Spectrum of qubit oscillations from Bloch equations

We have developed a formalism suitable for calculation of the output spectrum of a detector continuously measuring quantum coherent oscillations in a solid-state qubit, starting from microscopic Bloch equations. The results coincide with that obtained using Bayesian and master equation approaches. The previous results are generalized to the cases of arbitrary detector response and finite detector temperature.Comment: 8 page

Optical properties of Mn4+ ions in GaN:Mn codoped with Mg acceptors

The optical properties of Mn-Mg codoped epitaxial GaN were studied. Addition of Mg acceptors quenches the weak manganese-related photoluminescence (PL) band at 1.3 eV in GaN:Mn and a series of sharp PL peaks are observed at 1 eV in codoped epilayers. The change in PL spectra indicates that Mg addition stabilizes the Mn4+ charge state by decreasing the Fermi level. The 1 eV PL peaks are tentatively attributed to intra center transitions involving Mn4+ ions. Spin allowed 3d-shell 4T2-4T1 transitions and their phonon replicas are involved. The relative intensities of the sharp peaks are strongly dependent on the excitation wavelength, indicating the optically active Mn4+ centers involved in the separate peaks are different. The temperature dependence of the PL spectrum suggests the presence of at least three distinct Mn4+ complex centers.Comment: 14 pages, 3 figures, 1 table, accepted by Appl. Phys. Let

Full Frequency Back-Action Spectrum of a Single Electron Transistor during Qubit read-out

We calculate the spectral density of voltage fluctuations in a Single Electron Transistor (SET), biased to operate in a transport mode where tunneling events are correlated due to Coulomb interaction. The whole spectrum from low frequency shot noise to quantum noise at frequencies comparable to the SET charging energy $(E_{C}/\hbar)$ is considered. We discuss the back-action during read-out of a charge qubit and conclude that single-shot read-out is possible using the Radio-Frequency SET.Comment: 4 pages, 5 figures, submitted to PR

Nonideal quantum detectors in Bayesian formalism

The Bayesian formalism for a continuous measurement of solid-state qubits is derived for a model which takes into account several factors of the detector nonideality. In particular, we consider additional classical output and backaction noises (with finite correlation), together with quantum-limited output and backaction noises, and take into account possible asymmetry of the detector coupling. The formalism is first derived for a single qubit and then generalized to the measurement of entangled qubits.Comment: 10 page

Numerical analysis of the radio-frequency single-electron transistor operation

We have analyzed numerically the response and noise-limited charge sensitivity of a radio-frequency single-electron transistor (RF-SET) in a non-superconducting state using the orthodox theory. In particular, we have studied the performance dependence on the quality factor Q of the tank circuit for Q both below and above the value corresponding to the impedance matching between the coaxial cable and SET.Comment: 14 page

Continuous weak measurement of quantum coherent oscillations

We consider the problem of continuous quantum measurement of coherent oscillations between two quantum states of an individual two-state system. It is shown that the interplay between the information acquisition and the backaction dephasing of the oscillations by the detector imposes a fundamental limit, equal to 4, on the signal-to-noise ratio of the measurement. The limit is universal, e.g., independent of the coupling strength between the detector and system, and results from the tendency of quantum measurement to localize the system in one of the measured eigenstates

Statistics and noise in a quantum measurement process

The quantum measurement process by a single-electron transistor or a quantum point contact coupled to a quantum bit is studied. We find a unified description of the statistics of the monitored quantity, the current, in the regime of strong measurement and expect this description to apply for a wide class of quantum measurements. We derive the probability distributions for the current and charge in different stages of the process. In the parameter regime of the strong measurement the current develops a telegraph-noise behavior which can be detected in the noise spectrum.Comment: 4 pages, 2 figure

Feedback cooling of a nanomechanical resonator

Cooled, low-loss nanomechanical resonators offer the prospect of directly observing the quantum dynamics of mesoscopic systems. However, the present state of the art requires cooling down to the milliKelvin regime in order to observe quantum effects. Here we present an active feedback strategy based on continuous observation of the resonator position for the purpose of obtaining these low temperatures. In addition, we apply this to an experimentally realizable configuration, where the position monitoring is carried out by a single-electron transistor. Our estimates indicate that with current technology this technique is likely to bring the required low temperatures within reach.Comment: 10 pages, RevTex4, 4 color eps figure

Charge and current fluctuations in a superconducting single electron transistor near a Cooper pair resonance

We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even--odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasi-particle tunneling rates are comparable to the coherent Cooper-pair oscillation frequency. Furthermore the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.Comment: 10 pages, 11 figure

A Numerical Study of Transport and Shot Noise at 2D Hopping

We have used modern supercomputer facilities to carry out extensive Monte Carlo simulations of 2D hopping (at negligible Coulomb interaction) in conductors with the completely random distribution of localized sites in both space and energy, within a broad range of the applied electric field $E$ and temperature $T$, both within and beyond the variable-range hopping region. The calculated properties include not only dc current and statistics of localized site occupation and hop lengths, but also the current fluctuation spectrum. Within the calculation accuracy, the model does not exhibit $1/f$ noise, so that the low-frequency noise at low temperatures may be characterized by the Fano factor $F$. For sufficiently large samples, $F$ scales with conductor length $L$ as $(L_c/L)^{\alpha}$, where $\alpha=0.76\pm 0.08 < 1$, and parameter $L_c$ is interpreted as the average percolation cluster length. At relatively low $E$, the electric field dependence of parameter $L_c$ is compatible with the law $L_c\propto E^{-0.911}$ which follows from directed percolation theory arguments.Comment: 17 pages, 8 figures; Fixed minor typos and updated reference