Showing 1–46 of 46 results for author: Safi, I

Dynamic charge oscillation in a quantum conductor driven by ultrashort voltage pulses

Authors: Lucas Mazzella, Seddik Ouacel, Inès Safi

Abstract: Time-dependent driving with ultrashort voltage pulses brings quantum conductors into the non-adiabatic transport regime, where novel dynamical effects emerge. An example of this physics occurs in interferometric systems, where the transmitted charge oscillates as a function of the charge injected by an ultrashort voltage pulse. This behavior has been predicted in a variety of setups, including Fab… ▽ More Time-dependent driving with ultrashort voltage pulses brings quantum conductors into the non-adiabatic transport regime, where novel dynamical effects emerge. An example of this physics occurs in interferometric systems, where the transmitted charge oscillates as a function of the charge injected by an ultrashort voltage pulse. This behavior has been predicted in a variety of setups, including Fabry-Pérot and Mach-Zehnder interferometers, and more recently in quantum dots. It is commonly interpreted as resulting from interference between different propagating paths taken by the injected excitation. In this letter, we fully generalize the derivation of such dynamic charge oscillations beyond interferometric devices for a generic quantum conductor with the single assumption that its DC current is sublinear at large bias. Strikingly, they also extend perturbatively to strongly correlated conductors, showing in particular their robustness against arbitrarily strong Coulomb interactions. To illustrate the generality of our approach, we analyze in detail the case of a quantum point contact in the fractional quantum Hall regime, which fulfills the sublinearity condition. We demonstrate that this non-interferometric system exhibit dynamic charge oscillation. Finally, we propose a complementary interpretation of this phenomenon, rooted in the photo-assisted probabilities associated with the voltage pulse. △ Less

Submitted 16 April, 2026; v1 submitted 13 March, 2026; originally announced March 2026.

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

Authors: Aleksander Latyshev, Ines Safi

Abstract: 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 $\barθ$. For that, we inf… ▽ More 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 $\barθ$. For that, we infer a nonequilibrium fluctuation-dissipation relation that explicitly involves $\barθ$ 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, $\barθ$ is necessarily tied to the scaling dimension $δ$, 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. △ Less

Submitted 11 March, 2026; v1 submitted 23 October, 2025; originally announced October 2025.

Comments: 9 pages, 3 figures. Substantial changes (title, abstract, interpretation). Contains an additional section on DC backscattering current and noise in the "anyon collider" at finite temperature

Robust protocols to reveal anyonic time-exchange phase

Authors: Ines Safi

Abstract: 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 $θ$. Short-range inter-edge interactions split the universal anyon charge and phase into $N$ fractionalized charges associated with nonuniversal phases $πδ_m$. In contrast, their sum… ▽ More 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 $θ$. Short-range inter-edge interactions split the universal anyon charge and phase into $N$ fractionalized charges associated with nonuniversal phases $πδ_m$. In contrast, their sum $δ=\sum_{m=1}^Nδ_m$, which defines the local scaling dimension at the QPC, remains protected and is tied to the statistical angle through $πδ=θ$. If the injected anyon is of the same species as the one dominating backscattering at the QPC, time-domain braiding with phase $θ$ 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 $θ$ 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 $θ$. 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 $θ$ whenever $δ>1/2$. △ Less

Submitted 11 March, 2026; v1 submitted 12 October, 2025; originally announced October 2025.

Comments: 10 pages, 3 figures. Substancial changes. A whole section devoted to the braiding phase in the time domain, and its splitting in accordance with charge fractionalisation. A second method to determine the braiding phase based on DC current and noise

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

Authors: Aleksander Latyshev, Imen Taktak, Ipsita Mandal, Ines Safi

Abstract: 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… ▽ More 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. △ Less

Submitted 9 September, 2025; originally announced September 2025.

Comments: 7 pages, 5 figures

AC driven fractional quantum Hall systems: Uncovering unexpected features

Authors: Imen Taktak, Ines Safi

Abstract: 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 backscatt… ▽ More 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. △ Less

Submitted 25 February, 2025; v1 submitted 11 February, 2025; originally announced February 2025.

Comments: 15 pages, 6 figure. Modifications: Two new figures have been added to illustrate the "anyon collider". Additional formulas have been incorporated to enhance clarity and rigor. Several new citations have been included to strengthen the theoretical framework. Sections and subsections have been reorganized for improved flow and readability

Thermodynamic and energetic constraints on transition probabilities of small-scale quantum systems

Authors: Ludovico Tesser, Matteo Acciai, Christian Spånslätt, Inès Safi, Janine Splettstoesser

Abstract: We study the transition probabilities of a two-point measurement on a quantum system, initially prepared in a thermal state. We find two independent constraints on the difference between transition probabilities when the system is prepared at different temperatures, which both turn out to be particularly restrictive when the measured quantum system is small. These bounds take the form of a thermod… ▽ More We study the transition probabilities of a two-point measurement on a quantum system, initially prepared in a thermal state. We find two independent constraints on the difference between transition probabilities when the system is prepared at different temperatures, which both turn out to be particularly restrictive when the measured quantum system is small. These bounds take the form of a thermodynamic and of an energetic constraint, as they are associated with the dissipated heat and with the absorbed energy required to increase or to reduce the temperature of the system. The derived constraints apply to arbitrary system Hamiltonians, including interactions or non-linear energy spectra. We show the relevance of these constraints for the special case where transitions are induced by energy or particle exchange in weakly coupled bipartite systems out of equilibrium. This example is of interest for a wide range of experimentally relevant systems, from molecular junctions to coupled cavities, and can be tested by, for instance, measuring the out-of-equilibrium tunneling current and its noise. △ Less

Submitted 19 May, 2025; v1 submitted 2 September, 2024; originally announced September 2024.

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

Authors: Hugo Bartolomei, Elric Frigerio, Mélanie Ruelle, Giacomo Rebora, Yong Jin, Ulf Gennser, Antonella Cavanna, Emmanuel Baudin, Jean-Marc Berroir, Ines Safi, Pascal Degiovanni, Gerbold C. Ménard, Gwendal Fève

Abstract: 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 ti… ▽ More 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. △ Less

Submitted 23 August, 2024; originally announced August 2024.

Comments: Main (8 pages and 3 figures) and supplementary files (17 pages and 12 figures)

Quantum sensing of time dependent electromagnetic fields with single electron excitations

Authors: H. Souquet-Basiège, B. Roussel, G. Rebora, G. Ménard, I. Safi, G. Fève, P. Degiovanni

Abstract: In this study, we investigate the potential of electronic interferometers for probing the quantum state of electromagnetic radiation on a chip at sub-nanosecond time scales. We propose to use single electron excitations propagating within an electronic Mach-Zehnder interferometer in the Aharonov-Bohm dominated regime. We discuss how information about the quantum state of the electromagnetic radiat… ▽ More In this study, we investigate the potential of electronic interferometers for probing the quantum state of electromagnetic radiation on a chip at sub-nanosecond time scales. We propose to use single electron excitations propagating within an electronic Mach-Zehnder interferometer in the Aharonov-Bohm dominated regime. We discuss how information about the quantum state of the electromagnetic radiation is encoded into the interference contribution to the average outgoing electrical current. By investigating squeezed radiation and single edge magnetoplasmons probed by Leviton pulses in a realistic setup, we show that single electron interferometers have the potential to probe quantum radiation in the time domain with sub-nanosecond to pico-second time resolution. Our research could have significant implications for probing the fundamental properties of light in the microwave to tera-Hertz domains at extremely short time scales. △ Less

Submitted 9 May, 2024; originally announced May 2024.

Comments: 31 pages, 15 figures

Gate tunable edge magnetoplasmon resonators

Authors: E. Frigerio, G. Rebora, M. Ruelle, H. Souquet-Basiège, Y. Jin, U. Gennser, A. Cavanna, B. Plaçais, E. Baudin, J. -M. Berroir, I. Safi, P. Degiovanni, G. Fève, G. Ménard

Abstract: Quantum Hall systems are platforms of choice when it comes to study topological properties of condensed matter systems and anyonic exchange statistics. In this work we have developed a tunable radiofrequency edge magnetoplasmonic resonator meant to serve as a versatile platform for future interferometric devices. The resonance frequency of the system is controlled by both the magnetic field and a… ▽ More Quantum Hall systems are platforms of choice when it comes to study topological properties of condensed matter systems and anyonic exchange statistics. In this work we have developed a tunable radiofrequency edge magnetoplasmonic resonator meant to serve as a versatile platform for future interferometric devices. The resonance frequency of the system is controlled by both the magnetic field and a set of electrostatic gates. The gates allow us to change both the size of the resonant cavity and the electronic density of the two-dimensional electron gas. We show that we can continuously control the frequency response of our resonator, making it possible to develop an edge magnetoplasmon interferometer. As we reach smaller sizes of our resonator, finite size effects caused by the measurement probes manifest. We present a theoretical description of the system taking into account the spatial extension of the probing gates. In the future, such device will be a valuable tool to investigate the properties of non-abelian anyons in the fractional quantum Hall regime. △ Less

Submitted 23 September, 2024; v1 submitted 28 April, 2024; originally announced April 2024.

Evidence for correlated electron pairs and triplets in quantum Hall interferometers

Authors: Wenmin Yang, David Perconte, Corentin Déprez, Kenji Watanabe, Takashi Taniguchi, Sylvain Dumont, Edouard Wagner, Frédéric Gay, Inès Safi, Hermann Sellier, Benjamin Sacépé

Abstract: Pairing of electrons is ubiquitous in electronic systems featuring attractive inter-electron interactions, as exemplified in superconductors. Counter-intuitively, it can also be mediated in certain circumstances by the repulsive Coulomb interaction alone. Quantum Hall (QH) Fabry-Pérot interferometers (FPIs) tailored in two-dimensional electron gas under a perpendicular magnetic field has been argu… ▽ More Pairing of electrons is ubiquitous in electronic systems featuring attractive inter-electron interactions, as exemplified in superconductors. Counter-intuitively, it can also be mediated in certain circumstances by the repulsive Coulomb interaction alone. Quantum Hall (QH) Fabry-Pérot interferometers (FPIs) tailored in two-dimensional electron gas under a perpendicular magnetic field has been argued to exhibit such unusual electron pairing seemingly without attractive interaction. Here, we show evidence in graphene QH FPIs revealing not only a similar electron pairing at bulk filling factor nu=2 but also an unforeseen emergence of electron tripling characterized by a fractional Aharonov-Bohm flux period h/3e (h is the Planck constant and e the electron charge) at nu=3. Leveraging a novel plunger-gate spectroscopy, we demonstrate that electron pairing (tripling) involves correlated charge transport on two (three) entangled QH edge channels. This spectroscopy indicates a quantum interference flux-periodicity determined by the sum of the phases acquired by the distinct QH edge channels having slightly different interfering areas. While recent theory invokes the dynamical exchange of neutral magnetoplasmons -- dubbed neutralons -- as mediator for electron pairing, our discovery of three entangled QH edge channels with apparent electron tripling defies understanding and introduces a new three-body problem for interacting fermions. △ Less

Submitted 13 September, 2024; v1 submitted 22 December, 2023; originally announced December 2023.

Journal ref: Nat Commun 15, 10064 (2024)

AC driven strongly correlated quantum circuits and Hall edge states: Unified photo-assisted noise and revisited minimal excitations

Authors: Inès Safi

Abstract: We study the photo-assisted noise generated by time-dependent or random sources and transmission amplitudes. We show that it obeys a perturbative non-equilibrium fluctuation relation that fully extends the lateral-band transmission picture in terms of many-body correlated states. This relation holds in non-equilibrium strongly correlated systems such as the integer or fractional quantum Hall regim… ▽ More We study the photo-assisted noise generated by time-dependent or random sources and transmission amplitudes. We show that it obeys a perturbative non-equilibrium fluctuation relation that fully extends the lateral-band transmission picture in terms of many-body correlated states. This relation holds in non-equilibrium strongly correlated systems such as the integer or fractional quantum Hall regime as well as in quantum circuits formed by a normal or Josephson junctions strongly coupled to an electromagnetic environment, with a possible temperature bias. We then show that the photo-assisted noise is universally super-poissonian, giving an alternative to a theorem by L. Levitov {\it et al} which states that an ac voltage increases the noise. Restricted to a linear dc current, we show that the latter does not apply to a non-linear superconducting junction. Then we characterize minimal excitations in non-linear conductors by ensuring a poissonian photo-assisted noise, and show that these can carry a non-trivial charge value in the fractional quantum Hall regime. We also propose methods for shot noise spectroscopy and for a robust determination of the fractional charge which is more advantageous than those we have proposed previously and implemented experimentally. △ Less

Submitted 3 September, 2022; v1 submitted 20 March, 2022; originally announced March 2022.

Comments: 20 pages, 5 figures. Substantial changes and reorganization of the sections. Some results added: -The counter-example of a SIS junction -The second differential of the photo-assisted noise and its expression at low ac voltages -The injected charge by lorentzian pulses for hierarchy fractional edge states

Journal ref: Phys. Rev. B (2022) (under press)

Dynamical Coulomb blockade under a temperature bias

Authors: H. Duprez, F. Pierre, E. Sivre, A. Aassime, F. D. Parmentier, A. Cavanna, A. Ouerghi, U. Gennser, I. Safi, C. Mora, A. Anthore

Abstract: We observe and comprehend the dynamical Coulomb blockade suppression of the electrical conductance across an electronic quantum channel submitted to a temperature difference. A broadly tunable, spin-polarized Ga(Al)As quantum channel is connected on-chip, through a micron-scale metallic node, to a linear $RC$ circuit. The latter is made up of the node's geometrical capacitance $C$ in parallel with… ▽ More We observe and comprehend the dynamical Coulomb blockade suppression of the electrical conductance across an electronic quantum channel submitted to a temperature difference. A broadly tunable, spin-polarized Ga(Al)As quantum channel is connected on-chip, through a micron-scale metallic node, to a linear $RC$ circuit. The latter is made up of the node's geometrical capacitance $C$ in parallel with an adjustable resistance $R\in \{1/2,1/3,1/4\}\times h/e^2$ formed by 2--4 quantum Hall channels. The system is characterized by three temperatures: a temperature of the electrons in the large electrodes ($T$) and in the node ($T_\mathrm{node}$), and a temperature of the electromagnetic modes of the $RC$ circuit ($T_\mathrm{env}$). The temperature in the node is selectively increased by local Joule dissipation, and characterized from current fluctuations. For a quantum channel in the tunnel regime, a close match is found between conductance measurements and tunnel dynamical Coulomb blockade theory. In the opposite near ballistic regime, we develop a theory that accounts for different electronic and electromagnetic bath temperatures, again in very good agreement with experimental data. Beyond these regimes, for an arbitrary quantum channel set in the far out-of-equilibrium situation where the temperature in the node significantly exceeds the one in the large electrodes, the equilibrium (uniform temperature) prediction for the conductance is recovered, albeit at a rescaled temperature $αT_\mathrm{node}$. △ Less

Submitted 8 April, 2021; originally announced April 2021.

Comments: Submitted

Journal ref: Phys. Rev. Research 3, 023122 (2021)

Backscattering off a driven Rashba impurity at the helical edge

Authors: Lorenzo Privitera, Niccolò Traverso Ziani, Inès Safi, Björn Trauzettel

Abstract: The spin degree of freedom is crucial for both understanding and exploiting the particular properties of the edges of two-dimensional topological insulators. In the absence of superconductivity and magnetism, Rashba coupling is the most relevant single particle perturbation in this system. Since Rashba coupling does not break time reversal symmetry, its influence on transport properties is only vi… ▽ More The spin degree of freedom is crucial for both understanding and exploiting the particular properties of the edges of two-dimensional topological insulators. In the absence of superconductivity and magnetism, Rashba coupling is the most relevant single particle perturbation in this system. Since Rashba coupling does not break time reversal symmetry, its influence on transport properties is only visible if processes that do not conserve the single particle energy are included. Paradigmatic examples of such processes are electron-electron interactions and time dependent external drivings. We analyze the effects of a periodically driven Rashba impurity at the helical edge, in the presence of electron-electron interactions. Interactions are treated by means of bosonization and the backscattering current is computed perturbatively up to second order in the impurity strength. We show that the backscattering current is non-monotonic in the driving frequency. This property is a fingerprint of the Rashba impurity, being absent in the case of a magnetic impurity in the helical liquid. Moreover, the non-monotonic behaviour allows us to directly link the backscattering current to the Luttinger parameter $K$, encoding the strength of electron-electron interactions. △ Less

Submitted 28 May, 2020; originally announced May 2020.

Comments: 5+4 pages, 2 figures

Journal ref: Phys. Rev. B 102, 195413 (2020)

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

Authors: Ines Safi

Abstract: 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 incompressibl… ▽ More 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. △ Less

Submitted 19 June, 2020; v1 submitted 17 April, 2020; originally announced April 2020.

Comments: To be published in Physical Review B, Rapid Communications. 11 pages, including "Supplemental Material". 2 figures. Few changes; two references added

Journal ref: Phys. Rev. B 102, 041113 (2020)

Microwave photons emitted by fractionally charged quasiparticles

Authors: R. Bisognin, H. Bartolomei, M. Kumar, I. Safi, J. -M. Berroir, E. Bocquillon, B. Plaçais, A. Cavanna, U. Gennser, Y. Jin, G. Fève

Abstract: Strongly correlated low-dimensional systems can host exotic elementary excitations carrying a fractional charge $q$ and potentially obeying anyonic statistics. In the fractional quantum Hall effect, their fractional charge has been successfully determined owing to low frequency shot noise measurements. However, a universal method for sensing them unambiguously and unraveling their intricate dynami… ▽ More Strongly correlated low-dimensional systems can host exotic elementary excitations carrying a fractional charge $q$ and potentially obeying anyonic statistics. In the fractional quantum Hall effect, their fractional charge has been successfully determined owing to low frequency shot noise measurements. However, a universal method for sensing them unambiguously and unraveling their intricate dynamics was still lacking. Here, we demonstrate that this can be achieved by measuring the microwave photons emitted by such excitations when they are transferred through a potential barrier biased with a dc voltage $V_{\text{dc}}$. We observe that only photons at frequencies $f$ below $qV_{\text{dc}}/h$ are emitted. This threshold provides a direct and unambiguous determination of the charge $q$, and a signature of exclusion statistics. Derived initially within the Luttinger model, this feature is also predicted by universal non-equilibrium fluctuation relations which agree fully with our measurements. Our work paves the way for further exploration of anyonic statistics using microwave measurements. △ Less

Submitted 10 July, 2019; originally announced July 2019.

Comments: 16 pages, 4 figures

Journal ref: Nature Communications volume 10, Article number: 1708 (2019)

The Coulomb drag effect induced by the third cumulant of current

Authors: Artem Borin, Ines Safi, Eugene Sukhorukov

Abstract: 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 inve… ▽ More 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. △ Less

Submitted 11 May, 2019; v1 submitted 14 December, 2018; originally announced December 2018.

Comments: 9 pages, 2 figures

Journal ref: Phys. Rev. B 99, 165404 (2019)

Unified time-dependent perturbative relations applied to spectroscopy through photo-drag current

Authors: Inès Safi

Abstract: We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is non-perturbative with respect to strong coupling to an electromagnetic environment, or to Coulomb or superconducting correlations. We derive unifying relations between the current ge… ▽ More We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is non-perturbative with respect to strong coupling to an electromagnetic environment, or to Coulomb or superconducting correlations. We derive unifying relations between the current generated by coherent radiation or statistical mixture of radiations, superimposed on a dc voltage $V_{dc}$, and the out-of-equilibrium dc current which encodes the effects of interactions. Thus we extend fully the lateral band-transmission picture, thus quantum superposition, to coherent many-body correlated states. This provides methods for a determination of the carrier's charge q free from unknown parameters through the robustness of the Josephson-like frequency. Similar relations we have derived for noise have allowed, recently, to determine the fractional charge in the Fractional Quantum Hall Effect (FQHE) within the Jain series (M. Kapfer et al, Science 2018). The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates a photo-ratchet effect we exploit to propose a novel method to measure the charge $q$, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-gaussian statistical radiations. We apply the theory to the Tomonaga-Luttinger Liquid (TLL), showing a counterintuitive feature: a lorentzian pulse superimposed on $V_{dc}$ can reduce the current compared to its dc value, at the same $V_{dc}$, questioning the terminology "photo-assisted". Beyond a charge current, the theory applies to operators such as spin current in the spin Hall effect, or voltage drop across a phase-slip Josephson junction. △ Less

Submitted 4 December, 2018; v1 submitted 21 September, 2018; originally announced September 2018.

Comments: Accepted for publication in Phys. Rev. B. 19 pages, 5 appendices, 4 figures. Many changes in the form to shorten the main part of the paper. A figure is added

Journal ref: Phys. Rev. B 99, 045101 (2019)

Perturbative fluctuation dissipation relation for non-equilibrium finite frequency noise in quantum circuits

Authors: Benjamin Roussel, Pascal Degiovanni, Inès Safi

Abstract: We develop a general perturbative computation of finite-frequency quantum noise which applies, in particular, to both good or weakly transmitting strongly correlated conductors coupled to a generic environment. Under a minimal set of hypotheses, we show that the noise can be expressed through the non-equilibrium DC current only, generalizing a non-equilibrium fluctuation dissipation relation. We u… ▽ More We develop a general perturbative computation of finite-frequency quantum noise which applies, in particular, to both good or weakly transmitting strongly correlated conductors coupled to a generic environment. Under a minimal set of hypotheses, we show that the noise can be expressed through the non-equilibrium DC current only, generalizing a non-equilibrium fluctuation dissipation relation. We use this relation to derive explicit predictions for the non equilibrium finite frequency noise for a single channel conductor connected to an arbitrary Ohmic environment. △ Less

Submitted 8 May, 2015; originally announced May 2015.

Comments: 4 pages with 4 figures plus supplementary information as appendices

Journal ref: Phys. Rev. B 93, 045102 (2016)

Fluctuation-Dissipation Relations of a Tunnel Junction Driven by a Quantum Circuit

Authors: O. Parlavecchio, C. Altimiras, J. -R. Souquet, P. Simon, I. Safi, P. Joyez, D. Vion, P. Roche, D. Esteve, F. Portier

Abstract: We derive fluctuation-dissipation relations for a tunnel junction driven by a high impedance microwave resonator, displaying strong quantum fluctuations. We find that the fluctuation-dissipation relations derived for classical forces hold, provided the effect of the circuit's quantum fluctuations is incorporated into a modified non-linear $I(V)$ curve. We also demonstrate that all quantities measu… ▽ More We derive fluctuation-dissipation relations for a tunnel junction driven by a high impedance microwave resonator, displaying strong quantum fluctuations. We find that the fluctuation-dissipation relations derived for classical forces hold, provided the effect of the circuit's quantum fluctuations is incorporated into a modified non-linear $I(V)$ curve. We also demonstrate that all quantities measured under a coherent time dependent bias can be reconstructed from their dc counterpart with a photo-assisted tunneling relation. We confirm these predictions by implementing the circuit and measuring the dc current through the junction, its high frequency admittance and its current noise at the frequency of the resonator. △ Less

Submitted 30 March, 2015; v1 submitted 23 September, 2014; originally announced September 2014.

Comments: Publisehd as Physical Review Letters, 114, 126801

Journal ref: Physical Review Letters, American Physical Society, 2015, 114 (12)

Time-dependent Transport in arbitrary extended driven tunnel junctions

Authors: Ines Safi

Abstract: 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 syst… ▽ More 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. △ Less

Submitted 23 January, 2014; originally announced January 2014.

Comments: One figure, 7 pages (including Supplemental Material)

Dynamical Coulomb Blockade in an interacting 1D system coupled to an arbitrary environment

Authors: J. -R. Souquet, I. Safi, P. Simon

Abstract: We study the out-of-equilibrium transport in a Tomonaga-Luttinger liquid containing a weak or a tunneling barrier coupled to an arbitrary electromagnetic environment. This applies as well to a coherent one-channel non-interacting conductor with a transmission coefficient close to one or to zero. We derive formal expressions for the current and finite-frequency (FF) noise at arbitrary voltages, tem… ▽ More We study the out-of-equilibrium transport in a Tomonaga-Luttinger liquid containing a weak or a tunneling barrier coupled to an arbitrary electromagnetic environment. This applies as well to a coherent one-channel non-interacting conductor with a transmission coefficient close to one or to zero. We derive formal expressions for the current and finite-frequency (FF) noise at arbitrary voltages, temperatures and frequency-dependent impedance $Z(ω)$ in the regimes of weak and strong backscattering. We show that these two regimes are no longer related by duality at finite frequency. We then carry explicit computations of the nonlinear conductance and FF noise when $Z(ω)$ describes an harmonic oscillator such as a LC circuit or a cavity. △ Less

Submitted 24 November, 2013; v1 submitted 21 June, 2013; originally announced June 2013.

Comments: 13 pages, 9 figures

Journal ref: Phys. Rev. B 88, 205419 (2013)

Tomonaga-Luttinger physics in electronic quantum circuits

Authors: S. Jezouin, M. Albert, F. D. Parmentier, A. Anthore, U. Gennser, A. Cavanna, I. Safi, F. Pierre

Abstract: In one-dimensional conductors, interactions result in correlated electronic systems. At low energy, a hallmark signature of the so-called Tomonaga-Luttinger liquids (TLL) is the universal conductance curve predicted in presence of an impurity. A seemingly different topic is the quantum laws of electricity, when distinct quantum conductors are assembled in a circuit. In particular, the conductances… ▽ More In one-dimensional conductors, interactions result in correlated electronic systems. At low energy, a hallmark signature of the so-called Tomonaga-Luttinger liquids (TLL) is the universal conductance curve predicted in presence of an impurity. A seemingly different topic is the quantum laws of electricity, when distinct quantum conductors are assembled in a circuit. In particular, the conductances are suppressed at low energy, a phenomenon called dynamical Coulomb blockade (DCB). Here we investigate the conductance of mesoscopic circuits constituted by a short single-channel quantum conductor in series with a resistance, and demonstrate a proposed link to TLL physics. We reformulate and establish experimentally a recently derived phenomenological expression for the conductance using a wide range of circuits, including carbon nanotube data obtained elsewhere. By confronting both conductance data and phenomenological expression with the universal TLL curve, we demonstrate experimentally the predicted mapping between DCB and the transport across a TLL with an impurity. △ Less

Submitted 3 April, 2013; v1 submitted 17 January, 2013; originally announced January 2013.

Comments: 9p,6fig+SI; to be published in nature comm; v2: mapping extended to finite range interactions, added discussion and SI material, added references

Journal ref: Nat. Commun. 4:1802 (2013)

One-channel conductor coupled to a quantum of resistance: exact ac conductance and finite-frequency noise

Authors: R. Zamoum, A. Crepieux, I. Safi

Abstract: We consider a one-channel coherent conductor with a good transmission embedded into an ohmic environment whose impedance is equal to the quantum of resistance R_q=h/e^2 below the RC frequency. This choice is motivated by the mapping of this problem to a Tomonaga-Luttinger liquid with one impurity whose interaction parameter corresponds to the specific value K=1/2, allowing for a refermionization p… ▽ More We consider a one-channel coherent conductor with a good transmission embedded into an ohmic environment whose impedance is equal to the quantum of resistance R_q=h/e^2 below the RC frequency. This choice is motivated by the mapping of this problem to a Tomonaga-Luttinger liquid with one impurity whose interaction parameter corresponds to the specific value K=1/2, allowing for a refermionization procedure. The "new" fermions have an energy-dependent transmission amplitude which incorporates the strong correlation effects and yields the exact dc current and zero-frequency noise through expressions similar to those of the scattering approach. We recall and discuss these results for our present purpose. Then we compute, for the first time, the finite-frequency differential conductance and the finite-frequency non-symmetrized noise. Contrary to intuitive expectation, both cannot be expressed within the scattering approach for the new fermions, even though they are still determined by the transmission amplitude. Even more, the finite-frequency conductance obeys an exact relation in terms of the dc current which is similar to that derived perturbatively with respect to weak tunneling within the Tien-Gordon theory, and extended recently to arbitrary strongly interacting systems coupled eventually to an environment or/and with a fractional charge. We also show that the emission excess noise vanishes exactly above eV, even though the underlying Tomonaga-Luttinger liquid model corresponds to a many-body correlated system. Our results apply for all ranges of temperature, voltages and frequencies below the RC frequency, and they allow to explore fully the quantum regime. △ Less

Submitted 17 March, 2012; v1 submitted 3 February, 2012; originally announced February 2012.

Comments: 15 pages, 11 figures

Journal ref: Phys. Rev. B 85, 125421 (2012)

Determination of tunneling charge via current measurements

Authors: Ines Safi, Eugene V. Sukhorukov

Abstract: 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 so… ▽ More 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. △ Less

Submitted 29 September, 2010; v1 submitted 27 April, 2010; originally announced April 2010.

Comments: The form has been improved, with additional useful comments, citations have been added. 7 pages, one figure

Journal ref: Europhysics Letters (2010) (under press)

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

Authors: Ines Safi

Abstract: 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 cond… ▽ More 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. △ Less

Submitted 30 October, 2009; v1 submitted 31 August, 2009; originally announced August 2009.

Comments: 5 pages, 1 figure

Asymmetry of the excess finite-frequency noise

Authors: Ines Safi

Abstract: 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 o… ▽ More 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. △ Less

Submitted 25 June, 2009; originally announced June 2009.

Comments: 4 pages, 1 figure

Journal ref: AIP Conference Proceedings 1129, NOISE AND FLUCTUATIONS: 20th International Conference on Noise and Fluctuations (ICNF-2009), Massimo Macucci and Giovanni Basso, Pisa, Italy

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

Authors: Ines Safi

Abstract: 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… ▽ More 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. △ Less

Submitted 12 June, 2009; originally announced June 2009.

Comments: 37 pages, 3 figures

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

Authors: Ines Safi, Cristina Bena, Adeline Crépieux

Abstract: 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… ▽ More 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 $g$. △ Less

Submitted 20 November, 2008; v1 submitted 26 May, 2008; originally announced May 2008.

Journal ref: Physical Review B 78 (2008) 205422

Emission and absorption noise in the fractional quantum Hall effect

Authors: Cristina Bena, Ines Safi

Abstract: 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 u… ▽ More 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. △ Less

Submitted 1 May, 2007; originally announced May 2007.

Comments: 26 pages, 11 figures

Negativity of the excess noise in a quantum wire capacitively coupled to a gate

Authors: F. Dolcini, B. Trauzettel, I. Safi, H. Grabert

Abstract: The electrical current noise of a quantum wire is expected to increase with increasing applied voltage. We show that this intuition can be wrong. Specifically, we consider a single channel quantum wire with impurities and with a capacitive coupling to nearby metallic gates and find that its excess noise, defined as the change in the noise caused by the finite voltage, can be negative at zero tem… ▽ More The electrical current noise of a quantum wire is expected to increase with increasing applied voltage. We show that this intuition can be wrong. Specifically, we consider a single channel quantum wire with impurities and with a capacitive coupling to nearby metallic gates and find that its excess noise, defined as the change in the noise caused by the finite voltage, can be negative at zero temperature. This feature is present both for large ($c \gg c_q$) and small ($c \ll c_q$) capacitive coupling, where $c$ is the geometrical and $c_q$ the quantum capacitance of the wire. In particular, for $c \gg c_q$, negativity of the excess noise can occur at finite frequency when the transmission coefficients are energy dependent, i.e. in the presence of Fabry-Pérot resonances or band curvature. In the opposite regime $c \lesssim c_q$, a non trivial voltage dependence of the noise arises even for energy independent transmission coefficients: at zero frequency the noise decreases with voltage as a power law when $c < c_q/3$, while, at finite frequency, regions of negative excess noise are present due to Andreev-type resonances. △ Less

Submitted 23 January, 2007; v1 submitted 10 September, 2006; originally announced September 2006.

Comments: 11 pages, 5 figures. Revised version, references and technical details added, typos corrected

Journal ref: Phys. Rev. B 75, 045332 (2007)

Fractional charge in the noise of Luttinger liquid systems

Authors: B. Trauzettel, I. Safi, F. Dolcini, H. Grabert

Abstract: The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between shot noise and backscattering current crucially depends on the noise frequency relative to the ballistic frequency v_F/gL, where v_F is the Fermi… ▽ More The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between shot noise and backscattering current crucially depends on the noise frequency relative to the ballistic frequency v_F/gL, where v_F is the Fermi velocity, g the Luttinger liquid interaction parameter, and L the length of the wire. In contrast to chiral Luttinger liquids, the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but also depends on Andreev-type reflections of plasmons at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge e*=e g of the bulk excitations. We show that the frequencies needed to see interaction effects in the Fano factor are within experimental reach. △ Less

Submitted 30 May, 2005; originally announced May 2005.

Comments: 9 pages, 4 figures, conference proceedings of Fluctuations and Noise 2005, Austin, Texas

Journal ref: Fluctuations and Noise in Materials II, edited by P. Svedlindh, D. Popovic, and M.B.Weissmann, Proceedings of SPIE Vol. 5843 (SPIE, Bellingham, WA, 2005)

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

Authors: Fabrizio Dolcini, Bjoern Trauzettel, Ines Safi, Hermann Grabert

Abstract: 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 dependenc… ▽ More 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. △ Less

Submitted 14 April, 2005; v1 submitted 13 September, 2004; originally announced September 2004.

Comments: 28 pages, 19 figures, published version with minor changes

Journal ref: Phys. Rev. B 71, 165309 (2005)

Appearance of fractional charge in the noise of non-chiral Luttinger liquids

Authors: B. Trauzettel, I. Safi, F. Dolcini, H. Grabert

Abstract: The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between noise and backscattered current crucially depends on the noise frequency $ω$ relative to the ballistic frequency $v_F/gL$, where $v_F$ is the Ferm… ▽ More The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between noise and backscattered current crucially depends on the noise frequency $ω$ relative to the ballistic frequency $v_F/gL$, where $v_F$ is the Fermi velocity, $g$ the Luttinger liquid interaction parameter, and $L$ the length of the wire. In contrast to chiral Luttinger liquids the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but also depends on Andreev-type reflections at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge $e^*=e g$ of the bulk excitations. △ Less

Submitted 28 April, 2004; v1 submitted 18 February, 2004; originally announced February 2004.

Comments: 4 pages, 2 figures, final version, to appear in PRL

Journal ref: Phys. Rev. Lett. 92, 226405 (2004)

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

Authors: Ines Safi, Hubert Saleur

Abstract: 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 comp… ▽ More 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. △ Less

Submitted 14 June, 2004; v1 submitted 18 December, 2003; originally announced December 2003.

Comments: 5 pages, 2 figures, shortened version for publication in Phys. Rev. Lett

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

Authors: Fabrizio Dolcini, Hermann Grabert, Ines Safi, Bjoern Trauzettel

Abstract: 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. 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. △ Less

Submitted 7 November, 2003; originally announced November 2003.

Comments: 4 pages, two figures, accepted for publication in Phys. Rev. Lett

Journal ref: Phys. Rev. Lett. 91, 266402 (2003)

Andreev reflection off a fluctuating superconductor in the absence of equilibrium

Authors: P. Devillard, R. Guyon, T. Martin, I. Safi, B. K. Chakraverty

Abstract: Andreev reflection between a normal metal and a superconductor whose order parameter exhibits quantum phase fluctuations is examined. The approach chosen is non perturbative in the tunneling Hamiltonian and enables to probe the whole range of voltage biases up to the gap amplitude. Results are illustrated using the one-dimensional Josephson- Junction Array model previously introduced in the line… ▽ More Andreev reflection between a normal metal and a superconductor whose order parameter exhibits quantum phase fluctuations is examined. The approach chosen is non perturbative in the tunneling Hamiltonian and enables to probe the whole range of voltage biases up to the gap amplitude. Results are illustrated using the one-dimensional Josephson- Junction Array model previously introduced in the linear response regime. Phase fluctuations are shown to affect the differential conductance and are compared to the result of Blonder, Tinkham and Klapwijk for a rigid BCS superconductor. The noise spectrum of the Andreev current is also obtained and its second derivative with respect to frequency is proposed as a direct tool to analyze the phase fluctuations. △ Less

Submitted 2 August, 2002; v1 submitted 25 February, 2002; originally announced February 2002.

Comments: 13 pages, 6 figures

Klein Factors in multiple Fractional Quantum Hall edge tunneling

Authors: R. Guyon, P. Devillard, T. Martin, I. Safi

Abstract: A fractional quantum Hall liquid with multiple edges is considered. The computation of transport quantities such as current, noise and noise cross correlations in such multiple edge samples requires the implementation of so called Klein factors, which insure the correct quasiparticle exchange properties. The commutation relations of these factors are obtained by closing the system into a single… ▽ More A fractional quantum Hall liquid with multiple edges is considered. The computation of transport quantities such as current, noise and noise cross correlations in such multiple edge samples requires the implementation of so called Klein factors, which insure the correct quasiparticle exchange properties. The commutation relations of these factors are obtained by closing the system into a single edge. The non-equilibrium Green's function formalism associated with such factors is derived for a simple Laughlin fraction of the Hall effect. It is shown explicitly how Klein factors enter the calculation of the noise cross correlations, as well as the correction to the Poisson limit for the noise. △ Less

Submitted 14 January, 2002; v1 submitted 19 September, 2001; originally announced September 2001.

Comments: 4 pages, 1 figure

Journal ref: Phys. Rev. B 65, 153304 (2002)

Partition noise and statistics in the fractional quantum Hall effect

Authors: I. Safi, P. Devillard, T. Martin

Abstract: A microscopic theory of current partition in fractional quantum Hall liquids, described by chiral Luttinger liquids, is developed to compute the noise correlations, using the Keldysh technique. In this Hanbury-Brown and Twiss geometry, at Laughlin filling factor ν=1/3, the real time noise correlator exhibits oscillations which persist over larger time scales than that of an uncorrelated Hall flu… ▽ More A microscopic theory of current partition in fractional quantum Hall liquids, described by chiral Luttinger liquids, is developed to compute the noise correlations, using the Keldysh technique. In this Hanbury-Brown and Twiss geometry, at Laughlin filling factor ν=1/3, the real time noise correlator exhibits oscillations which persist over larger time scales than that of an uncorrelated Hall fluid. The zero frequency noise correlations are negative at filling factor 1/3 as for bare electrons (anti-bunching), but are strongly reduced in amplitude. These correlations become positive (bunching) for ν\leq 1/5, suggesting a tendency towards bosonic behavior. △ Less

Submitted 13 March, 2001; v1 submitted 14 April, 2000; originally announced April 2000.

Comments: revised version, curve for time correlations at nu=1/3 added

A dynamic scattering approach for a gated interacting wire

Authors: Ines Safi

Abstract: 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 lef… ▽ More 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. △ Less

Submitted 8 July, 1998; originally announced July 1998.

Comments: Five revtex pages, one Postscript figure

Interacting electrons with spin in a one-dimensional wire connected to leads

Authors: Inès Safi, H. J. Schulz

Abstract: We investigate a one--dimensional wire of interacting electrons connected to one--dimensional noninteracting leads in the absence and in the presence of a backscattering potential. The ballistic wire separates the charge and spin parts of an incident electron even in the noninteracting leads. The Fourier transform of nonlocal correlation functions are computed for $T\gg ω$. In particular, this a… ▽ More We investigate a one--dimensional wire of interacting electrons connected to one--dimensional noninteracting leads in the absence and in the presence of a backscattering potential. The ballistic wire separates the charge and spin parts of an incident electron even in the noninteracting leads. The Fourier transform of nonlocal correlation functions are computed for $T\gg ω$. In particular, this allows us to study the proximity effect, related to the Andreev reflection. A new type of proximity effect emerges when the wire has normally a tendency towards Wigner crystal formation. The latter is suppressed by the leads below a space--dependent crossover temperature; it gets dominated everywhere by the $2k_F$ CDW at $T<L^{3/2 (K-1)}$ for short range interactions with parameter $K<1/3$. The lowest--order renormalization equations of a weak backscattering potential are derived explicitly at finite temperature. A perturbative expression for the conductance in the presence of a potential with arbitrary spatial extension is given. It depends on the interactions, but is also affected by the noninteracting leads, especially for very repulsive interactions, $K<1/3$. This leads to various regimes, depending on temperature and on $K$. For randomly distributed weak impurities, we compute the conductance fluctuations, equal to that of $R=g-2e^2 /h$. While the behavior of $Var(R)$ depends on the interaction parameters, and is different for electrons with or without spin, and for $K<1/3$ or $K>1/3$, the ratio $Var(R)/R^2$ stays always of the same order: it is equal to $L_T/L\ll 1$ in the high temperature limit, then saturates at 1/2 in the low temperature limit, indicating that the relative fluctuations of $R$ increase as one lowers the temperature. △ Less

Submitted 26 March, 1998; originally announced March 1998.

Comments: 24 two-column revtex pages, five postscript figures. This paper is an extended version of cond-mat/9612173

Transport in a one-dimensional wire connected to leads and proximity effects

Authors: I. Safi, H. J. Schulz

Abstract: We investigate transport through a finite interacting wire connected to noninteracting leads. The conductance of the pure wire is not renormalized by the interactions for any spatial variation of the interaction parameters $u,K$, and not even for Coulomb interactions restricted to the wire. We rigorously relate the conductance to the transmission, that turns out to be perfect. If $K$ varies abru… ▽ More We investigate transport through a finite interacting wire connected to noninteracting leads. The conductance of the pure wire is not renormalized by the interactions for any spatial variation of the interaction parameters $u,K$, and not even for Coulomb interactions restricted to the wire. We rigorously relate the conductance to the transmission, that turns out to be perfect. If $K$ varies abruptly at the contacts, an electron incident on the wire is reflected into a series of partial spatially separated charges which sum up to unity. For attractive interactions, the reflection at the contact is similar to Andreev reflection on a gapless superconductor. This process affects the density-density or pairing correlation functions: they are enhanced on the bulk of the wire as in an infinite Luttinger liquid, then extend to the external noninteracting leads in a way reminiscent of the proximity effect. The effect of impurities is governed by the wire parameter but is affected by the leads close to the contacts. Our results give a possible explanation to recent experiments on quantum wires by Tarucha et al. △ Less

Submitted 10 November, 1997; originally announced November 1997.

Comments: 5 pages revtex, one figure. Journ-Ref: "Correlated Fermions and Transport in Mesoscopic Systems", edited by T. Martin, G. Montambaux and J. Tran Thanh Van. Editions Frontieres, Gif-sur-Yvette (1996)

Resonance in a Tomonaga-Luttinger liquid

Authors: Ines Safi

Abstract: We study a homogeneous Tomonaga-Luttinger liquid with backscattering potential. A perturbative computation of the conductance at and near resonance is given. We find that the backscattering of one electron dominates that of two electrons for an interaction parameter $K\geq 1/3$ and that the resonance point depends on temperature. Our results may be relevant for recent experiments on shot-noise i… ▽ More We study a homogeneous Tomonaga-Luttinger liquid with backscattering potential. A perturbative computation of the conductance at and near resonance is given. We find that the backscattering of one electron dominates that of two electrons for an interaction parameter $K\geq 1/3$ and that the resonance point depends on temperature. Our results may be relevant for recent experiments on shot-noise in FQHE, where the charge 1/3 and not $2*1/3$ is measured on resonance. △ Less

Submitted 22 September, 1997; v1 submitted 22 August, 1997; originally announced August 1997.

Comments: 15 pages, three Figures. v2: Definite version, Citations added, presentation improved. To appear in Phys. Rev. B, Rapid Com

Conductance of a quantum wire: Landauer's approach versus Kubo formula

Authors: Ines Safi

Abstract: The transport in a pure one-dimensional quantum wire is investigated for any range of interactions. First, the wire is connected to measuring leads. The transmission of an incident electron is found to be perfect, and the conductance is not renormalized by the interactions. Either Landauer's approach or Kubo formula can be used as long as the reservoirs impose the boundary conditions. Second, th… ▽ More The transport in a pure one-dimensional quantum wire is investigated for any range of interactions. First, the wire is connected to measuring leads. The transmission of an incident electron is found to be perfect, and the conductance is not renormalized by the interactions. Either Landauer's approach or Kubo formula can be used as long as the reservoirs impose the boundary conditions. Second, the Kubo formula as a response to the local field is reconsidered in a generic Luttinger liquid: the ``intrinsic'' conductance thus obtained is determined by the same combination of interaction parameters as that which renormalizes the current. △ Less

Submitted 9 September, 1997; v1 submitted 6 January, 1997; originally announced January 1997.

Comments: 5 revtex pages; an improved and definite version

Journal ref: Phys. Rev. B. 55, R7331 (1997-II)

Interacting electrons with spin in a one-dimensional dirty wire connected to leads

Authors: I. Safi, H. J. Schulz

Abstract: We investigate a one-dimensional wire of interacting electrons connected to semi-infinite leads in the absence and in the presence of a backscattering potential. An incident electron on the clean wire is perfectly transmitted into spatially separated spin and charge parts in the noninteracting leads, a result we extend to any finite-range interactions. The backscattering potential is renormalize… ▽ More We investigate a one-dimensional wire of interacting electrons connected to semi-infinite leads in the absence and in the presence of a backscattering potential. An incident electron on the clean wire is perfectly transmitted into spatially separated spin and charge parts in the noninteracting leads, a result we extend to any finite-range interactions. The backscattering potential is renormalized in a non-universal way and therefore the reduction in the conductance is more complicated than the laws derived up to now: it has power laws as a function of temperature, wire length, and also the distance of a barrier to the contacts. △ Less

Submitted 18 December, 1996; originally announced December 1996.

Comments: Latex pages, 2 figures

Transport through a single-band wire connected to measuring leads

Authors: Inès Safi, H. J. Schulz

Abstract: Transport through a one-dimensional wire of interacting electrons connected to semi infinite leads is investigated using a bosonization approach. The dynamic nonlocal conductivity is rigorously expressed in terms of the transmission. For abrupt variations of the interaction parameters at the junctions, an incident electron is transmitted as a sequence of partial charges: the central wire acts as… ▽ More Transport through a one-dimensional wire of interacting electrons connected to semi infinite leads is investigated using a bosonization approach. The dynamic nonlocal conductivity is rigorously expressed in terms of the transmission. For abrupt variations of the interaction parameters at the junctions, an incident electron is transmitted as a sequence of partial charges: the central wire acts as a Fabry-Pérot resonator. The dc conductance is shown to be given by the total transmission which turns out to be perfect. When the wire has a tendency towards superconducting order, partial Andreev reflection of an incident electron occurs. Finally, we study the role of a weak barrier at one contact or inside the wire by a renormalization group method at finite temperature. We compute the conductance in the presence of localized or extended disorder, and compare our results to recent experiments on quantum wires. △ Less

Submitted 10 September, 1997; v1 submitted 2 May, 1996; originally announced May 1996.

Comments: 14 pages, 3 Figures, crckapb style. The paper has not been changed, but replaced to solve technical problems

Journal ref: "Quantum Transport in Semiconductor Submicron Structures", edited by B. Kramer (Kluwer Academic Press, AA Dordrecht, 1995)

Transport in an inhomogeneous interacting one--dimensional system

Authors: I. Safi, H. J. Schulz

Abstract: Transport through a one--dimensional wire of interacting electrons connected to semi--infinite leads is investigated using a bosonization approach. An incident electron is transmitted as a sequence of partial charges. The dc conductance is found to be entirely determined by the properties of the leads. The dynamic nonlocal conductivity is rigorously expressed in terms of the transmission. For ab… ▽ More Transport through a one--dimensional wire of interacting electrons connected to semi--infinite leads is investigated using a bosonization approach. An incident electron is transmitted as a sequence of partial charges. The dc conductance is found to be entirely determined by the properties of the leads. The dynamic nonlocal conductivity is rigorously expressed in terms of the transmission. For abrupt variations of the interaction parameters at the junctions the central wire acts as a Fabry--Perot resonator. When one of the connected wires has a tendency towards superconducting order, partial Andreev reflection of an incident electron occurs. △ Less

Submitted 18 May, 1995; originally announced May 1995.

Comments: 11 pages, RevTeX 3.0, 1 postscript figure, everything in a uuencoded file

Journal ref: Phys. Rev. B 52, R17040 (1995)