Within the field of quantum electronic optics, one aims to manipulate electrons similarly to photons, and to probe individual or collective quantum phenomena within electronic nanostructures. This field has known a tremendous development both on the theoretical and experimental levels. Its privileged framework is a quantum Hall bar, formed in a 2-D electron gas confined laterally and subject to a perpendicular magnetic field. Due to quantization into Landau levels, the number n of filled levels determines a quantized conductance ; electric current circulates only along n chiral edge states which behave as optical waveguides. This is the so-called Integer Quantum Hall Effect (IQHE).
Nevertheless, contrary to photons, electrons are subject to Coulomb interactions (CIs) whose strength and screening depend on the nanostructure. Nonetheless, CIs lead to fascinating collective quantum phenomena. On the one hand, they can couple the n chiral edge states in the IQHE. Then excitations are no more given by elementary electrons, but rather by collective plasmonic modes, for which we have developed an adapted scattering approach in order to address time-dependent transport.1 On the other hand, in a partially filled Landau level, CIs generate atypical collective excitations carrying a fractional charge, leading to the so-called Fractional Quantum Hall Effect (FQHE).
An important challenge of quantum electronic optics, both in the IQHE and FQHE, consists into monitoring electron sources analogous to laser sources. One elegant method, proposed theoretically by L. Levitov et al, 2 consists into applying an ac voltage formed by a series of lorentzian pulses. The elementary charges, called “levitons”, have been created experimentally by C. Glattli’s group in CEA (Paris-Saclay) in a 2-D gas without a magnetic field. But within those approaches, CIs can be ignored.3
A theoretical breakthrough to include CIs has been made in Orsay through a unifying perturbative theory for time-dependent transport, which led to a different characterization of « levitons ». 4 Indeed, this theory provides remarkably simple but universal relations which link the average current and noise under ac voltages to their values under a dc voltage, and which have been checked experimentally in tunnel junctions embedded into electronic circuits.5
The robust relation for the noise thus obtained, independent on experimental details, magnetic field and CIs, has been tested and exploited to measure the fractional charge in the FQHE by C. D. Glattli’s group.6
The internship will consist first into learning this theory, which requires, interestingly, only basic theoretical tools. Then the implementation of fractional « levitons » could be addressed, in close interaction with C. D. Glattli’s group.
1-I. Safi and H. J. Schulz, Phys. Rev. B 52, R17040 (1995). For a review : C. Grenier et al, Proceedings of StatPhys 24 satellite on International Conference on Frustrated Spin Systems, Cold Atoms and Nanomaterials. Hanoi (2010)
2-J. Keeling, I. Klich, and L. S. Levitov, Phys. Rev. Lett. 97, 116403 (2006).
3-J. Dubois et al, Nature 502, 659 (2013). T. Jullien et al, Nature 514, 603607 (2014).
4. I. Safi and E. Sukhorukov, Eur. Phys. Lett. 91, 67008 (2010). I. Safi, arXiv:1401.5950. B. Roussel, P. Degiovanni & I. Safi, Phys. Rev. B 93, 045102 (2016). I. Safi, to appear in Phys. Rev. B. (2018) (ArXiv :1809.08290)
5-C. Altimiras et al. Phys. Rev. Lett. 112, 236803 (2014). O. Parlavecchio, C. Altimiras, J.-R. Souquet, P. Simon, I. Safi, P. Joyez, D. Vion, P. Roche, D. Estève, and F. Portier, Phys. Rev. Lett. 114, 126801 (2015). S. Houle et al, arXiv:1706.09337v1
6-M. Kapfer et al, Science (2018) (under press; Arxiv :1806.03117)
Dynamical Coulomb Blockade Theory - Apr 30, 2013 4:44:0 PM