Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0906.4658 · AIP conference proceedings

Asymmetry of the excess finite-frequency noise

Inès Safi A, Massimo Macucci, Giovanni Basso

Published Jan 1, 2009• 3 citations
arXivHTMLPDF

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 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.

DOI
10.1063/1.3140492

Related papers

Emission and Absorption Asymmetry in the Quantum Noise of a Josephson Junction

P.-M. Billangeon, F. Pierre, Hélène Bouchiat +1 more

We measure current fluctuations of mesoscopic devices in the quantum regime, when the frequency is of the order of or higher than the applied voltage or temperature. Detection is designed to probe separately the absorption and emission contributions of current fluctuations, i.e. the positive and negative frequencies of the Fourier transformed nonsymmetrized noise correlator. It relies on measuring the quasiparticles photon assisted tunneling current across a superconductor-insulator-superconductor junction (the detector junction) caused by the excess current fluctuations generated by quasiparticles tunneling across a Josephson junction (the source junction). We demonstrate unambiguously that the negative and positive frequency parts of the nonsymmetrized noise correlator are separately detected and that the excess current fluctuations of a voltage biased Josephson junction present a strong asymmetry between emission and absorption.

arXiv:cond-mat/0508676•Physical Review Letters•Apr 6, 2006•72 citations

Non-equilibrium quantum noise in chiral Luttinger liquids

Claudio Chamon, Denise E. Freed, Xiao-Gang Wen

We study non-equilibrium noise in Chiral Luttinger Liquids using the Landauer-Buttiker Scattering approach, obtaining the current/voltage noise spectrum for a four-terminal measurement scheme. Experimental consequences of the tunneling of charges are present in the four-terminal measurement of both the low-frequency shot noise ($ω$ near 0), and the high-frequency Josephson noise ($ω$ near $ω_J=e^*V/\hbar$). Within perturbation theory, an algebraic singularity is present (to all orders) at the Josephson frequency $ω_J=e^*V/\hbar$, whose position depends on the charge $e^*$ of the tunneling particles, either electrons or fractionally charged quasiparticles. We show in a non-perturbative calculation for an exactly solvable point that the singularity at the quasiparticle frequency exists only in the limit of vanishing coupling, whereas the singularity at the electron frequency is present for all coupling strengths. The vanishing coupling limit corresponds to perfectly quantized Hall conductance in the case of quasiparticle tunneling between edge states in the fractional quantum Hall regime, and thus tunneling destroys the singularity at the quasiparticle frequency concomitantly with the quantized current.

arXiv:cond-mat/9507064•Jul 18, 1995•0 citations

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

Redouane Zamoum, Adeline Crépieux C, Inès Safi A

We consider a one-channel coherent conductor with a good transmission embedded into an Ohmic environment, the impedance of which 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, the interaction parameter of which 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 the finite-frequency differential conductance and the finite-frequency nonsymmetrized noise. Contrary to intuitive expectation, both can not 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 and/or 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 us to explore fully the quantum regime.

arXiv:1202.0708•Physical Review B•Mar 16, 2012•24 citations

Nonequilibrium quantum noise in chiral Luttinger liquids

Claudio Chamon, Denise E. Freed, Xiao-Gang Wen

We study nonequilibrium noise in chiral Luttinger liquids using the Landauer-Buttiker scattering approach, obtaining the current and voltage noise spectrum for a four-terminal measurement scheme. Experimental consequences of the tunneling of charges are present in the four-terminal measurement of both the low-frequency shot noise (\ensuremath{\omega} near 0), and the high-frequency Josephson noise (\ensuremath{\omega} near ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$=${\mathit{e}}^{\mathrm{*}}$V/\ensuremath{\Elzxh}). Within perturbation theory, an algebraic singularity is present at the Josephson frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$=${\mathit{e}}^{\mathrm{*}}$V/\ensuremath{\Elzxh}, whose position depends on the charge ${\mathit{e}}^{\mathrm{*}}$ of the tunneling particles, either electrons or fractionally charged quasiparticles. These two types of tunneling are related by a strong-weak--coupling duality transformation. We show in a nonperturbative calculation for an exactly solvable point that the singularity at the quasiparticle frequency exists only in the limit of vanishing coupling, whereas the singularity at the electron frequency is present for all coupling strengths. The vanishing coupling limit corresponds to perfectly quantized Hall conductance in the case of quasiparticle tunneling between edge states in the fractional quantum Hall regime, and thus tunneling destroys the singularity at the quasiparticle frequency concomitantly with the quantized current. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Feb 15, 1996•83 citations

Nonequilibrium finite-frequency noise of a resonance-level quantum dot close to a dissipative quantum phase transition: Functional Renormalization Group approaches

Chung‐Hou Chung

We calculate the finite-frequency current noise of a nonequilibrium resonance-level quantum dot close to a dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a de-localized phase for weak dissipation and a localized phase for strong dissipation. The resonance-level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic boson bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. To compute the finite-frequency noise, we combine two recently developed Functional Renormalization Group (FRG) approaches in Refs.[17,22] and in Ref.[23]. The nonequilibrium current noise at zero-temperature and finite frequencies shows a singular dip in the de-localized phase for the magnitude of frequencies equal to the bias voltage; while the dip is smeared out as the system moves to the localized phase. The corresponding peak-to-dip crossover is found in the AC conductance for the magnitude of frequencies equal to the bias voltage. The relevance and applications of our results for the experiments and for tunnelings between Fractional Quantum Hall Edge (FQHE) states and chiral Luttinger liquids are discussed.

arXiv:1010.5248•Oct 25, 2010•0 citations

Fractional charge in the noise of Luttinger liquid systems (Invited Paper)

Björn Trauzettel, Inès Safi A, Fabrizio Dolcini +1 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 vF/gL, where vF 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 of the bulk excitations. We show that the frequencies needed to see interaction effects in the Fano factor are within experimental reach.

arXiv:cond-mat/0505722•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 23, 2005•1 citation
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.
We measure current fluctuations of mesoscopic devices in the quantum regime, when the frequency is of the order of or higher than the applied voltage or temperature. Detection is designed to probe separately the absorption and emission contributions of current fluctuations, i.e. the positive and negative frequencies of the Fourier transformed nonsymmetrized noise correlator. It relies on measuring the quasiparticles photon assisted tunneling current across a superconductor-insulator-superconductor junction (the detector junction) caused by the excess current fluctuations generated by quasiparticles tunneling across a Josephson junction (the source junction). We demonstrate unambiguously that the negative and positive frequency parts of the nonsymmetrized noise correlator are separately detected and that the excess current fluctuations of a voltage biased Josephson junction present a strong asymmetry between emission and absorption.
We study non-equilibrium noise in Chiral Luttinger Liquids using the Landauer-Buttiker Scattering approach, obtaining the current/voltage noise spectrum for a four-terminal measurement scheme. Experimental consequences of the tunneling of charges are present in the four-terminal measurement of both the low-frequency shot noise (ωωω near 0), and the high-frequency Josephson noise (ωωω near ωJ=e∗V/ℏω_J=e^*V/\hbarωJ​=e∗V/ℏ). Within perturbation theory, an algebraic singularity is present (to all orders) at the Josephson frequency ωJ=e∗V/ℏω_J=e^*V/\hbarωJ​=e∗V/ℏ, whose position depends on the charge e∗e^*e∗ of the tunneling particles, either electrons or fractionally charged quasiparticles. We show in a non-perturbative calculation for an exactly solvable point that the singularity at the quasiparticle frequency exists only in the limit of vanishing coupling, whereas the singularity at the electron frequency is present for all coupling strengths. The vanishing coupling limit corresponds to perfectly quantized Hall conductance in the case of quasiparticle tunneling between edge states in the fractional quantum Hall regime, and thus tunneling destroys the singularity at the quasiparticle frequency concomitantly with the quantized current.
We consider a one-channel coherent conductor with a good transmission embedded into an Ohmic environment, the impedance of which is equal to the quantum of resistance Rq=h/e2{R}_{q}=h/{e}^{2}Rq​=h/e2 below the RCRCRC frequency. This choice is motivated by the mapping of this problem to a Tomonaga-Luttinger liquid with one impurity, the interaction parameter of which corresponds to the specific value K=1/2K=1/2K=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 the finite-frequency differential conductance and the finite-frequency nonsymmetrized noise. Contrary to intuitive expectation, both can not 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 and/or with a fractional charge. We also show that the emission excess noise vanishes exactly above eVeVeV, 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 RCRCRC frequency, and they allow us to explore fully the quantum regime.
We study nonequilibrium noise in chiral Luttinger liquids using the Landauer-Buttiker scattering approach, obtaining the current and voltage noise spectrum for a four-terminal measurement scheme. Experimental consequences of the tunneling of charges are present in the four-terminal measurement of both the low-frequency shot noise (\ensuremath{\omega} near 0), and the high-frequency Josephson noise (\ensuremath{\omega} near ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$=e∗{\mathit{e}}^{\mathrm{*}}e∗V/\ensuremath{\Elzxh}). Within perturbation theory, an algebraic singularity is present at the Josephson frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$=e∗{\mathit{e}}^{\mathrm{*}}e∗V/\ensuremath{\Elzxh}, whose position depends on the charge e∗{\mathit{e}}^{\mathrm{*}}e∗ of the tunneling particles, either electrons or fractionally charged quasiparticles. These two types of tunneling are related by a strong-weak--coupling duality transformation. We show in a nonperturbative calculation for an exactly solvable point that the singularity at the quasiparticle frequency exists only in the limit of vanishing coupling, whereas the singularity at the electron frequency is present for all coupling strengths. The vanishing coupling limit corresponds to perfectly quantized Hall conductance in the case of quasiparticle tunneling between edge states in the fractional quantum Hall regime, and thus tunneling destroys the singularity at the quasiparticle frequency concomitantly with the quantized current. \textcopyright{} 1996 The American Physical Society.
We calculate the finite-frequency current noise of a nonequilibrium resonance-level quantum dot close to a dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a de-localized phase for weak dissipation and a localized phase for strong dissipation. The resonance-level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic boson bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. To compute the finite-frequency noise, we combine two recently developed Functional Renormalization Group (FRG) approaches in Refs.[17,22] and in Ref.[23]. The nonequilibrium current noise at zero-temperature and finite frequencies shows a singular dip in the de-localized phase for the magnitude of frequencies equal to the bias voltage; while the dip is smeared out as the system moves to the localized phase. The corresponding peak-to-dip crossover is found in the AC conductance for the magnitude of frequencies equal to the bias voltage. The relevance and applications of our results for the experiments and for tunnelings between Fractional Quantum Hall Edge (FQHE) states and chiral Luttinger liquids are discussed.
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 vF/gL, where vF 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 of the bulk excitations. We show that the frequencies needed to see interaction effects in the Fano factor are within experimental reach.