Résumé : In a partially filled Landau Level, the electron-electron interactions, for example Coulomb interactions, become dominant at high magnetic fields. It leads to manifestation of the many-body states like fractional quantum Hall (FQH) states where quasiparticle excitations carry fractional charges (e*=e/m, m = 3,5...); implying that many electrons acting in concert can create a quasiparticle with a charge smaller than that of an electron[1]. This apparent paradox has been well studied for last three decades using zero-frequency current noise[2,3]. However, unambiguous detection of the fractional charge of the quasiparticles is still missing; which is extremely susceptible to intricate dynamics of the bulk-edge correspondence[4]. Due to this dynamical feature, the emission and absorption of microwave by these quasiparticles will carries the imprints of fractional excitations. This require a measurement of current fluctuations at very high frequency[5] Here we developed the emission microwave spectroscopy for the FQH states by measuring non-equilibrium current fluctuations at frequency ν (hν > [kB*T, e*VB]). The microwave photons emitted by FQH states are independent of bias voltage (e*VB < hν); but for e*VB > hν, the current fluctuations cross over to the regular voltage-dependent shot noise. This crossover voltage carries the characteristics of the quasiparticle excitations namely their charge and statistics. Additionally, we use the non-equilibrium fluctuation dissipation relation [6,7] to connect the high and low frequency shot noise measurement, hence unambiguously determining the charge of the quasi-particle excitations which is found to be e*=e/3 for the case of n = 4/3 and 2/3. [8]
This measurement can be extended towards the study of non-classicality of these emitted photons in an ac-driven system and can probe the anyonic statistics of FQH systems, which are not yet experimentally demonstrated.
[1] R. B. Laughlin, Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations, Phys. Rev. Lett. 50, 1395 (1983).
[2] R. de Picciotto, et al. Direct observation of a fractional charge, Nature 389, 162 (1997).
[3] L. Saminadayar, D.C. Glattli, Y. Jin, and B. Etienne, Observation of the e/3 fractionally charged Laughlin quasiparticles, Phys. Rev. Lett. 79, 2526 (1997).
[4] M. Dolev, Y. Gross, Y. C. Chung, M. Heiblum, V. Umansky, and D. Mahalu, Dependence of the tunneling quasiparticle charge determined via shot noise measurements on the tunneling barrier and energetics, Phys. Rev. B 81, 161303(R) (2010).
[5] R. J. Schoelkopf, P. J. Burke, A. A. Kozhevnikov, D. E. Prober, and M. J. Rooks, Frequency Dependence of Shot Noise in a Diffusive Mesoscopic Conductor, Phys. Rev. Lett. 78, 3370 (1997).
[6] I Safi and P. Joyez, Time-dependent theory of nonlinear response and current fluctuations, Phys. Rev. B. 84, 205129 (2011).
[7] I. Safi, Time-dependent transport in arbitrary extended driven tunnel junctions, arxiv:1401.5950; see also B. Roussel, P. Degiovanni and I. Safi, Perturbative fluctuation dissipation relation for nonequilibrium finite-frequency noise in quantum circuits, Phys. Rev. B 93, 045102 (2016).
[8] R. Bisognin, H. Bartolomei, M. Kumar, I. Safi2, J.-M. Berroir, E. Bocquillon , B. Plaçais , A. Cavanna 3, U. Gennser, Y. Jin and G. Fève, Microwave photons emitted by fractionally charged quasiparticles, Nature Communications 10, 1708 (2019).
Also see: M. Kapfer, P. Roulleau, M. Santin, I. Farrer, D. A. Ritchie and D. C. Glattli, A Josephson relation for fractionally charged anyons, Science, 363, 846, (2019).
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