Abstract
Recent developments in the coherent manipulation of electrons in ballistic conductors include the generation of time-periodic electrical currents involving one to few electronic excitations per period. However, using individual electrons as carrier of quantum information for flying qubit computation or quantum metrology applications calls for a general method to unravel the single-particle excitations embedded in a quantum electrical current and how quantum information is encoded within it. Here, we propose a general signal processing algorithm to extract the elementary single-particle states, called electronic atoms of signal, present in any periodic quantum electrical current. These excitations and their mutual quantum coherence describe the excess single-electron coherence in the same way musical notes and score describe a sound signal emitted by a music instrument. This method, which is the first step towards the development of signal processing of quantum electrical currents is illustrated by assessing the quality of experimentally relevant single electron sources. The example of randomized quantum electrical currents obtained by regularly clocked but randomly injected unit charge Lorentzian voltage pulses enables us to discuss how interplay of the coherence of the applied voltage and of the Pauli principle alter the quantum coherence between the emitted single particle excitations.
Highlights
These recent years have seen a spectacular breakthrough in the manipulation of quantum electric circuits
We introduce a representation of the singleelectron coherence of a periodic electron source in terms of perfectly distinguishable normalized single-particle wave functions associated with each period, which we call “electronic atoms of signals” [29]
This description, which is the counterpart of the Karhunen-Loève decomposition for classical signals [75], enables us to obtain a simple description of the single-particle content emitted by the source in discrete terms
Summary
These recent years have seen a spectacular breakthrough in the manipulation of quantum electric circuits. This, leaves open the question of decoding classical or quantum information encoded within quantum electrical currents This requires finding appropriate representations of electronic coherences. We show in full generality that such a description exists: any excess time-periodic single-electron coherence admits a minimal description in terms of quasiperiodic single-electron and single-hole excitations, which are the time-domain counterparts of Bloch waves in solid-state physics [36]. Whenever interactions can be neglected, this description can be used to describe the full many-body state of the electron fluid and, to access many-particle quantities such as the electron-hole entanglement entropies This connection can be made explicit using time-periodic single-particle scattering theory and has been used to obtain the full counting statistics of single-particle excitations [44].
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