Charge Relaxation in the Presence of Shot Noise in Coulomb Coupled Mesoscopic Systems

In the presence of shot noise the charge on a mesoscopic conductor fluctuates. We are interested in the charge fluctuations which arise if the conductor is in the proximity of a gate to which it is coupled by long range Coulomb forces only. Specifically we consider a gate coupled to the edge of a Hall bar subject to a quantizing magnetic field which contains a quantum point contact. The gate is located away from the quantum point contact. We evaluate the charge relaxation resistance for this geometry. The charge relaxation resistance determines the current fluctuations and potential fluctuations induced into the gate. If there is only one edge channel the charge relaxation resistance is determined by transmission and reflection probabilities alone, but in the presence of many channels the density of states of all edge states determines this resistance.Comment: To appear in "Quantum Physics at Mesoscopic Scale" edited by D.C. Glattli, M. Sanquer and J. Tran Thanh Van Editions "Frontieres", 199

Irreversibility and Dephasing from Vacuum Fluctuations

We investigate the role of vacuum (zero-point) fluctuations in generating decoherence in a number of simple models. First we discuss a harmonic oscillator coupled to a semi-infinite elastic string and discuss the irreversible nature of such a bath. We investigate the fluctuations in energy of the oscillator and discuss the trace the oscillator leaves in the bath. Most of the work deals with two-level systems coupled to a bosonic bath (a transmission line). For two-level systems with a Hamiltonian that commutes with the total Hamiltonian (system plus coupling plus bath) the ground state is a pure state. The energy of the system is a constant of motion. For the general case, the energy of the two-level system fluctuates, and the ground state is only partially coherent. A particular realization of such a two level system consists of a mesoscopic ring with a quantum dot coupled capacitively to a transmission line. In the presence of an Aharonov-Bohm flux this system exhibits a persistent current. This current is a measure of the coherence of the ground state. As a function of the coupling strength the ground state undergoes a crossover from a state characterized by a time-averaged persistent current which is much larger than its time-averaged mean squared fluctuations to a state characterized by a persistent current with an average amplitude that is much smaller than its mean squared fluctuations.Comment: 27 pages, 6 figures: submitted for "Complexity from Microscopic to Macroscopic Scales: Coherence and Large Deviations", NATO ASI, Geilo, Norway, April 17-27 (2001) edited by Arne T. Skjeltorp and Tamas Vicsek, (Kluwer, Dordrecht

Decoherence from Vacuum Fluctuations

Vacuum fluctuations are a source of irreversibility and decoherence. We investigate the persistent current and its fluctuations in a ring with an in-line quantum dot with an Aharonov-Bohm flux through the hole of the ring. The Coulomb blockade leads to persistent current peaks at values of the gate voltage at which two charge states of the dot have the same free energy. We couple the structure to an external circuit and investigate the effect of the zero-temperature (vacuum fluctuations) on the ground state of the ring. We find that the ground state of the ring undergoes a crossover from a state with an average persistent current much larger than the (time-dependent) mean squared fluctuations to a state with a small average persistent current and large mean squared fluctuations. We discuss the spectral density of charge fluctuations and discuss diffusion rates for angle variables characterizing the ground state in Bloch representation.Comment: 6 pages, 2 figures, submitted for "Electronic Correlations: from meso- to nano-physics", edited by G. Montambaux and T. Martin, Rencontres de Moriond, (unpublished

Shot noise induced charge and potential fluctuations of edge states in proximity of a gate

We evaluate the RC-time of edge states capacitively coupled to a gate located away from a QPC which allows for partial transmission of an edge channel. At long times or low frequencies the RC-time governs the relaxation of charge and current and governs the fluctuations of the equilibrium electrostatic potential. The RC-time in mesoscopic structures is determined by an electrochemical capacitance which depends on the density of states of the edge states and a charge relaxation resistance. In the non-equilibrium case, in the presence of transport, the shot noise leads to charge fluctuations in proximity of the gate which are again determined by the equilibrium electrochemical capacitance but with a novel resistance. The case of multiple edge states is discussed and the effect of a dephasing voltage probe on these resistances is investigated. The potential fluctuations characterized by these capacitances and resistances are of interest since they determine the dephasing rate in Coulomb coupled mesoscopic conductors.Comment: To appear in the Proceedings of the XVI Sitges Conference, Statistical and Dynamical Aspects of Mesoscopic Systems, (Lecture Notes in Physics, Springer

Distribution functions and current-correlations in normal-metal--superconductor hetero-structures

We introduce electron-like and hole-like distribution functions, which determine the currents and the fluctuation spectra of the currents measured at a normal-conductor--superconductor hetero-structure. These distribution functions are expressed with the help of newly defined partial densities of states for hetero-structures. Voltage measurements using a weakly coupled contact on such a structure show the absence of a contact resistance to the superconducting reservoir and illustrate how the interface to the superconductor acts as an Andreev mirror. We also discuss the current-current correlations measured at two normal contacts and argue that the appearance of positive correlations is a purely mesoscopic effect, which vanishes in the limit of a large number of channels and in the average over an ensemble.Comment: 8 pages REVTeX, 1 figur

Chirality in Coulomb-blockaded quantum dots

We investigate the two-terminal nonlinear conductance of a Coulomb-blockaded quantum dot attached to chiral edge states. Reversal of the applied magnetic field inverts the system chirality and leads to a different polarization charge. As a result, the current--voltage characteristic is not an even function of the magnetic field. We show that the corresponding magnetic-field asymmetry arises from single-charge effects and vanishes in the limit of high temperature.Comment: 5 pages, 4 figure

Local Friedel sum rule on graphs

We consider graphs made of one-dimensional wires connected at vertices and on which may live a scalar potential. We are interested in a scattering situation where the graph is connected to infinite leads. We investigate relations between the scattering matrix and the continuous part of the local density of states, the injectivities, emissivities and partial local density of states. Those latter quantities can be obtained by attaching an extra lead at the point of interest and by investigating the transport in the limit of zero transmission into the additional lead. In addition to the continuous part related to the scattering states, the spectrum of graphs may present a discrete part related to states that remain uncoupled to the external leads. The theory is illustrated with the help of a few simple examples.Comment: 25 pages, LaTeX, 8 figure

Role of coherence in resistance quantization

The quantization of resistances in the quantum Hall effect and ballistic transport through quantum point contacts is compared with the quantization of the charge relaxation resistance of a coherent mesoscopic capacitor. While the former two require the existence of a perfectly transmitting channel, the charge relaxation resistance remains quantized for arbitrary backscattering. The quantum Hall effect and the quantum point contact require only local phase coherence. In contrast quantization of the charge relaxation resistance requires global phase coherence.Comment: 9 pages, 5 figure

Entanglement Energetics at Zero Temperature

We show how many-body ground state entanglement information may be extracted from sub-system energy measurements at zero temperature. Generically, the larger the measured energy fluctuations are, the larger the entanglement is. Examples are given with the two-state system and the harmonic oscillator. Comparisons made with recent qubit experiments show this type of measurement provides another method to quantify entanglement with the environment.Comment: 4 pages, 2 figure