Full counting statistics for voltage and dephasing probes

We present a stochastic path integral method to calculate the full counting statistics of conductors with energy conserving dephasing probes and dissipative voltage probes. The approach is explained for the experimentally important case of a Mach-Zehnder interferometer, but is easily generalized to more complicated setups. For all geometries where dephasing may be modeled by a single one-channel dephasing probe we prove that our method yields the same full counting statistics as phase averaging of the cumulant generating function.Comment: 4 pages, 2 figure

Entanglement in Anderson Nanoclusters

We investigate the two-particle spin entanglement in magnetic nanoclusters described by the periodic Anderson model. An entanglement phase diagram is obtained, providing a novel perspective on a central property of magnetic nanoclusters, namely the temperature dependent competition between local Kondo screening and nonlocal Ruderman-Kittel-Kasuya-Yoshida spin ordering. We find that multiparticle entangled states are present for finite magnetic field as well as in the mixed valence regime and away from half filling. Our results emphasize the role of charge fluctuations.Comment: 5 pages, 3 figure

Noise and Full Counting Statistics of Incoherent Multiple Andreev Reflection

We present a general theory for the full counting statistics of multiple Andreev reflections in incoherent superconducting-normal-superconducting contacts. The theory, based on a stochastic path integral approach, is applied to a superconductor-double barrier system. It is found that all cumulants of the current show a pronounced subharmonic gap structure at voltages $V=2\Delta/en$. For low voltages $V\ll\Delta/e$, the counting statistics results from diffusion of multiple charges in energy space, giving the $p$th cumulant $\propto V^{2-p}$, diverging for $p\geq 3$. We show that this low-voltage result holds for a large class of incoherent superconducting-normal-superconducting contacts.Comment: 4 pages, 4 figure

Orbital entanglement and violation of Bell inequalities in mesoscopic conductors

We propose a spin-independent scheme to generate and detect two-particle entanglement in a mesoscopic normal-superconductor system. A superconductor, weakly coupled to the normal conductor, generates an orbitally entangled state by injecting pairs of electrons into different leads of the normal conductor. The entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current cross-correlators. It is shown that the Bell inequality can be violated for arbitrary strong dephasing in the normal conductor.Comment: 4 pages, 2 figure

Elastic Stars in General Relativity: II. Radial perturbations

We study radial perturbations of general relativistic stars with elastic matter sources. We find that these perturbations are governed by a second order differential equation which, along with the boundary conditions, defines a Sturm-Liouville type problem that determines the eigenfrequencies. Although some complications arise compared to the perfect fluid case, leading us to consider a generalisation of the standard form of the Sturm-Liouville equation, the main results of Sturm-Liouville theory remain unaltered. As an important consequence we conclude that the mass-radius curve for a one-parameter sequence of regular equilibrium models belonging to some particular equation of state can be used in the same well-known way as in the perfect fluid case, at least if the energy density and the tangential pressure of the background solutions are continuous. In particular we find that the fundamental mode frequency has a zero for the maximum mass stars of the models with solid crusts considered in Paper I of this series.Comment: 22 pages, no figures, final version accepted for publication in Class. Quantum Grav. The treatment of the junction conditions has been improve

Quantum pump driven fermionic Mach-Zehnder interferometer

We have investigated the characteristics of the currents in a pump-driven fermionic Mach-Zehnder interferometer. The system is implemented in a conductor in the quantum Hall regime, with the two interferometer arms enclosing an Aharonov-Bohm flux $\Phi$. Two quantum point contacts with transparency modulated periodically in time drive the current and act as beam-splitters. The current has a flux dependent part $I^{(\Phi)}$ as well as a flux independent part $I^{(0)}$. Both current parts show oscillations as a function of frequency on the two scales determined by the lengths of the interferometer arms. In the non-adiabatic, high frequency regime $I^{(\Phi)}$ oscillates with a constant amplitude while the amplitude of the oscillations of $I^{(0)}$ increases linearly with frequency. The flux independent part $I^{(0)}$ is insensitive to temperature while the flux dependent part $I^{(\Phi)}$ is exponentially suppressed with increasing temperature. We also find that for low amplitude, adiabatic pumping rectification effects are absent for semitransparent beam-splitters. Inelastic dephasing is introduced by coupling one of the interferometer arms to a voltage probe. For a long charge relaxation time of the voltage probe, giving a constant probe potential, $I^{(\Phi)}$ and the part of $I^{(0)}$ flowing in the arm connected to the probe are suppressed with increased coupling to the probe. For a short relaxation time, with the potential of the probe adjusting instantaneously to give zero time dependent current at the probe, only $I^{(\Phi)}$ is suppressed by the coupling to the probe.Comment: 10 pages, 4 figure

Electrical current noise of a beam splitter as a test of spin-entanglement

We investigate the spin entanglement in the superconductor-quantum dot system proposed by Recher, Sukhorukov and Loss, coupling it to an electronic beam-splitter. The superconductor-quantum dot entangler and the beam-splitter are treated within a unified framework and the entanglement is detected via current correlations. The state emitted by the entangler is found to be a linear superposition of non-local spin-singlets at different energies, a spin-entangled two-particle wavepacket. Colliding the two electrons in the beam-splitter, the singlet spin-state gives rise to a bunching behavior, detectable via the current correlators. The amount of bunching depends on the relative positions of the single particle levels in the quantum dots and the scattering amplitudes of the beam-splitter. The singlet spin entanglement, insensitive to orbital dephasing but suppressed by spin dephasing, is conveniently quantified via the Fano factors. It is found that the entanglement-dependent contribution to the Fano factor is of the same magnitude as the non-entangled, making an experimental detection feasible. A detailed comparison between the current correlations of the non-local spin-singlet state and other states, possibly emitted by the entangler, is performed. This provides conditions for an unambiguous identification of the non-local singlet spin entanglement.Comment: 13 pages, 8 figures, section on quantification of entanglement adde

Charge qubit entanglement in double quantum dots

We study entanglement of charge qubits in a vertical tunnel-coupled double quantum dot containing two interacting electrons. Exact diagonalization is used to compute the negativity characterizing entanglement. We find that entanglement can be efficiently generated and controlled by sidegate voltages, and describe how it can be detected. For large enough tunnel coupling, the negativity shows a pronounced maximum at an intermediate interaction strength within the Wigner molecule regime.Comment: revised version of the manuscript, as published in EPL, 7 pages, 4 figure

Two-particle Aharonov-Bohm effect and Entanglement in the electronic Hanbury Brown Twiss setup

We analyze a Hanbury Brown Twiss geometry in which particles are injected from two independent sources into a mesoscopic electrical conductor. The set-up has the property that all partial waves end in different reservoirs without generating any single particle interference. There is no single particle Aharonov-Bohm effect. However, exchange effects lead to two-particle Aharonov-Bohm oscillations in current correlations. We demonstrate that the two-particle Aharonov-Bohm effect is connected to orbital entanglement which can be used for violation of a Bell Inequality.Comment: 4 pages, 2 figures, discussion of postselected electron-electron entanglement adde

Quantum state tomography with quantum shotnoise

We propose a scheme for a complete reconstruction of one- and two-particle orbital quantum states in mesoscopic conductors. The conductor in the transport state continuously emits orbital quantum states. The orbital states are manipulated by electronic beamsplitters and detected by measurements of average currents and zero frequency current shotnoise correlators. We show how, by a suitable complete set of measurements, the elements of the density matrices of the one- and two-particle states can be directly expressed in terms of the currents and current correlators.Comment: 4 pages, 2 figure