Biomedical subjects

C W J Beenakker

Publications and source records attributed to C W J Beenakker.

At least 19 recordsLinked to original sources

PubMed2006

Specular Andreev reflection in graphene.

By combining the Dirac equation of relativistic quantum mechanics with the Bogoliubov-de Gennes equation of superconductivity we investigate the electron-hole conversion at a normal-metal-superconductor interface in graphene. We find that the Andreev reflection of Dirac fermions has several unusual features: (1) the electron and hole occupy different valleys of the band structure; (2) at normal incidence the electron-hole conversion happens with unit efficiency in spite of the large mismatch in Fermi wavelengths at the two sides of the interface; and, most fundamentally: (3) away from normal incidence the reflection angle may be the same as the angle of incidence (retroreflection) or it may be inverted (specular reflection). Specular Andreev reflection dominates in weakly doped graphene, when the Fermi wavelength in the normal region is large compared to the superconducting coherence length.

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PubMed2006

Sub-Poissonian shot noise in graphene.

We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip of graphene (length L, width W, no impurities or defects) to obtain the conductance and shot noise as a function of Fermi energy. We find that the minimum conductivity of order e2/h at the Dirac point (when the electron and hole excitations are degenerate) is associated with a maximum of the Fano factor (the ratio of noise power and mean current). For short and wide graphene strips the Fano factor at the Dirac point equals 1/3, 3 times smaller than for a Poisson process. This is the same value as for a disordered metal, which is remarkable since the classical dynamics of the Dirac fermions is ballistic.

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PubMed2005

Emission of polarization-entangled microwave photons from a pair of quantum dots.

We describe a mechanism for the production of polarization-entangled microwaves using intraband transitions in a pair of quantum dots. This proposal relies neither on spin-orbit coupling nor on control over electron-electron interactions. The quantum correlation of microwave polarizations is obtained from orbital degrees of freedom in an external magnetic field. We calculate the concurrence of emitted microwave photon pairs and show that a maximally entangled Bell pair is obtained in the limit of weak interdot coupling.

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PubMed2005

Optimal spin-entangled electron-hole pair pump.

A nonperturbative theory is presented for the creation by an oscillating potential of spin-entangled electron-hole pairs in the Fermi sea. In the weak potential limit, considered earlier by Samuelsson and Büttiker, the entanglement production is much less than 1 bit per cycle. We demonstrate that a strong potential oscillation can produce an average of one Bell pair per two cycles, making it an efficient source of entangled flying qubits.

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PubMed2004

Exponential sensitivity to dephasing of electrical conduction through a quantum dot.

According to random-matrix theory, interference effects in the conductance of a ballistic chaotic quantum dot should vanish proportional to (tau(phi)/tau(D))(p) when the dephasing time tau(phi) becomes small compared to the mean dwell time tau(D). Aleiner and Larkin have predicted that the power law crosses over to an exponential suppression proportional to exp((-tau(E)/tau(phi)) when tau(phi) drops below the Ehrenfest time tau(E). We report the first observation of this crossover in a computer simulation of universal conductance fluctuations. Their theory also predicts an exponential suppression proportional to exp((-tau(E)/tau(D)) in the absence of dephasing--which is not observed. We show that the effective random-matrix theory proposed previously for quantum dots without dephasing explains both observations.

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PubMed2004

Antibunched photons emitted by a quantum point contact out of equilibrium.

Motivated by the experimental search for "GHz nonclassical light," we identify the conditions under which current fluctuations in a narrow constriction generate sub-Poissonian radiation. Antibunched electrons generically produce bunched photons, because the same photon mode can be populated by electrons decaying independently from a range of initial energies. Photon antibunching becomes possible at frequencies close to the applied voltage V x e/variant Planck's over 2pi, when the initial energy range of a decaying electron is restricted. The condition for photon antibunching in a narrow frequency interval below eV/variant Planck's over 2pi reads [SigmanTn(1-Tn)]2<2Sigman[Tn(1-Tn)]2, with Tn an eigenvalue of the transmission matrix. This condition is satisfied in a quantum point contact, where only a single Tn differs from 0 or 1. The photon statistics is then a superposition of binomial distributions.

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PubMed2004

Charge detection enables free-electron quantum computation.

It is known that a quantum computer operating on electron-spin qubits with single-electron Hamiltonians and assisted by single-spin measurements can be simulated efficiently on a classical computer. We show that the exponential speedup of quantum algorithms is restored if single-charge measurements are added. These enable the construction of a CNOT (controlled NOT) gate for free fermions, using only beam splitters and spin rotations. The gate is nearly deterministic if the charge detector counts the number of electrons in a mode, and fully deterministic if it only measures the parity of that number.

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PubMed2004

Quantum teleportation by particle-hole annihilation in the Fermi sea.

We point out that the mutual annihilation of an electron-hole pair at a tunnel barrier leads to teleportation of the state of the annihilated electron to a second, distant electron--if the latter was previously entangled with the annihilated hole. We propose an experiment, involving low-frequency noise measurements on a two-dimensional electron gas in a high magnetic field, to detect teleportation of electrons and holes in the two lowest Landau levels.

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PubMed2003

Proposal for production and detection of entangled electron-hole pairs in a degenerate electron gas.

We demonstrate theoretically that the shot noise produced by a tunnel barrier in a two-channel conductor violates a Bell inequality. The nonlocality is shown to originate from entangled electron-hole pairs created by tunneling events-without requiring electron-electron interactions. The degree of entanglement (concurrence) equals 2(T1T2)(1/2)(T1+T2)(-1), with T1,T2<<1 the transmission eigenvalues. A pair of edge channels in the quantum Hall effect is proposed as an experimental realization.

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PubMed2003

Distribution of voltage fluctuations in a current-biased conductor.

We calculate the fluctuating voltage V(t) over a conductor driven out of equilibrium by a current source. This is the dual of the shot noise problem of current fluctuations I(t) in a voltage-biased circuit. In the single-channel case the distribution of the accumulated phase Phi=(e/ variant Planck's over 2pi ) integral Vdt is the Pascal (or binomial waiting-time) distribution-distinct from the binomial distribution of transferred charge Q= integral Idt. The weak-coupling limit of a Poissonian P(Phi) is reached in the limit of a ballistic conductor, while in the tunneling limit P(Phi) has the chi-square form.

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PubMed2003

Quantum Andreev map: a paradigm of quantum chaos in superconductivity.

We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations. We have observed the universal distribution of the excitation gap for a large Lyapunov exponent and the logarithmic reduction of the gap when the Ehrenfest time becomes comparable to the quasiparticle dwell time.

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PubMed2003

Temperature-dependent third cumulant of tunneling noise.

Poisson statistics predicts that the shot noise in a tunnel junction has a temperature independent third cumulant e(2)I, determined solely by the mean current I. Experimental data, however, show a puzzling temperature dependence. We demonstrate theoretically that the third cumulant becomes strongly temperature dependent and may even change sign as a result of feedback from the electromagnetic environment. In the limit of a noninvasive (zero-impedance) measurement circuit in thermal equilibrium with the junction, we find that the third cumulant crosses over from e(2)I at low temperatures to -e(2)I at high temperatures.

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PubMed2003

Adiabatic quantization of Andreev quantum billiard levels.

We identify the time T between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent lambda), coupled to a superconductor by an N-mode constriction. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods T(n), which in turn generate a ladder of excited states epsilon (nm)=(m+1/2)pi(h) /T(n). The largest quantized period is the Ehrenfest time T(0)=lambda(-1)ln(N). Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension W/sqrt[N], much below the width W of the constriction.

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PubMed2003

Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics.

We reexamine the problem of the "Loschmidt echo," that measures the sensitivity to perturbation of quantum-chaotic dynamics. The overlap squared M(t) of two wave packets evolving under slightly different Hamiltonian is shown to have the double-exponential initial decay proportional to exp(-constant x e(2lambda(0)t)) in the main part of the phase space. The coefficient lambda(0) is the self-averaging Lyapunov exponent. The average decay (-)M proportional to e(-lambda(1)t) is single exponential with a different coefficient lambda(1). The volume of phase space that contributes to (-)M vanishes in the classical limit variant Planck-->0 for times less than the Ehrenfest time tau(E)=1/2lambda0(-1)|ln Planck|. It is only after the Ehrenfest time that the average decay is representative for a typical initial condition.

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PubMed2002

Ehrenfest-time-dependent excitation gap in a chaotic Andreev billiard.

A semiclassical theory is developed for the appearance of an excitation gap in a ballistic chaotic cavity connected by a point contact to a superconductor. Diffraction at the point contact is a singular perturbation in the limit variant Planck's over 2pi -->0, which opens up a gap E(gap) in the excitation spectrum. The time scale variant Planck's over 2pi /E(gap) proportional, variant alpha(-1)ln( variant Planck's over 2pi (with alpha the Lyapunov exponent) is the Ehrenfest time, the characteristic time scale of quantum chaos.

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PubMed2002

Decay of the Loschmidt echo for quantum states with sub-planck-scale structures.

Quantum states extended over a large volume in phase space have oscillations from quantum interferences in their Wigner distribution on scales smaller than variant Planck's over 2pi [W. H. Zurek, Nature (London) 412, 712 (2001)]]. We investigate the influence of those sub-Planck-scale structures on the sensitivity to an external perturbation of the state's time evolution. While we do find an accelerated decay of the Loschmidt Echo for an extended state in comparison to a localized wave packet, the acceleration is described entirely by the classical Lyapunov exponent and hence cannot originate from quantum interference.

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PubMed2002

Quantum optical communication rates through an amplifying random medium.

We study the competing effects of stimulated and spontaneous emission on the information capacity of an amplifying disordered waveguide. At the laser threshold the capacity reaches a "universal" limit, independent of the degree of disorder. Whether or not this limit is larger or smaller than the capacity without amplification depends on the disorder, as well as on the input power. Explicit expressions are obtained for heterodyne detection of coherent states, and generalized for an arbitrary detection scheme.

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PubMed2002

Electromechanical noise in a diffusive conductor.

Electrons moving in a conductor can transfer momentum to the lattice via collisions with impurities and boundaries, giving rise to a fluctuating mechanical stress tensor. The root-mean-squared momentum transfer per scattering event in a disordered metal (of dimension L greater than the mean-free path l and screening length xi) is found to be reduced below the Fermi momentum by a factor of order l/L for shear fluctuations and (xi/L)(2) for pressure fluctuations. The excitation of an elastic bending mode by the shear fluctuations is estimated to fall within current experimental sensitivity for a nanomechanical oscillator.

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