arXiv subjects

Thierry Martin

Publications and source records attributed to Thierry Martin.

72 records · Page 4Linked to original sources

arXiv2005

Noise in mesoscopic physics

This is a course on noise which covers some of the scattering theory for normal metals, Hanbury Brown and Twiss analogs for noise correlations with electrons, noise correlations in superconducting/normal metal junctions. Entanglement in such NS systems is described with a criterion for violating Bell inegalities. The last section is devoted to the perturbative derivation of noise in a particular one dimensional correlated electron system (Luttinger liquid): edge states in the fractional quantum Hall effect, where the comparison of the quasiparticle tunneling current and noise allow to identidy the fractional charge of quasiparticles.

cond-mat.mes-hall↗

arXiv2004

Electron injection in a nanotube with leads: finite frequency noise-correlations and anomalous charges

The non-equilibrium transport properties of a carbon nanotube which is connected to Fermi liquid leads, where electrons are injected in the bulk, are computed. A previous work which considered an infinite nanotube showed that the zero frequency noise correlations, measured at opposite ends of the nanotube, could be used to extract the anomalous charges of the chiral excitations which propagate in the nanotube. Here, the presence of the leads have the effect that such-noise cross-correlations vanish at zero frequency. Nevertheless, information concerning the anomalous charges can be recovered when considering the spectral density of noise correlations at finite frequencies, which is computed perturbatively in the tunneling amplitude. The spectrum of the noise cross-correlations is shown to depend crucially on the ratio of the time of flight of quasiparticles traveling in the nanotube to the ``voltage'' time which defines the width of the quasiparticle wave-packets injected when an electron tunnels. Potential applications toward the measurement of such anomalous charges in non-chiral Luttinger liquids (nanotubes or semiconductor quantum wires) are discussed.

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arXiv2004

Electron backscattering from dynamical impurities in a Luttinger liquid

Electron backscattering in a Luttinger liquid with an impurity is investigated in the presence of zero point motion of the phonon lattice. The impurity can mean either a mass defect, an elastic defect or a pinning defect. The phonon spectrum is then affected by the presence of the defect, which enters in the renormalization group equations for backscattering. The RG equation becomes dependent on the energy cutoff for finite Debye frequency $ω_D$ giving rise to finite energy effects. We compute the local density of states and show how the renormalization group flow is affected by a finite $ω_D$.

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arXiv2004

Realistic operation of an entangler : a density matrix approach

The detailed operation of an electron spin entangler is studied, using density matrix equations. The device is made of a superconductor, two quantum dots and two normal leads. The treatment takes into account coherent tunneling in a non-perturbative way, and analyzes the various parasitic effects, in addition to the main process (crossed Andreev reflection) : those include singlet pairs passing through a single dot, or cotunneling between dots through the superconductor. The optimum operation of the device is characterized.

cond-mat.mes-hall↗

arXiv2004

Quantum master equations for the superconductor--dot entangler

The operation of a source of entangled electron spins, based on a superconductor and two quantum dots in parallel\cite{loss}, is described in detail with the help of quantum master equations. These are derived including the main parasitic processes in a fully consistent and non-perturbative way, starting from a microscopic Hamiltonian. The average current is calculated, including the contribution of entangled and non-entangled pairs. The constraints on the operation of the device are illustrated by a calculation of the various charge state probabilities.

cond-mat.mes-hall↗

arXiv2003

Electron spin teleportation current through a quantum dot array operating in the stationary regime

An electron spin state teleportation scheme is described in detail. It is based on the protocol by Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)], and involves the production and detection by superconductors of entangled pairs of electrons. Quantum dots filter individual electron transitions, and the whole teleportation sequence is selected in a five-dot cell by electrostatic gating in the stationary regime (no time dependent gate voltages): i) a normal dot carry the electron spin state to be teleported, two others carry the ancillary entangled pair; ii) two superconducting dots, coupled by a superconducting circuit, control the injection of the source electron and the detection of the teleported electron. This teleportation cell is coupled to emitter and receiver reservoirs. In a steady state, a spin-conserving current flows between the reservoirs, most exclusively carried by the teleportation channel. This current is perfectly correlated to a Cooper pair current flowing in the superconducting circuit, and which triggers detection of the teleported electron. This latter current indeed carries the classical information, which is necessary to achieve teleportation. The average teleportation current is calculated using the Bloch equations, for weakly coupled spin reservoirs. A diagnosis of teleportation is proposed using noise correlations.

cond-mat.mes-hall↗

arXiv2002

Bell inequalities and entanglement in solid state devices

Bell-inequality checks constitute a probe of entanglement -- given a source of entangled particles, their violation are a signature of the non-local nature of quantum mechanics. Here, we study a solid state device producing pairs of entangled electrons, a superconductor emitting Cooper pairs properly split into the two arms of a normal-metallic fork with the help of appropriate filters. We formulate Bell-type inequalities in terms of current-current cross-correlators, the natural quantities measured in mesoscopic physics; their violation provides evidence that this device indeed is a source of entangled electrons.

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arXiv2001

Electronic Entanglement in the Vicinity of a Superconductor

A weakly biased normal-metal-superconductor junction is considered as a potential device injecting entangled pairs of quasi-particles into a normal-metal lead. The two-particle states arise from Cooper pairs decaying into the normal lead and are characterized by entangled spin- and orbital degrees of freedom. The separation of the entangled quasi-particles is achieved with a fork geometry and normal leads containing spin- or energy-selective filters. Measuring the current-current cross-correlator between the two normal leads allows to probe the efficiency of the entanglement.

cond-mat.mes-hall↗

arXiv2001

Tunable decoherence in the vicinity of a normal metal-superconducting junction

The decoherence rate of a quantum dot coupled to a fluctuating environment described by a normal-metal superconductor junction is considered. The density-density correlator at low frequencies constitutes the kernel which enters the calculation of the phase coherence time. The density fluctuations are connected to the finite frequency current-current correlations in the point contact via the continuity equation. Below and above the gap, at zero temperature the density correlator contains spatial oscillations at half of the Fermi wave length on the normal side. As the bias crosses the superconducting gap, the opening of new scattering channels enhances the decoherence rate dramatically, suggesting the possibility of tuning the decoherence rate in a controllable manner.

cond-mat.mes-hall↗

arXiv2000

Effective charges and statistical signatures in the noise of normal metal--superconductor junctions at arbitrary bias

Shot noise is studied in a single normal metal-superconductor (N-S) junction at finite frequency, and for branched N-S junctions at zero frequency. The noise spectral density displays a singularity at the Josephson frequency ($ω= 2eV/\hbar$) when the applied bias is smaller than gap of the superconductor. Yet, in the limit $eV\gg Δ$, quasiparticle contributions yield a singularity at $ω= eV/\hbar$ analogous to that of a normal metal. The crossover between these two regimes shows new structures in the noise characteristic, pointing out the failure of the effective charge model. As an alternative to a finite frequency measurement, if a sinusoidal external field is superposed to the constant bias (non stationary Aharonov--Bohm effect), the second derivative of the zero frequency noise with respect to the voltage exhibits peaks when the frequency of the perturbation is commensurate with the Josephson frequency. Finally, the statistical aspects of noise are studied with an analog of the Hanbury-Brown and Twiss experiment for fermions: a superconductor connected to two normal leads. Noise correlations are found to be either negative (fermionic) or positive (bosonic), due to the presence of evanescent Cooper pairs in the normal side of the junction, in the latter case.

cond-mat.mes-hall↗

arXiv1999

Positive and negative Hanbury-Brown and Twiss correlations in normal metal-superconducting devices

In the light of the recent analogs of the Hanbury--Brown and Twiss experiments in mesoscopic beam splitters, negative current noise correlations are recalled to be the consequence of an exclusion principle. Here, positive (bosonic) correlations are shown to exist in a fermionic system, composed of a superconductor connected to two normal reservoirs. In the Andreev regime, the correlations can either be positive or negative depending on the reflection coefficient of the beam splitter. For biases beyond the gap, the transmission of quasiparticles favors fermionic correlations. The presence of disorder enhances positive noise correlations. Potential experimental applications are discussed.

cond-mat.mes-hall↗

arXiv1999

Josephson Frequency Singularity in the Noise of Normal Metal-Superconductor Junctions

A singularity at the Josephson frequency in the noise spectral density of a disordered normal metal -- superconductor junction is predicted for bias voltages below the superconducting gap. The non-stationary Aharonov-Bohm effect, recently introduced for normal metals, is proposed as a tool for detecting this singularity. In the presence of a harmonic external field, the derivative of the noise with respect to the voltage bias reveals jumps when the applied frequency is commensurate with the Josephson frequency associated with this bias. The height of these jumps is non-monotonic in the amplitude of the periodic field. The superconducting flux quantum enters this dependence. Additional singularities in the frequency dependent noise are predicted above gap.

cond-mat.mes-hall↗

arXiv1998

Conductance and Shot Noise for Particles with Exclusion Statistics

The first quantized Landauer approach to conductance and noise is generalized to particles obeying exclusion statistics. We derive an explicit formula for the crossover between the shot and thermal noise limits and argue that such a crossover can be used to determine experimentally whether charge carriers in FQHE devices obey exclusion statistics.

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arXiv1994

Switching Nano-Device based on Rabi Oscillations

We consider a potential landscape composed of a well region separated from a "free" region by a barrier, such that one bound state and one quasi level exist in the well. A particle initially in the ground state can be activated to the quasi level by application of a micro wave field, and subsequently tunnel in the free region. The wave function is then emitted by "bursts" after each Rabi oscillation is completed, and the leakage current can be controlled by varying the amplitude of the external field, the barrier height/width, and the frequency mismatch.

cond-mat↗

arXiv1994

Gauge invariance and wave packet simulations in the presence of dipole fields

A method for performing wave packet simulations in dipole fields is presented. Starting from a Hamiltonian with non commuting terms, a gauge transformation leads to a new Hamiltonian which allows to calculate explicitly the evolution operator. In this new gauge, the dipole field is fully included in the {\it vector} potential. The method of Goldberg, Schwartz and Schey based on the Caley form of the evolution operator is then generalized, and the resulting scheme is applied to describe a switching device based on Rabi oscillations. The probability to tunnel in the free region exhibits a plateaux structure as the wave function is emitted by ``bursts'' after each Rabi oscillation has been completed.

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arXiv1994

Wentzel-Bardeen singularity in coupled Luttinger liquids: transport properties

The recent progress on 1 D interacting electrons systems and their applications to study the transport properties of quasi one dimensional wires is reviewed. We focus on strongly correlated electrons coupled to low energy acoustic phonons in one dimension. The Wentzel--Bardeen singularity suppresses antiferromagnetic fluctuations and pushes the system toward the metallic phase via an intermediate, metallic phase. The implications of this phenomenon on the transport properties of an ideal wire as well as the properties of a wire with weak or strong scattering are analyzed in a perturbative renormalization group calculation. This allows to recover the three regimes predicted from the divergence criteria of the response functions.

cond-mat↗

arXiv1994

Wentzel-Bardeen singularity and phase diagram for interacting electrons coupled to acoustic phonons in one dimension

Using a Luttinger liquid description, the correlation function exponents of various response functions are calculated. Their striking sensitivity to the non perturbative Wentzel-Bardeen singularity is discussed. For the Hubbard model coupled to phonons, the equivalent of a phase diagram is established. By increasing the filling factor towards half filling, the Wentzel-Bardeen singularity is rapidly approached. This suppresses antiferromagnetic fluctuations and drives the system in a metallic phase, and ultimately in the triplet superconducting regime.

cond-mat↗

arXiv1994

Phase Diagram for a Luttinger Liquid coupled to Phonons in one dimension

The Green function and the ordering correlation functions of a system of electrons coupled to acoustic phonons are calculated explicitly. The sensitivity of the correlation function exponents to the Wentzel-Bardeen singularity is discussed. A phase diagram is established for the Hubbard model coupled to phonons, using the integral equations of Lieb and Wu. By increasing the filling factor towards half filling, the Wentzel-Bardeen singularity can be reached for arbitrary phonon coupling. This suppresses antiferromagnetic fluctuations and drives the system in a metallic phase, and ultimately in the triplet superconducting regime.

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