phys. Rev. B, in pres

A practical scheme for error control using feedback

We describe a scheme for quantum error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols (for example Ahn et. al, PRA, 65, 042301 (2001)), is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit-flips. We also consider implementation in a solid-state quantum computation architecture and estimate the maximal error rate which could be corrected with current technology.Comment: 12 pages, 3 figures. Minor typographic change

Effects of J-gate potential and interfaces on donor exchange coupling in the Kane quantum computer architecture

We calculate the electron exchange coupling for a phosphorus donor pair in silicon perturbed by a J-gate potential and the boundary effects of the silicon host geometry. In addition to the electron-electron exchange interaction we also calculate the contact hyperfine interaction between the donor nucleus and electron as a function of the varying experimental conditions. Donor separation, depth of the P nuclei below the silicon oxide layer and J-gate voltage become decisive factors in determining the strength of both the exchange coupling and the hyperfine interaction - both crucial components for qubit operations in the Kane quantum computer. These calculations were performed using an anisotropic effective-mass Hamiltonian approach. The behaviour of the donor exchange coupling as a function of the device parameters varied provides relevant information for the experimental design of these devices.Comment: 15 pages, 15 figures. Accepted for Journal of Physics: Condensed Matte

Ion trap transducers for quantum electromechanical oscillators

An enduring challenge for contemporary physics is to experimentally observe and control quantum behavior in macroscopic systems. We show that a single trapped atomic ion could be used to probe the quantum nature of a mesoscopic mechanical oscillator precooled to 4K, and furthermore, to cool the oscillator with high efficiency to its quantum ground state. The proposed experiment could be performed using currently available technology.Comment: 4 pages, 2 figure

Simultaneous readout of two charge qubits

We consider a system of two solid state charge qubits, coupled to a single read-out device, consisting of a single-electron transistor (SET). The conductance of each tunnel junction is influenced by its neighboring qubit, and thus the current through the transistor is determined by the qubits' state. The full counting statistics of the electrons passing the transistor is calculated, and we discuss qubit dephasing, as well as the quantum efficiency of the readout. The current measurement is then compared to readout using real-time detection of the SET island's charge state. For the latter method we show that the quantum efficiency is always unity. Comparing the two methods a simple geometrical interpretation of the quantum efficiency of the current measurement appears. Finally, we note that full quantum efficiency in some cases can be achieved measuring the average charge of the SET island, in addition to the average current.Comment: 11 pages with 5 figure

Voltage Control of Exchange Coupling in Phosphorus Doped Silicon

Motivated by applications to quantum computer architectures we study the change in the exchange interaction between neighbouring phosphorus donor electrons in silicon due to the application of voltage biases to surface control electrodes. These voltage biases create electro-static fields within the crystal substrate, perturbing the states of the donor electrons and thus altering the strength of the exchange interaction between them. We find that control gates of this kind can be used to either enhance, or reduce the strength of the interaction, by an amount that depends both on the magnitude and orientation of the donor separation.Comment: 5 Pages, 5 Figure