Quantum tomography of electrical currents

Abstract

In quantum nanoelectronics, time-dependent electrical currents are built from few elementary excitations emitted with well-defined wavefunctions. However, despite the realization of sources generating quantized numbers of excitations, and despite the development of the theoretical framework of time-dependent quantum electronics, extracting electron and hole wavefunctions from electrical currents has so far remained out of reach, both at the theoretical and experimental levels. In this work, we demonstrate a quantum tomography protocol which extracts the generated electron and hole wavefunctions and their emission probabilities from any electrical current. It combines two-particle interferometry with signal processing. Using our technique, we extract the wavefunctions generated by trains of Lorentzian pulses carrying one or two electrons. By demonstrating the synthesis and complete characterization of electronic wavefunctions in conductors, this work offers perspectives for quantum information processing with electrical currents and for investigating basic quantum physics in many-body systems.

Time-energy filtering of single electrons in ballistic waveguides

“…To see this, we consider a gate voltage V(t) that is the sum of a linear part a + V t 0 , as in the experiment of [40], and an additional perturbation ¢( ) V t . This scenario is discussed theoretically at the end of section 3.2, see equations (33) and (34). Analogously to equation (51), the modified Wigner function corresponding to the perturbation ¢( ) V t only, can be expressed as…”

“…However, most of the existing electron quantum optics experiments have focused on single-electron sources that emit electrons close to the Fermi sea [3,31]. These excitations can be accessed by perturbing the Fermi sea through the application of periodic gate potentials allowing for quantum state reconstruction through correlation measurements between the unknown and the reference signal [32][33][34]. Such an approach is not possible in the case of 'high-energy' electrons [19,[35][36][37][38][39] emitted far above (tens of meV) the Fermi sea, because they do not overlap with perturbations around the Fermi energy.…”

Spatial and energy resolution of electronic states by shot noise

“…(1) is the essence of the local noise spectroscopy we develop here. Analogous expressions, already contained in the pioneering theory of the local noise probe [26], were later derived for the auto-correlation noise [36] and cross-correlation noise [37] in nonequilibrium Tomonaga-Luttinger liquids for studies of an AC-biased TJ [20], used for quantum tomography purposes [24] and for semiconducting nanowire-based local noise sensors [38,39]. For nonequilibrium f (ε) with possibly many steplike features, each step is associated with the change of the slope in the S I (V ) dependence.…”

“…Recently, shot noise was utilized to study electronic wave functions emitted by the time-dependent currents in a phasecoherent conductor [23,24]. Essentially, the implemented to-mographic approach uses antibunching of fermions due to Pauli principle in the geometry of a beam splitter.…”

Spectral properties of interacting helical channels driven by Lorentzian pulses

“…Indeed, it has been measured that these voltage pulses, called Levitons, produce zero excess noise, equivalent to the absence of extra electron-hole pairs [21,49]. Levitons are currently on the spotlight in EQO and an intense research activity dealing with their peculiar properties is being carried out [66][67][68][69][70][71][72][73][74][75][76][77][78][79].…”