arXiv subjects

Eugene V. Sukhorukov

Publications and source records attributed to Eugene V. Sukhorukov.

At least 37 records · Page 2Linked to original sources

arXiv2011

Direct access to quantum fluctuations through cross-correlation measurements

Detection of the quantum fluctuations by conventional methods meets certain obstacles, since it requires high frequency measurements. Moreover, quantum fluctuations are normally dominated by classical noise, and are usually further obstructed by various accompanying effects such as a detector backaction. In present work, we demonstrate that these difficulties can be bypassed by performing the cross-correlation measurements. We propose to use a pair of two-level detectors, weakly coupled to a collective mode of an electric circuit. Fluctuations of the current source accumulated in the collective mode induce stochastic transitions in the detectors. These transitions are then read off by quantum point contact (QPC) electrometers and translated into two telegraph processes in the QPC currents. Since both detectors interact with the same collective mode, this leads to a certain fraction of the correlated transitions. These correlated transitions are fingerprinted in the cross-correlations of the telegraph processes, which can be detected at zero frequency, i.e., with a long time measurements. Concerning the dependance of the cross-correlator on the detectors' energy splittings, the most interesting region is at the degeneracy points, where it exhibits a sharp non-local resonance, that stems from higher order processes. We find that at certain conditions the main contribution to this resonance comes from the quantum noise. Namely, while the resonance line shape is weakly broadened by the classical noise, the height of the peak is directly proportional to the square of the quantum component of the noise spectral function.

cond-mat.mes-hall↗

arXiv2011

Energy relaxation at quantum Hall edge

In this work we address the recent experiment of Altimiras and collaborators, where an electron distribution function at the quantum Hall (QH) edge at filling factor 2 has been measured with high precision. It has been reported that the energy of electrons injected into one of the two chiral edge channels with the help of a quantum point contact (QPC) is equally distributed between them, in agreement with earlier predictions, one being based on the Fermi gas approach, and the other utilizing the Luttinger liquid theory. We argue that the physics of the energy relaxation process at the QH edge may in fact be more rich, providing the possibility for discriminating between two physical pictures in experiment. Namely, using the recently proposed non-equilibrium bosonization technique we evaluate the electron distribution function and find that the initial "double-step" distribution created at a QPC evolves through several intermediate asymptotics, before reaching eventual equilibrium state. At short distances the distribution function is found to be asymmetric due to non-Gaussian current noise effects. At larger distances, where noise becomes Gaussian, the distribution function acquires symmetric Lorentzian shape. Importantly, in the regime of low QPC transparencies T the width of the Lorentzian scales linearly with T, in contrast to the case of equilibrium Fermi distribution, whose width scales as square root of T. Therefore, we propose to do measurements at low QPC transparencies. We suggest that the missing energy paradox may be explained by the nonlinear dispersion of the spectrum of edge states.

cond-mat.mes-hall↗

arXiv2010

Determination of tunneling charge via current measurements

We consider a tunnel junction between two arbitrary non-linear systems in any dimension, which can be different. We show that the tunneling charge can be detected using three alternative methods based on current measurements. Besides being technically easier compared to noise measurements, these methods present valuable advantages: they do not require the knowledge of the underlying models, and some are accessible in the experimentally convenient low-voltage regime, where heating effects are reduced. The first method is based on the AC conductance, while the two others are based on photo-assisted current (PAC) and can be implemented for any time-dependence of the tunneling amplitude. These are promising for edge states in the regime of the fractional quantum Hall effect (FQHE): the Hamiltonian does not have to be specified and can incorporate non-universal interactions between the edges, and it is more convenient to use an AC gate voltage rather than an AC bias. These methods apply for instance to weak barriers in 1-D systems, Superconductor-Insulator-Normal (SIN) or graphene-like structures.

cond-mat.mes-hall↗

arXiv2009

Mach-Zehnder interferometry of fractional quantum Hall edge states

We propose direct experimental tests of the effective models of fractional quantum Hall edge states. We first recall a classification of effective models based on the requirement of anomaly cancellation and illustrate the general classification with the example of a quantum Hall fluid at filling factor 2/3. We show that, in this example, it is impossible to describe the edge states with only one chiral channel and that there are several inequivalent models of the edge states with two fields. We focus our attention on the four simplest models of the edge states of a fluid with filling factor 2/3 and evaluate charges and scaling dimensions of quasi-particles. We study transport through an electronic Mach-Zehnder interferometer and show that scaling properties of the Fourier components of Aharonov-Bohm oscillations in the current provide information about the electric charges and scaling dimensions of quasi-particles. Thus Mach-Zehnder interferometers can be used to discriminate between different effective models of fluids corresponding to the same filling factor. They therefore can be used to test fundamental postulates underlying the low-energy effective theory of edge states. An important ingredient of our analysis is the tunneling Hamiltonian of quasi-particles, the form of which is discussed in detail.

cond-mat.mes-hall↗

arXiv2009

Noise-induced phase transition in the electronic Mach-Zehnder interferometer

We consider dephasing in the electronic Mach-Zehnder interferometer strongly coupled to current noise created by a voltage biased quantum point contact (QPC). We find the visibility of Aharonov-Bohm oscillations as a function voltage bias and express it via the cumulant generating function of noise. In the large-bias regime, high-order cumulants of current add up to cancel the dilution effect of a QPC. This leads to an abrupt change in the dependence of the visibility on voltage bias which occurs at the QPC's transparency T=1/2. Quantum fluctuations in the vicinity of this point smear out the sharp transition.

cond-mat.mes-hall↗

arXiv2009

Achieving the threshold regime with an over-screened Josephson junction

We demonstrate that by utilizing an over-screened Josephson junction as a noise detector it is possible to achieve the threshold regime, whereby the tails of the fluctuating current distribution are measured. This situation is realized by placing the Josephson junction and mesoscopic conductor in an external circuit with very low impedance. In the underdamped limit, over-screening the junction inhibits the energy diffusion in the junction, effectively creating a tunable activation barrier to the dissipative state. As a result, the activation rate is qualitatively different from the Arrhenius form.

cond-mat.mes-hall↗

arXiv2008

Decay of a metastable state activated by non-Gaussian noise: A critical review of the generalized Kramers problem

We review the problem of the noise activated escape from a metastable state in the presence of non-Gaussian noise, and present connections between various theoretical approaches. We also respond to criticism of our work by Tomáš Novotný [arXiv:0807.0387] concerning the weak damping limit. The discrepancy between our results is linked to uncontrolled approximations made by Novotný.

cond-mat.mes-hall↗

arXiv2008

Resonant dephasing in the electronic Mach-Zehnder interferometer

We address the recently-observed unexpected behavior of Aharonov-Bohm oscillations in the electronic Mach-Zehnder interferometer that was realized experimentally in a quantum Hall system [1]. We argue that the measured lobe structure in the visibility of oscillations and the phase rigidity result from a strong long-range interaction between two adjacent counter-propagating edge states, which leads to a resonant scattering of plasmons. The visibility and phase shift, which we expressed in terms of the transmission coefficient for plasmons, can be used for the tomography of edge states.

cond-mat.mes-hall↗

arXiv2008

Theory of quantum noise detectors based on resonant tunneling

We propose to use the phenomenon of resonant tunneling for the detection of noise. The main idea of this method relies on the effect of homogeneous broadening of the resonant tunneling peak induced by the emission and absorption of collective charge excitations in the measurement circuit. In thermal equilibrium, the signal to noise ratio of the detector as a function of the detector bandwidth (the detector function) is given by the universal hyperbolic tangent, which is the statement of the fluctuation-dissipation theorem. The universality breaks down if non-equilibrium processes take place in the measurement circuit. We propose the theory of this phenomenon and make predictions for the detector function in case when non-equilibrium noise is created by a mesoscopic conductor. We investigate measurement circuit effects and prove the universality of the classical noise detection. Finally, we evaluate the contribution of the third cumulant of current and make suggestions of how it can be measured.

cond-mat.mes-hall↗

arXiv2008

Dephasing in the electronic Mach-Zehnder interferometer at filling factor 2

We propose a simple physical model which describes dephasing in the electronic Mach-Zehnder interferometer at filling factor 2. This model explains very recent experimental results, such as the unusual lobe-type structure in the visibility of Aharonov-Bohm oscillations, phase rigidity, and the asymmetry of the visibility as a function of transparencies of quantum point contacts. According to our model, dephasing in the interferometer originates from strong Coulomb interaction at the edge of two-dimensional electron gas. The long-range character of the interaction leads to a separation of the spectrum of edge excitations on slow and fast mode. These modes are excited by electron tunneling and carry away the phase information. The new energy scale associated with the slow mode determines the temperature dependence of the visibility and the period of its oscillations as a function of voltage bias. Moreover, the variation of the lobe structure from one experiment to another is explained by specific charging effects, which are different in all experiments. We propose to use a strongly asymmetric Mach-Zehnder interferometer with one arm being much shorter than the other for the spectroscopy of quantum Hall edge states.

cond-mat.mes-hall↗

arXiv2007

Conditional statistics of electron transport in interacting nanoscale conductors

Interactions between nanoscale semiconductor structures form the basis for charge detectors in the solid state. Recent experimental advances have demonstrated the on-chip detection of single electron transport through a quantum dot (QD). The discreteness of charge in units of e leads to intrinsic fluctuations in the electrical current, known as shot noise. To measure these single-electron fluctuations a nearby coherent conductor, called a quantum point contact (QPC), interacts with the QD and acts as a detector. An important property of the QPC charge detector is noninvasiveness: the system physically affects the detector, not visa-versa. Here we predict that even for ideal noninvasive detectors such as the QPC, when a particular detector result is observed, the system suffers an informational backaction, radically altering the statistics of transport through the QD as compared to the unconditional shot noise. We develop a theoretical model to make predictions about the joint current probability distributions and conditional transport statistics. The experimental findings reported here demonstrate the reality of informational backaction in nanoscale systems as well as a variety of new effects, such as conditional noise enhancement, which are in essentially perfect agreement with our model calculations. This type of switching telegraph process occurs abundantly in nature, indicating that these results are applicable to a wide variety of systems.

cond-mat.mes-hall↗

arXiv2006

Stochastic dynamics of a Josephson junction threshold detector

We generalize the stochastic path integral formalism by considering Hamiltonian dynamics in the presence of general Markovian noise. Kramers' solution of the activation rate for escape over a barrier is generalized for non-Gaussian driving noise in both the overdamped and underdamped limit. We apply our general results to a Josephson junction detector measuring the electron counting statistics of a mesoscopic conductor. Activation rate dependence on the third current cumulant includes an additional term originating from the back-action of the measurement circuit.

cond-mat.mes-hall↗

arXiv2005

Counting statistics and detector properties of quantum point contacts

Quantum detector properties of the quantum point contact (QPC) are analyzed for arbitrary electron transparency and coupling strength to the measured system and are shown to be determined by the electron counting statistics. Conditions of the quantum-limited operation of the QPC detector which prevent information loss through the scattering time and scattering phases are found for arbitrary coupling. We show that the phase information can be restored and used for the quantum-limited detection by inclusion of the QPC detector in the electronic Mach-Zehnder interferometer.

cond-mat.mes-hall↗

arXiv2005

Mesoscopic threshold detectors: Telegraphing the size of a fluctuation

We propose a two-terminal method to measure shot noise in mesoscopic systems based on an instability in the current-voltage characteristic of an on-chip detector. The microscopic noise drives the instability, which leads to random switching of the current between two values, the telegraph process. In the Gaussian regime, the shot noise power driving the instability may be extracted from the I-V curve, with the noise power as a fitting parameter. In the threshold regime, the extreme value statistics of the mesoscopic conductor can be extracted from the switching rates, which reorganize the complete information about the current statistics in an indirect way, "telegraphing" the size of a fluctuation. We propose the use of a quantum double dot as a mesoscopic threshold detector.

cond-mat.mes-hall↗

arXiv2004

Transport Statistics of Bistable Systems

We consider the transport statistics of classical bistable systems driven by noise. The stochastic path integral formalism is used to investigate the dynamics and distribution of transmitted charge. Switching rates between the two stable states are found from an instanton calculation, leading to an effective two-state system on a long time scale. In the bistable current range, the telegraph noise dominates the distribution, whose logarithm is found to be universally described by a tilted ellipse.

cond-mat.stat-mech↗

arXiv2004

Stochastic Field Theory for Transport Statistics in Diffusive Systems

We present a field theory for the statistics of charge and current fluctuations in diffusive systems. The cumulant generating function is given by the saddle-point solution for the action of this field theory. The action depends on two parameters only: the local diffusion and noise coefficients, which naturally leads to the universality of the transport statistics for a wide class of multi-dimensional diffusive models. Our theory can be applied to semi-classical mesoscopic systems, as well as beyond mesoscopic physics.

cond-mat.mes-hall↗

arXiv2004

Fluctuation Statistics in Networks: a Stochastic Path Integral Approach

We investigate the statistics of fluctuations in a classical stochastic network of nodes joined by connectors. The nodes carry generalized charge that may be randomly transferred from one node to another. Our goal is to find the time evolution of the probability distribution of charges in the network. The building blocks of our theoretical approach are (1) known probability distributions for the connector currents, (2) physical constraints such as local charge conservation, and (3) a time-scale separation between the slow charge dynamics of the nodes and the fast current fluctuations of the connectors. We derive a stochastic path integral representation of the evolution operator for the slow charges. Once the probability distributions on the discrete network have been studied, the continuum limit is taken to obtain a statistical field theory. We find a correspondence between the diffusive field theory and a Langevin equation with Gaussian noise sources, leading nevertheless to non-trivial fluctuation statistics. To complete our theory, we demonstrate that the cascade diagrammatics, recently introduced by Nagaev, naturally follows from the stochastic path integral. We extend the diagrammatics to calculate current correlation functions for an arbitrary network. One primary application of this formalism is that of full counting statistics (FCS). We stress however, that the formalism is suitable for general classical stochastic problems as an alternative to the traditional master equation or Doi-Peliti technique. The formalism is illustrated with several examples: both instantaneous and time averaged charge fluctuation statistics in a mesoscopic chaotic cavity, as well as the FCS and new results for a generalized diffusive wire.

cond-mat.mes-hall↗

arXiv2004

Quantum-to-Classical Crossover in Full Counting Statistics

The reduction of quantum scattering leads to the suppression of shot noise. In the present paper, we analyze the crossover from the quantum transport regime with universal shot noise, to the classical regime where noise vanishes. By making use of the stochastic path integral approach, we find the statistics of transport and the transmission properties of a chaotic cavity as a function of a system parameter controlling the crossover. We identify three different scenarios of the crossover.

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