arXiv subjects

Ines Safi

Publications and source records attributed to Ines Safi.

At least 19 recordsLinked to original sources

arXiv2025

Anyonic exchange in the time domain is tied to Luttinger type scaling

We consider Fractional Quantum Hall (FQH) edges with a spatially local Quantum Point Contact (QPC). Within the Unified Nonequilibrium Perturbative (UNEP) framework, without assumptions on the underlying Hamiltonian $H_{0}$ for the edges, we search for the associated backscattering DC current and noise compatible with the anyonic time exchange (ATE) constraint with a phase $\bar{\theta}$. For that, we infer a nonequilibrium fluctuation-dissipation relation that explicitly involves $\bar{\theta}$ and yields an integral equation connecting the nonequilibrium DC current and noise. On one hand, we assume initial thermal states, so that the DC noise is Poissonian. Then the integral equation for the DC current is shown, through the Wiener-Hopf technique, to admit the unique TLL local solution. Therefore, $\bar{\theta}$ is necessarily tied to the scaling dimension $\delta$, which is robust with respect to edge interactions. On the other hand, we address the "anyon collider" setup where DC noise is super-Poissonian. As the difference between nonequilibrium and equilibrium correlators is fixed, the integral equation admits a unique solution for both nonequilibrium DC backscattering current and super-Poissonian noise, whose explicit temperature dependence is thus determined.

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arXiv2025

Robust protocols to reveal anyonic time-exchange phase

We consider hierarchical quantum Hall edge states with $N$ modes and a spatially local quantum point contact (QPC). In general, the field of an injected anyon does not directly acquire the universal statistical phase $\theta$. Short-range inter-edge interactions split the universal anyon charge and phase into $N$ fractionalized charges associated with nonuniversal phases $\pi\delta_m$. In contrast, their sum $\delta=\sum_{m=1}^N\delta_m$, which defines the local scaling dimension at the QPC, remains protected and is tied to the statistical angle through $\pi\delta=\theta$. If the injected anyon is of the same species as the one dominating backscattering at the QPC, time-domain braiding with phase $\theta$ is recovered either in the absence of inter-edge interactions with equal mode velocities, or by performing a spatially local anyon injection at the QPC. We then exploit a more robust \emph{local} anyonic time-exchange (ATE) link between anyons and quasiholes at the QPC, which is also a necessary ingredient for realizing such braiding. This allows us to propose minimal single-QPC protocols that do not rely on diluted anyon sources and that disentangle the role of $\theta$ as a genuine statistical phase from that as a scaling dimension. From the ATE link we derive two novel nonequilibrium fluctuation--dissipation relations (FDRs) that isolate $\theta$. They relate the DC backscattering noise either to an integral over the DC current or to the phase shift of the AC current with respect to an applied AC voltage (i.e., the phase of the admittance), accessible down to low frequencies. For thermalized edges, we show that in the quantum regime this admittance phase directly yields $\theta$ whenever $\delta>1/2$.

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arXiv2025

Hong-Ou-Mandel interferometry for fractional excitations: Unified framework and dip width scaling

Extending Hong--Ou--Mandel (HOM) interferometry to the fractional quantum Hall effect (FQHE) promises direct access to anyonic statistics, yet remains challenging: on-demand anyon injection is hindered by integer-charged minimal excitations, and recent HOM experiments in the FQHE lack a fully consistent theoretical framework. Here we provide a general theory of time-resolved HOM interferometry in quantum Hall systems. Combining the nonequilibrium bosonized edge theory (NEBET) with the unifying non-equilibrium perturbative theory (UNEPT), we derive exact and perturbative relations obeyed by the relevant cross-correlations of chiral currents valid for spatially extended tunneling operators and generic quadratic edge dynamics. Then, within the Tomonaga--Luttinger liquid (TLL) framework, we analyze the width of the HOM dip for injected pulses carrying integer and fractional charges. We show that it is governed by the width of the pulses and, for the fractional charge, by a non-trivial power-law behavior of the scaling dimension. Our results establish a robust theoretical foundation for interpreting recent experiments on anyonic statistics and electronic interferometry in the quantum Hall regime.

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arXiv2025

AC driven fractional quantum Hall systems: Uncovering unexpected features

We investigate the challenges of reaching the quantum regime and generating minimal excitations in the fractional quantum Hall effect (FQHE) under AC driving. Using the unifying non-equilibrium perturbative (UNEP) approach, we analyze weak backscattering through a quantum point contact (QPC). In both two-terminal geometries and the "anyon collider" setup, the lower bound on photoassisted backscattering noise is set by the photoassisted current rather than the DC noise predicted by Levitov's theorem. This super-Poissonian character is confirmed within the Tomonaga-Luttinger liquid (TLL) framework, where Levitov's theorem is violated, challenging the conventional interpretation of "photoassisted" noise. In the two-terminal geometry, we show that when the QPC has a low scaling dimension, two challenges arise: first, achieving the expected power-law behavior in the DC regime, and second, maintaining the AC quantum regime, where the drive frequency exceeds the temperature, when the DC voltage component is resonant with that drive frequency. The validity of the UNEP relations imposes a lower bound on temperature and a persisting equilibrium contribution to backscattering noise. This forces us to choose a high enough scaling dimension, for which we find that it is rather the photoconductance, often overlooked, that might exhibit spikes at resonant DC voltages, providing a reliable probe of fractional charge. Moreover, we highlight that the zero-temperature limit, frequently assumed in prior studies, including X. G. Wen's foundational work, is inappropriate in this context. Our findings extend beyond the FQHE to coherent conductors and Josephson or phase-slip junctions strongly coupled to an ohmic environment under AC bias, with broader implications for quantum transport and minimal excitation engineering.

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arXiv2024

Time-resolved sensing of electromagnetic fields with single-electron interferometry

Characterizing quantum states of the electromagnetic field at microwave frequencies requires fast and sensitive detectors that can simultaneously probe the field time-dependent amplitude and its quantum fluctuations. In this work, we demonstrate a quantum sensor that exploits the phase of a single electron wavefunction, measured in an electronic Fabry-Perot interferometer, to detect a classical time-dependent electric field. The time resolution, limited by the temporal width of the electronic wavepacket, is a few tens of picoseconds. The interferometry technique provides a voltage resolution of a few tens of microvolts, corresponding to a few microwave photons. Importantly, our detector simultaneously probes the amplitude of the field from the phase of the measured interference pattern and its fluctuations from the interference contrast. This capability paves the way for on-chip detection of quantum radiation, such as squeezed or Fock states.

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arXiv2020

Fluctuation dissipation relations for strongly correlated out-of-equilibrium circuits

We consider strongly correlated quantum circuits where a dc drive is added on top of an initial out-of-equilibrium (OE) stationary state. Within a perturbative approach, we derive unifying OE fluctuation relations for high frequency current noise, shown to be completely determined by zero-frequency noise and dc current. We apply them to the fractional quantum Hall effect at arbitrary incompressible filling factors, driven by OE sources, without knowledge of the underlying model. We show that such OE relations provide robust methods for an unambiguous determination of the fractional charge or of key interaction parameters entering in the exploration of anyonic statistics within an anyon collider.

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arXiv2018

The Coulomb drag effect induced by the third cumulant of current

The Coulomb drag effect arises due to electron-electron interactions, when two metallic conductors are placed in close vicinity to each other. It manifests itself as a charge current or voltage drop induced in one of the conductors, if the current flows through the second one. Often it can be interpreted as an effect of rectification of the non-equilibrium $quantum$ noise of current. Here, we investigate the Coulomb drag effect in mesoscopic electrical circuits and show that it can be mediated by $classical$ fluctuations of the circuit collective mode. Moreover, by considering this phenomenon in the context of the full counting statistics of charge transport we demonstrate that not only the noise power, but also the third cumulant of current may contribute to the drag current. We discuss the situations, where this contribution becomes dominant.

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arXiv2014

Time-dependent Transport in arbitrary extended driven tunnel junctions

We develop a very general perturbative theory of time-dependent transport in a weak tunneling junction which is independent of experimental details and on many-body correlated states in the coupled conductors. These can be similar or different, with arbitrary internal or mutual interactions, superconducting correlations, disorder, and coupled to an electromagnetic environment or other quantum systems. The junction can be spatially extended, and is subject, simultaneously, to time-dependent voltage, local magnetic field and modulation of the tunneling amplitudes. All observables at arbitrary frequencies: average current, non-equilibrium admittance and current correlations can be expressed in a universal way through the out-of-equilibrium DC current only, yielding perturbative time-dependent non-equilibrium fluctuation relations. In particular, charge fluctuations are shown to be universally super-poissonian, and to become poissonian if the junction is driven by a series of Lorentzian pulses. We also generalize, for constant voltage and tunneling, the poissonian shot noise and the fluctuation relation between the derivatives of the noise and the conductance. Thus we provide a compact, general and transparent unifying theory at arbitrary dimension, in contrast with involved derivations based explicitly on particular models and profiles of a single time-varying field.

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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.

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arXiv2009

Time-dependent theory of non-linear response and current fluctuations

A general non-linear response theory is derived for an arbitrary time-dependent Hamiltonian, not necessarily obeying time-reversal symmetry. This allows us to obtain a greatly generalized Kubo type formula. Applied to a mesoscopic system with any type of interactions, and coupled to multiple probes and gates with arbitrarily time-dependent voltages, we derive current-conserving differential conductance and current fluctuation matrices obeying a generalized Fluctuation-Dissipation Theorem. This relation provides a common explanation for asymmetries of the excess noise in several non-linear mesoscopic systems, as well as of its surprising negative sign.

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arXiv2009

Asymmetry of the excess finite-frequency noise

We consider finite frequency noise in a mesoscopic system with arbitrary interactions, connected to many terminals kept at finite electrochemical potentials. We show that the excess noise, obtained by subtracting the noise at zero voltage from that at finite voltage, can be asymmetric with respect to positive/negative frequencies if the system is non-linear. This explains a recent experimental observation in Josephson junctions as well as strong asymmetry obtained in typical non-linear and strongly correlated systems described by the Luttinger liquid (LL): edge states in the fractional quantum Hall effect, quantum wires and carbon nanotubes. Another important problem where the LL model applies is that of a coherent conductor embedded in an ohmic environment.

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arXiv2009

Out-of-equilibrium transport in a typical multi-terminal setup

We develop a general out-of-equilibrium framework for a typical three-terminal setup of common use: an injector, which can be interacting, coupled by both extended tunneling and Coulomb interactions to an inhomogeneous wire with any range of interactions and scattering processes. Some of the crucial results we obtain are of relevance to other muti-terminal geometries. We show that the voltage of the injector does not cut the flow of relevant scattering processes in the wire. Either a grounded or a semi-infinite wire at too low temperature is driven into the strong coupling regime. We show that the injector induce invasive effects. They are due to non-local backscattering processes generated both by virtual higher order tunneling processes and by Coulomb interactions with the injector. The latter induce in addition screening of interactions in the wire. For an STM, those effects can drastically mask the probed density of states (DOS). In the limit of zero temperature, a long and grounded wire is driven to its fixed point where it is disconnected at the tunneling point. Thus instead of the bulk expected DOS, the STM probes the end one. We analyze current auto- and cross-correlations. We show that the cross-correlations are dominated by their value in the two-terminal geometry. As these are opposite to the current auto-correlations, they are always negative for local scattering processes. We give novel scaling laws to all orders with respect to a local backscattering.

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arXiv2008

AC conductance and non-symmetrized noise at finite frequency in quantum wires and carbon nanotubes

We calculate the AC conductance and the finite-frequency non-symmetrized noise in interacting quantum wires and single-wall carbon nanotubes in the presence of an impurity. We observe a strong asymmetry in the frequency spectrum of the non-symmetrized excess noise, even in the presence of the metallic leads. We find that this asymmetry is proportional to the differential excess AC conductance of the system, defined as the difference between the AC differential conductances at finite and zero voltage, and thus disappears for a linear system. In the quantum regime, for temperatures much smaller than the frequency and the applied voltage, we find that the emission noise is exactly equal to the impurity partition noise. For the case of a weak impurity we expand our results for the AC conductance and the noise perturbatively. In particular, if the impurity is located in the middle of the wire or at one of the contacts, our calculations show that the noise exhibits oscillations with respect to frequency, whose period is directly related to the value of the interaction parameter $g$.

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arXiv2007

Emission and absorption noise in the fractional quantum Hall effect

We compute the high-frequency emission and absorption noise in a fractional quantum Hall effect (FQHE) sample at arbitrary temperature. We model the edges of the FQHE as chiral Luttinger liquids (LL) and we use the non-equilibrium perturbative Keldysh formalism. We find that the non-symmetrized high frequency noise contains important signatures of the electron-electron interactions that can be used to test the Luttinger liquid physics, not only in FQHE edge states, but possibly also in other one-dimensional systems such as carbon nanotubes. In particular we find that the emission and absorption components of the excess noise (defined as the difference between the noise at finite voltage and at zero voltage) are different in an interacting system, as opposed to the non-interacting case when they are identical. We study the resonance features which appear in the noise at the Josephson frequency (proportional to the applied voltage), and we also analyze the effect of the distance between the measurement point and the backscattering site. Most of our analysis is performed in the weak backscattering limit, but we also compute and discuss briefly the high-frequency noise in the tunneling regime.

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arXiv2005

Transport properties of single channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise

The inhomogeneous Tomonaga Luttinger liquid model describing an interacting quantum wire adiabatically coupled to non-interacting leads is analyzed in the presence of a weak impurity within the wire. Due to strong electronic correlations in the wire, the effects of impurity backscattering, finite bias, finite temperature, and finite length lead to characteristic non-monotonic parameter dependencies of the average current. We discuss oscillations of the non-linear current voltage characteristics that arise due to reflections of plasmon modes at the impurity and quasi Andreev reflections at the contacts, and show how these oscillations are washed out by decoherence at finite temperature. Furthermore, the finite frequency current noise is investigated in detail. We find that the effective charge extracted in the shot noise regime in the weak backscattering limit decisively depends on the noise frequency $ω$ relative to $v_F/gL$, where $v_F$ is the Fermi velocity, $g$ the Tomonaga Luttinger interaction parameter, and $L$ the length of the wire. The interplay of finite bias, finite temperature, and finite length yields rich structure in the noise spectrum which crucially depends on the electron-electron interaction. In particular, the excess noise, defined as the change of the noise due to the applied voltage, can become negative and is non-vanishing even for noise frequencies larger than the applied voltage, which are signatures of correlation effects.

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arXiv2004

A one-channel conductor in an ohmic environment: mapping to a TLL and full counting statistics

It is shown that a one-channel mesoscopic conductor in an ohmic environment can be mapped to the problem of a backscattering impurity in a Tomonaga-Luttinger liquid (TLL). This allows to determine non perturbatively the effect of the environment on $I-V$ curves, and to find an exact relationship between dynamic Coulomb blockade and shot noise. We investigate critically how this relationship compares to recent proposals in the literature. The full counting statistics is determined at zero temperature.

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arXiv2003

Oscillatory non-linear conductance of an interacting quantum wire with an impurity

The nonlinear conductance of a one-dimensional quantum wire adiabatically coupled to Fermi Liquid electron reservoirs is determined in presence of an impurity. We show that electron-electron interaction in connection with the finite length of the wire leads to characteristic oscillations in the current as a function of the applied voltage.

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arXiv1998

A dynamic scattering approach for a gated interacting wire

A new scattering approach for correlated one-dimensional systems is developed. The adiabatic contact to charge reservoirs is encoded in time-dependent boundary conditions. The conductance matrix for an arbitrary gated wire, respecting charge conservation, is expressed through a dynamic scattering matrix. It is shown that the dc conductance is equal to e^2/h for any model with conserved total left- and right-moving charges. The ac conductance matrix is explicitly computated for the interacting Tomonaga-Luttinger model.

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