Abstract
Strongly correlated low-dimensional systems can host exotic elementary excitations carrying a fractional charge q and potentially obeying anyonic statistics. In the fractional quantum Hall effect, their fractional charge has been successfully determined owing to low frequency shot noise measurements. However, a universal method for sensing them unambiguously and unraveling their intricate dynamics was still lacking. Here, we demonstrate that this can be achieved by measuring the microwave photons emitted by such excitations when they are transferred through a potential barrier biased with a dc voltage Vdc. We observe that only photons at frequencies f below qVdc/h are emitted. This threshold provides a direct and unambiguous determination of the charge q, and a signature of exclusion statistics. Derived initially within the Luttinger model, this feature is also predicted by universal non-equilibrium fluctuation relations which agree fully with our measurements. Our work paves the way for further exploration of anyonic statistics using microwave measurements.
Highlights
As revealed by Shottky[1], the random transmission of charged carriers in an electrical circuit leads to low frequency fluctuations of the current that are directly proportional to the transmission probability and the charge of the carriers
For specific filling factors of the fractional quantum Hall effect, these measurements do not provide an unambiguous determination of the charge, which is found to depend on external parameters such as electronic temperature or conductor transmission[8,9,10]
We observe that photon emission resulting from quasiparticle transfer only occurs if the photon energy hf is smaller than the energy qVdc of the quasiparticles, thereby revealing their exclusion statistics[14]: quasiparticles cannot emit photons at energies higher than qVdc as no empty states are available at energy qVdc − hf
Summary
As revealed by Shottky[1], the random transmission of charged carriers in an electrical circuit leads to low frequency fluctuations of the current that are directly proportional to the transmission probability and the charge of the carriers. By measuring the emission threshold as a function of frequency, we provide a direct measurement of the fractional charge without any need for noise calibration or knowledge of the conductor scattering properties This emission threshold, derived initially within the Luttinger model[15,16], is predicted by universal non-equilibrium fluctuation relations[17,18] which agree perfectly with our measurement and do not rely on any assumption on the microscopic description of the system. This agreement establishes the role of the fractional charge in the dynamics of quasiparticle transfer through the characteristic frequency scale fJ = qVdc/h called the Josephson frequency[15,16,19] in analogy with the Josephson relation fJ = 2eVdc/h in superconductors. They are complementary to recent experiments[19] of photo-assisted low frequency noise in the fractional quantum Hall regime[24] with the advantage of not requiring to shine microwaves on the sample
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