Transmission Phase of an Isolated Coulomb-Blockade Resonance

In two recent papers, O. Entin-Wohlman et al. studied the question: ``Which physical information is carried by the transmission phase through a quantum dot?'' In the present paper, this question is answered for an islolated Coulomb-blockade resonance and within a theoretical model which is more closely patterned after the geometry of the actual experiment by Schuster et al. than is the model of O. Entin-Wohlman et al. We conclude that whenever the number of leads coupled to the Aharanov-Bohm interferometer is larger than two, and the total number of channels is sufficiently large, the transmission phase does reflect the Breit-Wigner behavior of the resonance phase shift.Comment: 6 pages and one figur

Crossing of two Coulomb-Blockade Resonances

We investigate theoretically the transport of non--interacting electrons through an Aharanov--Bohm (AB) interferometer with two quantum dots (QD) embedded into its arms. In the Coulomb-blockade regime, transport through each QD proceeds via a single resonance. The resonances are coupled through the arms of the AB device but may also be coupled directly. In the framework of the Landauer--Buttiker approach, we present expressions for the scattering matrix which depend explicitly on the energies of the two resonances and on the AB phase. We pay particular attention to the crossing of the two resonances.Comment: 15 pages, 1 figur

Field quantization for chaotic resonators with overlapping modes

Feshbach's projector technique is employed to quantize the electromagnetic field in optical resonators with an arbitray number of escape channels. We find spectrally overlapping resonator modes coupled due to the damping and noise inflicted by the external radiation field. For wave chaotic resonators the mode dynamics is determined by a non--Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.Comment: 4 pages, 1 figur

Interference Effects on Kondo-Assisted Transport through Double Quantum Dots

We systematically investigate electron transport through double quantum dots with particular emphasis on interference induced via multiple paths of electron propagation. By means of the slave-boson mean-field approximation, we calculate the conductance, the local density of states, the transmission probability in the Kondo regime at zero temperature. It is clarified how the Kondo-assisted transport changes its properties when the system is continuously changed among the serial, parallel and T-shaped double dots. The obtained results for the conductance are explained in terms of the Kondo resonances influenced by interference effects. We also discuss the impacts due to the spin-polarization of ferromagnetic leads.Comment: 9 pages, 11 figures ; minor corrections and references adde

A Mesoscopic Quantum Eraser

Motivated by a recent experiment by Buks et al. [Nature 391, 871 (1998)] we consider electron transport through an Aharonov-Bohm interferometer with a quantum dot in one of its arms. The quantum dot is coupled to a quantum system with a finite number of states acting as a which-path detector. The Aharonov-Bohm interference is calculated using a two-particle scattering approach for the joint transitions in detector and quantum dot. Tracing over the detector yields dephasing and a reduction of the interference amplitude. We show that the interference can be restored by a suitable measurement on the detector and propose a mesoscopic quantum eraser based on this principle.Comment: 7 pages, 2 figures, to appear in Europhys. Lett., uses EuroPhys.sty and EuroMacro.tex (included

Scattering phases in quantum dots: an analysis based on lattice models

The properties of scattering phases in quantum dots are analyzed with the help of lattice models. We first derive the expressions relating the different scattering phases and the dot Green functions. We analyze in detail the Friedel sum rule and discuss the deviation of the phase of the transmission amplitude from the Friedel phase at the zeroes of the transmission. The occurrence of such zeroes is related to the parity of the isolated dot levels. A statistical analysis of the isolated dot wave-functions reveals the absence of significant correlations in the parity for large disorder and the appearance, for weak disorder, of certain dot states which are strongly coupled to the leads. It is shown that large differences in the coupling to the leads give rise to an anomalous charging of the dot levels. A mechanism for the phase lapse observed experimentally based on this property is discussed and illustrated with model calculations.Comment: 18 pages, 9 figures. to appear in Physical Review

Friedel phases and phases of transmission amplitudes in quantum scattering systems

We illustrate the relation between the scattering phase appearing in the Friedel sum rule and the phase of the transmission amplitude for quantum scatterers connected to two one-dimensional leads. Transmission zero points cause abrupt phase changes $\pm\pi$ of the phase of the transmission amplitude. In contrast the Friedel phase is a continuous function of energy. We investigate these scattering phases for simple scattering problems and illustrate the behavior of these models by following the path of the transmission amplitude in the complex plane as a function of energy. We verify the Friedel sum rule for these models by direct calculation of the scattering phases and by direct calculation of the density of states.Comment: 12 pages, 12 figure

Classical orbit bifurcation and quantum interference in mesoscopic magnetoconductance

We study the magnetoconductance of electrons through a mesoscopic channel with antidots. Through quantum interference effects, the conductance maxima as functions of the magnetic field strength and the antidot radius (regulated by the applied gate voltage) exhibit characteristic dislocations that have been observed experimentally. Using the semiclassical periodic orbit theory, we relate these dislocations directly to bifurcations of the leading classes of periodic orbits.Comment: 4 pages, including 5 figures. Revised version with clarified discussion and minor editorial change

Microscopic mechanisms of dephasing due to electron-electron interactions

We develop a non-perturbative numerical method to study tunneling of a single electron through an Aharonov-Bohm ring where several strongly interacting electrons are bound. Inelastic processes and spin-flip scattering are taken into account. The method is applied to study microscopic mechanisms of dephasing in a non-trivial model. We show that electron-electron interactions described by the Hubbard Hamiltonian lead to strong dephasing: the transmission probability at flux $\Phi=\pi$ is high even at small interaction strength. In addition to inelastic scattering, we identify two energy conserving mechanisms of dephasing: symmetry-changing and spin-flip scattering. The many-electron state on the ring determines which of these mechanisms will be at play: transmitted current can occur either in elastic or inelastic channels, with or without changing the spin of the scattering electron.Comment: 11 pages, 16 figures Submitted to Phys. Rev.

Quantum statistics of overlapping modes in open resonators

We study the quantum dynamics of optical fields in weakly confining resonators with overlapping modes. Employing a recently developed quantization scheme involving a discrete set of resonator modes and continua of external modes we derive Langevin equations and a master equation for the resonator modes. Langevin dynamics and the master equation are proved to be equivalent in the Markovian limit. Our open-resonator dynamics may be used as a starting point for a quantum theory of random lasers.Comment: 6 pages, corrected typo