Abstract
Quantum dynamics is very sensitive to dimensionality. While two-dimensional electronic systems form Fermi liquids, one-dimensional systems—Tomonaga–Luttinger liquids—are described by purely bosonic excitations, even though they are initially made of fermions. With the advent of coherent single-electron sources, the quantum dynamics of such a liquid is now accessible at the single-electron level. Here, we report on time-of-flight measurements of ultrashort few-electron charge pulses injected into a quasi one-dimensional quantum conductor. By changing the confinement potential we can tune the system from the one-dimensional Tomonaga–Luttinger liquid limit to the multi-channel Fermi liquid and show that the plasmon velocity can be varied over almost an order of magnitude. These results are in quantitative agreement with a parameter-free theory and demonstrate a powerful probe for directly investigating real-time dynamics of fractionalisation phenomena in low-dimensional conductors.
Highlights
Quantum dynamics is very sensitive to dimensionality
The reduced dimensionality influences the interaction between particles and can lead to fascinating phenomena such as spin–charge separation[3], charge fractionalisation[4] or Wigner crystallisation[5]
The low-energy collective bosonic excitations consist of charge and spin density waves that propagate at two different velocities
Summary
Quantum dynamics is very sensitive to dimensionality. While two-dimensional electronic systems form Fermi liquids, one-dimensional systems—Tomonaga–Luttinger liquids—are described by purely bosonic excitations, even though they are initially made of fermions. By changing the confinement potential we can tune the system from the onedimensional Tomonaga–Luttinger liquid limit to the multi-channel Fermi liquid and show that the plasmon velocity can be varied over almost an order of magnitude These results are in quantitative agreement with a parameter-free theory and demonstrate a powerful probe for directly investigating real-time dynamics of fractionalisation phenomena in low-dimensional conductors. In an ultrafast quantum nanoelectronics setup, the experimentalist controls the—bosonic—electromagnetic degrees of the system and aims at injecting a single—fermionic—coherent electron in the system This interplay between bosonic and fermionic statistics is a central feature in one-dimensional quantum systems as it provides a unique playground for the study of interaction effects[1,2]. We show that our self-consistent calculations capture well the results of the measurements, validating the construction of the bosonic collective modes from the fermionic degrees of freedom
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