Full counting statistics of Andreev tunneling

Spectral signatures of symmetry-breaking dynamical phase transitions

Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. Some of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While macroscopic fluctuation theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete Z_{n} symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. In particular, we show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate subspace. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in several paradigmatic many-body systems, including (1) the one-dimensional boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (2) the three- and four-state Potts model for spin dynamics, which displays discrete rotational symmetry-breaking DPTs for energy fluctuations, and (3) the closed WASEP which presents a continuous symmetry-breaking DPT into a time-crystal phase characterized by a rotating condensate.

Real-time observation of Cooper pair splitting showing strong non-local correlations

Controlled generation and detection of quantum entanglement between spatially separated particles constitute an essential prerequisite both for testing the foundations of quantum mechanics and for realizing future quantum technologies. Splitting of Cooper pairs from a superconductor provides entangled electrons at separate locations. However, experimentally accessing the individual split Cooper pairs constitutes a major unresolved issue as they mix together with electrons from competing processes. Here, we overcome this challenge with the first real-time observation of the splitting of individual Cooper pairs, enabling direct access to the time-resolved statistics of Cooper pair splitting. We determine the correlation statistics arising from two-electron processes and find a pronounced peak that is two orders of magnitude larger than the background. Our experiment thereby allows to unambiguously pinpoint and select split Cooper pairs with 99% fidelity. These results open up an avenue for performing experiments that tap into the spin-entanglement of split Cooper pairs.

The splitting of Cooper pairs in superconductors has been challenging to detect experimentally. Here, the authors observe the real-time splitting of individual Cooper pairs in a superconducting device.

Suppression of shot noise in a spin-orbit coupled quantum dot

We study theoretically the transport properties of electrons in a quantum dot system with spin-orbit coupling. By using the quantum master equation approach, the shot noise and skewness of the transport electrons are calculated. We obtain super-Poisson noise behaviour by investigating the full counting statistics of the transport system. We discover super-Poisson behaviour is more obvious with the spin polarization increasing. More importantly, we discover the suppression of shot noise induced by spin-orbit coupling. The value of shot noise is gradually decreasing when spin-orbit coupling strength increases.

Large deviations and fluctuation theorem for the quantum heat current in the spin-boson model

We study the heat current flowing between two baths consisting of harmonic oscillators interacting with a qubit through a spin-boson coupling. An explicit expression for the generating function of the total heat flowing between the right and left baths is derived by evaluating the corresponding Feynman-Vernon path integral by performing the noninteracting blip approximation (NIBA). We recover the known expression, obtained by using the polaron transform. This generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. We also verify that the heat conductance is proportional to the variance of the heat current, retrieving the well-known fluctuation dissipation relation. Finally, we present numerical results for the heat current.

Electron waiting times in hybrid junctions with topological superconductors

We investigate the waiting time distributions (WTDs) of superconducting hybrid junctions, considering both conventional and topologically nontrivial superconductors hosting Majorana bound states at their edges. To this end, we employ a scattering matrix formalism that allows us to evaluate the waiting times between the transmissions and reflections of electrons or holes. Specifically, we analyze normal-metal–superconductor (NIS) junctions and NISIN junctions, where Cooper pairs are spatially split into different leads. The distribution of waiting times is sensitive to the simultaneous reflection of electrons and holes, which is enhanced by the zero-energy state in topological superconductors. For the NISIN junctions, the WTDs of trivial superconductors feature a sharp dependence on the applied voltage, while for topological ones they are mostly independent of it. This particular voltage dependence is again connected to the presence of topological edge states, showing that WTDs are a promising tool for identifying topological superconductivity.

Non-Gaussian Current Fluctuations in a Short Diffusive Conductor

We report the measurement of the third moment of current fluctuations in a short metallic wire at low temperature. The data are deduced from the statistics of voltage fluctuations across the conductor using a careful determination of environmental contributions. Our results at low bias agree very well with theoretical predictions for coherent transport with no fitting parameter. By increasing the bias voltage we explore the crossover from elastic to inelastic transport.

Experimental Determination of Dynamical Lee-Yang Zeros

Statistical physics provides the concepts and methods to explain the phase behavior of interacting many-body systems. Investigations of Lee-Yang zeros-complex singularities of the free energy in systems of finite size-have led to a unified understanding of equilibrium phase transitions. The ideas of Lee and Yang, however, are not restricted to equilibrium phenomena. Recently, Lee-Yang zeros have been used to characterize nonequilibrium processes such as dynamical phase transitions in quantum systems after a quench or dynamic order-disorder transitions in glasses. Here, we experimentally realize a scheme for determining Lee-Yang zeros in such nonequilibrium settings. We extract the dynamical Lee-Yang zeros of a stochastic process involving Andreev tunneling between a normal-state island and two superconducting leads from measurements of the dynamical activity along a trajectory. From the short-time behavior of the Lee-Yang zeros, we predict the large-deviation statistics of the activity which is typically difficult to measure. Our method paves the way for further experiments on the statistical mechanics of many-body systems out of equilibrium.

Dynamical Scheme for Interferometric Measurements of Full-Counting Statistics

We propose a dynamical scheme for measuring the full-counting statistics in a mesoscopic conductor using an electronic Mach-Zehnder interferometer. The conductor couples capacitively to one arm of the interferometer and causes a phase shift which is proportional to the number of transferred charges. Importantly, the full-counting statistics can be obtained from average current measurements at the outputs of the interferometer. The counting field can be controlled by varying the time delay between two separate voltage signals applied to the conductor and the interferometer, respectively. As a specific application, we consider measuring the entanglement entropy generated by partitioning electrons on a quantum point contact. Our scheme is robust against moderate environmental dephasing and may be realized thanks to recent advances in gigahertz quantum electronics.

Finite-time full counting statistics and factorial cumulants for transport through a quantum dot with normal and superconducting leads

We study the finite-time full counting statistics for subgap transport through a single-level quantum dot tunnel-coupled to one normal and one superconducting lead. In particular, we determine the factorial and the ordinary cumulants both for finite times and in the long-time limit. We find that the factorial cumulants violate the sign criterion, indicating a non-binomial distribution, even in absence of Coulomb repulsion due to the presence of superconducting correlations. At short times the cumulants exhibit oscillations which are a signature of the coherent transfer of Cooper pairs between the dot and the superconductor.

Non-Markovian full counting statistics in quantum dot molecules

Full counting statistics of electron transport is a powerful diagnostic tool for probing the nature of quantum transport beyond what is obtainable from the average current or conductance measurement alone. In particular, the non-Markovian dynamics of quantum dot molecule plays an important role in the nonequilibrium electron tunneling processes. It is thus necessary to understand the non-Markovian full counting statistics in a quantum dot molecule. Here we study the non-Markovian full counting statistics in two typical quantum dot molecules, namely, serially coupled and side-coupled double quantum dots with high quantum coherence in a certain parameter regime. We demonstrate that the non-Markovian effect manifests itself through the quantum coherence of the quantum dot molecule system, and has a significant impact on the full counting statistics in the high quantum-coherent quantum dot molecule system, which depends on the coupling of the quantum dot molecule system with the source and drain electrodes. The results indicated that the influence of the non-Markovian effect on the full counting statistics of electron transport, which should be considered in a high quantum-coherent quantum dot molecule system, can provide a better understanding of electron transport through quantum dot molecules.