Charge-Relaxation and Dwell Time in the fluctuating Admittance of a Chaotic Cavity

We consider the admittance of a chaotic quantum dot, capacitively coupled to a gate and connected to two electron reservoirs by multichannel ballistic point contacts. For a dot in the regime of weak-localization and universal conductance fluctuations, we calculate the average and variance of the admittance using random-matrix theory. We find that the admittance is governed by two time-scales: the classical admittance depends on the RC-time of the quantum dot, but the relevant time scale for the weak-localization correction and the admittance fluctuations is the dwell time. An extension of the circular ensemble is used for a statistical description of the energy dependence of the scattering matrix.Comment: 7 pages, RevTeX, 1 figur

Parity meter for charge qubits: an efficient quantum entangler

We propose a realization of a charge parity meter based on two double quantum dots alongside a quantum point contact. Such a device is a specific example of the general class of mesoscopic quadratic quantum measurement detectors previously investigated by Mao et al. [Phys. Rev. Lett. 93, 056803 (2004)]. Our setup accomplishes entangled state preparation by a current measurement alone, and allows the qubits to be effectively decoupled by pinching off the parity meter. Two applications of the parity meter are discussed: the measurement of Bell's inequality in charge qubits and the realization of a controlled NOT gate.Comment: 8 pages, 4 figures; v2: discussion of measurement time, references adde

Distribution of parametric conductance derivatives of a quantum dot

The conductance G of a quantum dot with single-mode ballistic point contacts depends sensitively on external parameters X, such as gate voltage and magnetic field. We calculate the joint distribution of G and dG/dX by relating it to the distribution of the Wigner-Smith time-delay matrix of a chaotic system. The distribution of dG/dX has a singularity at zero and algebraic tails. While G and dG/dX are correlated, the ratio of dG/dX and $\sqrt{G(1-G)}$ is independent of G. Coulomb interactions change the distribution of dG/dX, by inducing a transition from the grand-canonical to the canonical ensemble. All these predictions can be tested in semiconductor microstructures or microwave cavities.Comment: 4 pages, RevTeX, 3 figure

Transmission time of wave packets through tunneling barriers

The transmission of wave packets through tunneling barriers is studied in detail by the method of quantum molecular dynamics. The distribution function of the times describing the arrival of a tunneling packet in front of and behind a barrier and the momentum distribution function of the packet are calculated. The behavior of the average coordinate of a packet, the average momentum, and their variances is investigated. It is found that under the barrier a part of the packet is reflected and a Gaussian barrier increases the average momentum of the transmitted packet and its variance in momentum space.Comment: 23 pages, 5 figure

Wave attenuation model for dephasing and measurement of conditional times

Inelastic scattering induces dephasing in mesoscopic systems. An analysis of previous models to simulate inelastic scattering in such systems is presented and also a relatively new model based on wave attenuation is introduced. The problem of Aharonov-Bohm(AB) oscillations in conductance of a mesoscopic ring is studied. We have shown that conductance is symmetric under flux reversal and visibility of AB oscillations decay to zero as function of the incoherence parameter, signalling dephasing. Further wave attenuation is applied to a fundamental problem in quantum mechanics, i.e., the conditional(reflection/transmission) times spent in a given region of space by a quantum particle before scattering off from that region.Comment: 8 pages, 6 figures. Based on presentations by A. M. J and C. B at the 2nd Winter Institute on Foundations of Quantum theory, Quantum Optics and QIP held at S N Bose National Centre for Basic Sciences, Kolkata, India, from January 2-11, 200

Is there a renormalization of the 1D conductance in Luttinger Liquid model?

Properties of 1D transport strongly depend on the proper choice of boundary conditions. It has been frequently stated that the Luttinger Liquid (LL) conductance is renormalized by the interaction as $g \frac{e^2} {h}$. To contest this result I develop a model of 1D LL wire with the interaction switching off at the infinities. Its solution shows that there is no renormalization of the universal conductance while the electrons have a free behavior in the source and drain reservoirs.Comment: 5 pages, RevTex 2.0, attempted repair of tex error

Shot noise suppression in multimode ballistic Fermi conductors

We have derived a general formula describing current noise in multimode ballistic channels connecting source and drain electrodes with Fermi electron gas. In particular (at $eV\gg k_{B}T$), the expression describes the nonequilibrium ''shot'' noise, which may be suppressed by both Fermi correlations and space charge screening. The general formula has been applied to an approximate model of a 2D nanoscale, ballistic MOSFET. At large negative gate voltages, when the density of electrons in the channel is small, shot noise spectral density $S_{I}(0)$ approaches the Schottky value $2eI$, where $I$ is the average current. However, at positive gate voltages, when the maximum potential energy in the channel is below the Fermi level of the electron source, the noise can be at least an order of magnitude smaller than the Schottky value, mostly due to Fermi effects.Comment: 4 page

Edge state transmission, duality relation and its implication to measurements

The duality in the Chalker-Coddington network model is examined. We are able to write down a duality relation for the edge state transmission coefficient, but only for a specific symmetric Hall geometry. Looking for broader implication of the duality, we calculate the transmission coefficient $T$ in terms of the conductivity $\sigma_{xx}$ and $\sigma_{xy}$ in the diffusive limit. The edge state scattering problem is reduced to solving the diffusion equation with two boundary conditions $(\partial_y-(\sigma_{xy})/(\sigma_{xx})\partial_x)\phi=0$ and $[\partial_x+(\sigma_{xy}-\sigma_{xy}^{lead})/(\sigma_{xx}) \partial_y]\phi=0$. We find that the resistances in the geometry considered are not necessarily measures of the resistivity and $\rho_{xx}=L/W R/T h/e^2$ ($R=1-T$) holds only when $\rho_{xy}$ is quantized. We conclude that duality alone is not sufficient to explain the experimental findings of Shahar et al and that Landauer-Buttiker argument does not render the additional condition, contrary to previous expectation.Comment: 16 pages, 3 figures, to appear in Phys. Rev.

Quantum Force in Superconductor

Transitions between states with continuous (called as classical state) and discrete (called as quantum state) spectrum of permitted momentum values is considered. The persistent current can exist along the ring circumference in the quantum state in contrast to the classical state. Therefore the average momentum can changes at the considered transitions. In order to describe the reiterated switching into and out the quantum state an additional term is introduced in the classical Boltzmann transport equation. The force inducing the momentum change at the appearance of the persistent current is called as quantum force. It is shown that dc potential difference is induced on ring segments by the reiterated switching if the dissipation force is not homogeneous along the ring circumference. The closing of the superconducting state in the ring is considered as real example of the transition from classical to quantum stateComment: 4 pages, RevTex, 0 figure

Zero Frequency Current Noise for the Double Tunnel Junction Coulomb Blockade

We compute the zero frequency current noise numerically and in several limits analytically for the coulomb blockade problem consisting of two tunnel junctions connected in series. At low temperatures over a wide range of voltages, capacitances, and resistances it is shown that the noise measures the variance in the number of electrons in the region between the two tunnel junctions. The average current, on the other hand, only measures the mean number of electrons. Thus, the noise provides additional information about transport in these devices which is not available from measuring the current alone.Comment: 33 pages, 10 figure