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physica status solidi (b)

Electron and electron–hole excitations in a driven Fermi sea

Mihajlo Vanević A, Yuli V. Nazarov, Wolfgang Belzig

Published Dec 28, 2016• 7 citations
Publisher

Abstract

Abstract We study the response of a degenerate Fermi sea to a time‐dependent perturbation. We find that elementary excitations in the Fermi sea are electrons and electron–hole quasiparticle pairs whose number and probability of creation depend on amplitude and shape of the drive. The excitations can be probed in a driven quantum contact at low temperature. While electronic excitations are associated to the dc voltage offset and determine the average current, the electron–hole pairs are created by the ac voltage component and give rise to the excess current noise power in a junction. We also obtain the many‐body state created by the drive. The constituent quasiparticle states can be probed by a Hong–Ou–Mandel type of correlation experiment where electrons emitted from the terminals with a relative time delay collide at the contact. The current noise power in the junction is directly related to the wave packet overlap at the contact. This is confirmed in recent experiments, demonstrating an unprecedented degree of control of elementary excitations in a coherent mesoscopic junction.

DOI
10.1002/pssb.201600551

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Abstract We study the response of a degenerate Fermi sea to a time‐dependent perturbation. We find that elementary excitations in the Fermi sea are electrons and electron–hole quasiparticle pairs whose number and probability of creation depend on amplitude and shape of the drive. The excitations can be probed in a driven quantum contact at low temperature. While electronic excitations are associated to the dc voltage offset and determine the average current, the electron–hole pairs are created by the ac voltage component and give rise to the excess current noise power in a junction. We also obtain the many‐body state created by the drive. The constituent quasiparticle states can be probed by a Hong–Ou–Mandel type of correlation experiment where electrons emitted from the terminals with a relative time delay collide at the contact. The current noise power in the junction is directly related to the wave packet overlap at the contact. This is confirmed in recent experiments, demonstrating an unprecedented degree of control of elementary excitations in a coherent mesoscopic junction.
We study the many-body electronic state created by a time-dependent drive of a mesoscopic contact. The many-body state is expressed manifestly in terms of single-electron and electron-hole quasiparticle excitations with the amplitudes and probabilities of creation which depend on the details of the applied voltage. We experimentally probe the time dependence of the constituent electronic states by using an analog of the optical Hong-Ou-Mandel correlation experiment where electrons emitted from the terminals with a relative time delay collide at the contact. The electron wave packet overlap is directly related to the current noise power in the contact. We have confirmed the time dependence of the electronic states predicted theoretically by measurements of the current noise power in a tunnel junction under harmonic excitation.
We study the motion of a particle in a degenerate Fermi sea in one dimension by calculating numerically the one-particle spectral function as well as a number of two-particle response functions. The problem is formulated in terms of the eigenstates of the static case, in which the particle is localized at a particular site. In spite of the Anderson orthogonality catastrophe, accurate results for small systems (up to 100 sites and electrons) are obtained with relatively few basis states, i.e., 0 and 1 particle-hole pair excitations. The mobile particle in one dimension does not display ``quasiparticle'' behavior, and most response functions show power-law threshold behavior as in the case of a localized particle, in complete agreement with exact results. We discuss practical applications to optical spectra and to the dynamical mobility of optically generated holes in doped semiconductor quantum wires.
Building on a previous proposal for the entanglement of electron-hole pairs in the Fermi sea, we show how three qubits can be entangled without using electron-electron interactions. As in the two-qubit case, this electronic scheme works even if the sources are in (local) thermal equilibrium---in contrast to the photonic analog. The three qubits are represented by four edge-channel excitations in the quantum Hall effect (two hole excitations plus two electron excitations with identical channel index). The entangler consists of an adiabatic point contact flanked by a pair of tunneling point contacts. The irreducible three-qubit entanglement is characterized by the tangle, which is expressed in terms of the transmission matrices of the tunneling point contacts. The maximally entangled Greenberger-Horne-Zeilinger (GHZ) state is obtained for channel-independent tunnel probabilities. We show how low-frequency noise measurements can be used to determine an upper and lower bound to the tangle. The bounds become tighter the closer the electron-hole state is to the GHZ state.
Abstract Theory predicts that electrons emitted from independent electron sources (metallic contacts) can nevertheless interfere. This interference is manifest in an exchange contribution to the shot noise correlation of currents at different contacts of a mesoscopic conductor. A geometry has been proposed in which second order (single particle) interference due to superposition of amplitudes is absent but fourth order (two‐particle) interference exhibits Aharonov‐Bohm oscillations. Recently such a geometry has been realized in an experiment and the theoretically predicted two‐particle Aharonov‐Bohm effect has been detected. We discuss Bell measurements and quantum state tomography using shot noise correlations. We discuss in addition structures in which two‐particle interference effects are generated dynamically by varying electrostatic potentials with the help of gates or by generating electron‐hole pairs by irradiating contacts of a mesoscopic conductor. These examples emphasize that two‐particle processes are not related to a particular geometry but are a general feature of multiparticle observables like shot noise correlations.
Levitons are minimal-excitation electronic wave packets generated by Lorentzian voltage pulses and constitute a central resource for electron quantum optics. Their creation and defining properties are usually formulated in continuum scattering descriptions, whereas many candidate platforms for integrated electronic quantum circuits are finite, discrete, and strongly shaped by lattice dispersion. We study leviton generation in finite one-dimensional tight-binding chains of non-interacting fermions driven by time-dependent voltage pulses. Using the single-particle density matrix, we resolve the excitation above the initial Fermi sea and quantify its quality through the average excitation number and its fluctuations. We find that clean leviton-like states emerge only in an intermediate regime where the pulse is slow enough to be resolved by the dynamics on the lattice, but not so slow that truncation and finite-size effects distort the Lorentzian profile in the time domain. Lorentzian pulses (even if truncated) systematically outperform non-Lorentzian pulse shapes in approaching the low-noise limit with increasing system size. We further identify finite-lattice signatures associated with band filling, pulse amplitude, linear voltage-drop geometry, and residual deviations from the continuum integer-charge condition. These results establish a microscopic framework for understanding leviton formation beyond the ideal continuum limit and for evaluating lattice-based platforms for coherent few-electron transport.
The standard entanglement test using the Clauser-Horne-Shimony-Holt inequality is known to fail in mesoscopic junctions at finite temperatures. Since this is due to the bidirectional particle flow, a similar failure is expected to occur in an ac-driven contact. We develop a continuous-variable entanglement test suitable for electrons and holes that are created by the ac drive. At low enough temperatures the generalized Bell inequality is violated in junctions with low conductance or a small number of transport channels and with ac voltages which create few electron-hole pairs per cycle. Our ac-entanglement test depends on the total number of electron-hole pairs and on the distribution of probabilities of pair creations similar to the Fano factor.