Minimal Excitation States of Electrons in One-Dimensional Wires

Abstract

A strategy is proposed to excite particles from a Fermi sea in a noise-free fashion by electromagnetic pulses with realistic parameters. We show that by using quantized pulses of simple form one can suppress the particle-hole pairs which are created by a generic excitation. The resulting many-body states are characterized by one or several particles excited above the Fermi surface accompanied by no disturbance below it. These excitations carry charge which is integer for noninteracting electron gas and fractional for Luttinger liquid. The operator algebra describing these excitations is derived, and a method of their detection which relies on noise measurement is proposed. Controlling single electrons is one of the main avenues of research in nanoelectronics. Once advanced far enough, it will bring about a range of quantum-coherent singleparticle sources with full control over the orbital and spin degrees of freedom. Currently efforts are mostly focused on employing localized electron states, trapped on metal islands [1] or quantum dots [2] and shuttled between the dots or islands by electric pulses [1,2] or acoustic fields [3]. It is of interest, however, to extend the concept of singleparticle sources to the situation when electrons propagate freely as part of a degenerate Fermi system. If proved feasible, it would allow one to harness particle dynamics, characterized by high Fermi velocity, v F 10 8 cm=s, to transmit quantum states in a solid and, at low temperature, to use Fermi-Dirac statistics for generating many-particle entangled states [4].In this Letter we propose a scheme which allows the creation of ''clean'' electric current pulses, free of particlehole excitations. We consider a 1d electron gas, serving as a prototype for carbon nanotube, quantum wire, and point contact systems, in which current is driven by voltage pulses with a typical frequency small compared to the Fermi energy. In this quasistationary regime the electric response is described as It g 0 Vt with g 0 e 2 =h the Landauer conductance. A current pulse, which carries total charge q g 0 R Vtdt, is a collective many-body state involving a number of fermions excited to a higher energy [5]. Microscopically, such a current pulse is described by a number of particle-hole excitations, with energies of the order @=, where is the duration of the pulse. As discussed in Refs. [5][6][7] and below, these excitations can be probed by noise measurement [8].Here we show that, quite strikingly, by engineering the pulse profile one can inhibit the particle-hole excitations. We analyze the particle-hole content of current pulses in a single-channel conductor, and pose and solve the problem of minimizing the number of such excitations. The condition required for the excitation number to be small is area quantization, R Vdt nh=e, where n is an integer. We show that such pulses, carrying integer charge q ne, are accompanied by fewer excitations than noninteger pulses. Also, we show how to optimize the Vt profile, by designing pulses which are totally free...

Dynamical control of interference using voltage pulses in the quantum regime

“…Note that contrary to the noise properties [13][14][15] , the total number of transmitted electrons is to a wide extent insensitive to the precise shape of the pulse.…”

“…However, each of its two sub terms spread over the entire band of the model, so one should refrain from calculating these two terms separately, if possible. Equation (14) has a nice straightforward interpretation: one simply sums over the (incoherent) incoming states and calculate their total transmission probabilities regardless of the final energy. In the absence of voltage pulse, the vanishing n t comes from the compensation between electrons coming from the left and from the right.…”

“…A voltage pulse will be said to be in the quantum regime when roughly " n % 1 electron is injected and the electronic temperature is smaller than the energy scales associated with the height V P and duration t P of the pulse ' =t P ð Þ. In a series of seminal works, Levitov and colleagues [12][13][14][15] studied the properties of pulses of Lorentzian shape. While they found a featureless time-dependent current, they predicted that, in contrast, the current noise could oscillate with the amplitude of the pulse, with the possibility to build noiseless quantum excitations for the particular Lorentzian shape.…”

Integer and fractional charge Lorentzian voltage pulses analyzed in the framework of photon-assisted shot noise

“…Here spin is disregarded for simplicity. The principle, proposed by Levitov et al in [14,15] uses voltage pulses V (t) applied to one contact. For a quantized action e ∞ −∞ V (t)dt = nh, n integer and h the Planck constant, exactly n charges are injected.…”

“…Injecting more than one electron requires a different practical approach which is the subject of this paper. We will consider the more general case of coherent trains of few undistinguishable electrons [14,15] which opens the way to entangle several quasi-particles but also to probe the full counting statistics [16] with a finite number of electrons [17]. The injection of single or of few electrons injected in a ballistic one dimensional conductor lets envisage to parallel the flying qubit approach developed for photons [18][19][20].…”