Noise correlations, entanglement, and Bell inequalities

The aim of this chapter is to describe two situations where positive noise correlations can be directly monitored using a transport experiment, either with a superconductor or with a correlated electron system. To be more precise, the present text reflects the presentations made by the three authors during the Delft NATO workshop. Bell inequalities and quantum mechanical non-locality with electrons injected from a superconductor will be addressed first. Next, noise correlations will be computed in a carbon nanotube where electrons are injected in the bulk from a STM tip. The first topic is the result of an ongoing collaboration with G. Lesovik and G. Blatter over the years. The unifying theme is that in both branched quantum circuits, entanglement is explicit and can be illustrated via noise correlations. Entanglement can be achieved either for pairs of electrons in the case of superconductor sources connected to Fermi liquid leads, or alternatively for pairs of quasiparticle excitations of the correlated electron fluid.Comment: 24 pages, 7 figures, Proceedings of the NATO ARW workshop on Quantum Noise, Y. Nazarov and Y. Blanter editors (Kluwer 2002

Photo-assisted shot noise in the fractional quantum Hall regime

The effect of an ac perturbation on the shot noise of a fractional quantum Hall fluid is studied at finite temperature. For a normal metal, it is known that the zero-frequency noise derivative exhibits steps as a function of bias voltage. In contrast, at Laughlin fractions, the backscattering noise exhibits evenly spaced singularities, which are reminiscent of tunneling density-of-states singularities for quasiparticles. The spacing is determined by the quasiparticle charge $\nu e$ and the ratio of the dc bias with respect to the drive frequency. Photo-assisted transport can thus be considered as a probe for effective charges of the quantum Hall effect.Comment: Proceeding of the 18th International Conference on Noise and Fluctuations, Salamanca, Spai

Measurement of finite frequency noise cross-correlations with a resonant circuit

The measurement of finite frequency noise cross-correlations represents an experimental challenge in mesoscopic physics. Here we propose a generalisation of the resonant LC circuit setup of Lesovik and Loosen which allow to probe directly such cross-correlations by measuring the charge fluctuations on the plates of a capacitor. The measuring circuit collects noise contributions at the resonant frequency of the LC circuit. Auto-correlation noise can be canceled out by switching the wires and making two distinct measurements. The measured cross-correlations then depend of four non-symmetrized correlators. This detection method is applied to a normal metal three terminal device. We subsequently discuss to what extent the measurement circuit can detect electron-antibunching and what singularities appear in the spectral density of noise cross-correlations

Anomalous Hall effect in ferromagnetic disordered metals

The anomalous Hall effect in disordered band ferromagnets is considered in the framework of quantum transport theory. A microscopic model of electrons in a random potential of identical impurities including spin-orbit coupling is used. The Hall conductivity is calculated from the Kubo formula for both, the skew scattering and the side-jump mechanisms. The recently discussed Berry phase induced Hall current is also evaluated within the model. The effect of strong impurity scattering is analyzed and it is found to affect the ratio of the non-diagonal (Hall) and diagonal components of the conductivity as well as the relative importance of different mechanisms.Comment: Invited paper for Ann. Physik commemorating Paul Drud

Photo-assisted shot noise in Coulomb interacting systems

We consider the fluctuations of the electrical current (shot noise) in the presence of a voltage time-modulation. For a non-interacting metal, it is known that the derivative of the photo-assisted noise has a staircase behavior. In the presence of Coulomb interactions, we show that the photo-assisted noise presents a more complex profile, in particular for the two following systems: 1) a two-dimensional electron gas in the fractional quantum Hall regime for which we have obtained evenly spaced singularities in the noise derivative, with a spacing related to the filling factor and, 2) a carbon nanotube for which a smoothed staircase in the noise derivative is obtained.Comment: Proceedings of the 6th Rencontres du Vietnam, Hanoi (2006

Quantum dot dephasing by fractional quantum Hall edge states

We consider the dephasing rate of an electron level in a quantum dot, placed next to a fluctuating edge current in the fractional quantum Hall effect. Using perturbation theory, we show that this rate has an anomalous dependence on the bias voltage applied to the neighboring quantum point contact, which originates from the Luttinger liquid physics which describes the Hall fluid. General expressions are obtained using a screened Coulomb interaction. The dephasing rate is strictly proportional to the zero frequency backscattering current noise, which allows to describe exactly the weak to strong backscattering crossover using the Bethe-Ansatz solution

Follicle-stimulating hormone (FSH) activates extracellular signal-regulated kinase phosphorylation independently of beta-arrestin- and dynamin-mediated FSH receptor internalization

BACKGROUND: The follicle-stimulating hormone receptor (FSH-R) is a seven transmembrane spanning receptor (7TMR) which plays a crucial role in male and female reproduction. Upon FSH stimulation, the FSH-R activates the extracellular signal-regulated kinases (ERK). However, the mechanisms whereby the agonist-stimulated FSH-R activates ERK are poorly understood. In order to activate ERK, some 7 TMRs require beta-arrestin-and dynamin-dependent internalization to occur, whereas some others do not. In the present study, we examined the ability of the FSH-activated FSH-R to induce ERK phosphorylation, in conditions where its beta-arrestin- and dynamin-mediated internalization was impaired. METHODS: Human embryonic kidney (HEK) 293 cells were transiently transfected with the rat FSH-R. Internalization of the FSH-R was manipulated by co-expression of either a beta-arrestin (319–418) dominant negative peptide, either an inactive dynamin K44A mutant or of wild-type beta-arrestin 1 or 2. The outcomes on the FSH-R internalization were assayed by measuring 125I-FSH binding at the cell surface when compared to internalized 125I-FSH binding. The resulting ERK phosphorylation level was visualized by Western blot analysis. RESULTS: In HEK 293 cells, FSH stimulated ERK phosphorylation in a dose-dependent manner. Co-transfection of the beta- arrestin (319–418) construct, or of the dynamin K44A mutant reduced FSH-R internalization in response to FSH, without affecting ERK phosphorylation. Likewise, overexpression of wild-type beta-arrestin 1 or 2 significantly increased the FSH-R internalization level in response to FSH, without altering FSH-induced ERK phosphorylation. CONCLUSION: From these results, we conclude that the FSH-R does not require beta-arrestin- nor dynamin-mediated internalization to initiate ERK phosphorylation in response to FSH

Towards the convergent therapeutic potential of GPCRs in autism spectrum disorders

Changes in genetic and/or environmental factors to developing neural circuits and subsequent synaptic functions are known to be a causative underlying the varied socio-emotional behavioural patterns associated with autism spectrum disorders (ASD). Seven transmembrane G protein-coupled receptors (GPCRs) comprising the largest family of cell-surface receptors, mediate the transfer of extracellular signals to downstream cellular responses. Disruption of GPCR and their signalling have been implicated as a convergent pathologic mechanism of ASD. Here, we aim to review the literature about the 23 GPCRs that are genetically associated to ASD pathology according to Simons Foundation Autism Research Initiative (SFARI) database such as oxytocin (OXTR) and vasopressin (V1A, V1B) receptors, metabotropic glutamate (mGlu5, mGlu7) and gamma-aminobutyric acid (GABAB) receptors, dopamine (D1, D2), serotoninergic (5-HT1B and additionally included the 5-HT2A, 5-HT7 receptors for their strong relevance to ASD), adrenergic ($\beta$2) and cholinergic (M3) receptors, adenosine (A2A, A3) receptors, angiotensin (AT2) receptors, cannabinoid (CB1) receptors, chemokine (CX3CR1) receptors, orphan (GPR37, GPR85) and olfactory (OR1C1, OR2M4, OR2T10, OR52M1) receptors. We discussed the genetic variants, relation to core ASD behavioural deficits and update on pharmacological compounds targeting these 23 GPCRs. Of these OTR, V1A, mGlu5, D2, 5-HT2A, CB1, and GPR37 serve as the best therapeutic targets and have potential towards core domains of ASD pathology. With a functional crosstalk between different GPCRs and converging pharmacological responses, there is an urge to develop novel therapeutic strategies based on multiple GPCRs to reduce the socioeconomic burden associated with ASD and we strongly emphasize the need to prioritize the increased clinical trials targeting the multiple GPCRs

Transient thermoelectricity in a vibrating quantum dot in Kondo regime

We investigate the time evolution of the thermopower in a vibrating quantum dot suddenly shifted into the Kondo regime via a gate voltage by adopting the time-dependent non-crossing approximation and linear response Onsager relations. Behaviour of the instantaneous thermopower is studied for a range of temperatures both in zero and strong electron-phonon coupling. We argue that inverse of the saturation value of decay time of thermopower to its steady state value might be an alternative tool in determination of the Kondo temperature and the value of the electron-phonon coupling strength.Comment: 5 pages, 4 figures, to appear in Physics Letters