Minimal States of Fermionic Excitations : the n-electron Levitov source

Christian Glattli

Nanoelectronics group, SPEC, CEA Saclay

Mon, Apr. 02nd 2012, 14:00

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

Manipulating few degrees of freedom in a quantum systems has always lead to better understanding of quantum systems and eventually to practical applications of quantum effects. This is what we have learned from the history of the field of quantum optics, atomic physics and more recently from condensed matter with qubit implementation in superconducting circuits or spins in quantum dots. par Here we adress the question : can we manipulate few electronic excitations on top of the Fermi sea of a quantum conductor? Thanks to the advance in the realization of clean ballistic one-dimensional like conductors where electronic beam-splitters and interferometers are available, the controlled injection of one or few charges in a conductor may lead to new type of quantum experiments with fermions and eventually to
quantum information processing. par The answer to the previous question is not obvious as it is believed that any spatial or time localized perturbation of the Fermi sea leads to collective excitations involving a log divergent number of electron-hole pairs [1]. Also for delocalized electrons in a Fermi sea, we do not expect to observe manifestations of the charge quantization as in the case of isolated systems such as metallic islands, quantum dots or Millikan oil droplets. par We will discuss a simple way to circumvent these problems following the seventeen years old theoretical observation by Levitov et al [2] that clean electron excitations free of holes excitations can be simply realized by applying Lorentzian shape voltage pulses on the contact of a one-dimensional conductor. The mathematical analytical property of the time dependent phase acquired by all electrons of the Fermi sea leads to an upward shift in energy (or momentum) of the Fermi sea which completely washes out the hole creation. The complete effect occurs for pulses carrying exactly an integer number of charges, which thus generate minimal excitation states of n electrons, while for non-integer charges spurious electron-hole excitation reappear. Finally we will present preliminary on-going experiments based on current noise, a measurement sensitive to the
total number of excitations of the Fermi sea [3]. par All these concepts seem generalizable to 1D interacting Fermion such as Luttinger Liquids, FQHE, where the elementary charge excitation can be fractional [4]. \ \ {[1]} Orthogonality catastrophe in a mesoscopic conductor due to a time dependent flux, H. Lee and L. Levitov arXiv:cond-mat/9312013v1 (1993). \ {[2]} Electron counting statistics and coherent states of the electric current, L. Levitov; H. Lee and G. Lesovik, J. Math. Phys. 37, 4845 (1996). \ {[3]} J. Dubois et al in prepartion. \ {[4]} Minimal excitation states of electrons in one-dimensional wires, J. Keeling, I. Klich, and L. Levitov, Phys. Rev. Letters 97, 116403 (2006).

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