1. Separation of neutral and charge modes in one dimensional chiral edge channels vincent.freulon@ens.fr

2. f=2.1 GHz bosons 12 34 12 34 fermions 12 3 4 Single electron emitter Dip not going to zero. Decoherence effect ! Electronic Hong-Ou-Mandel dip E. Bocquillon et al., Science 339 no. 6123 pp. 1054-1057 GDR méso Aussois 2013 – vincent.freulon@ens.fr

3. VGVG Gaz 2D V V G(mV) An electronic Mach-Zehnder interferometer visibility : 62% Y. Ji et al., Nature 422, 415 (2003) P. Roulleau et al., Phys. Rev. Lett.100, 126802 (2008) P. Roulleau et al., Phys. Rev. Lett.101, 186803 (2008) P.-A. Huynh et al., Phys. Rev. Lett. 108, 256802 (2012) GDR méso Aussois 2013 – vincent.freulon@ens.fr

4. Energy relaxation between channels at υ=2 H. Le Sueur et al., PRL 105, 056803 (2010). Outer edge channel driven out of equilibrium. non-equilibrium double dip relaxes over ~3µm. broader dip than equilibrium. Inner edge channel driven out of equilibrium. dip broadens as L is increased. outer edge channel heats up. Energy exchanges between copropagating channels. GDR méso Aussois 2013 – vincent.freulon@ens.fr

5. Separation in charge and neutral modes In nanowires: O.M. Auslaender et al., Science 308 5718 (2005) H. Steinberg et al., Nat. Phys. 4 3 (2007) I.P. Levkivskyi et al., PRB 78, 045322 (2008) P. Degiovanni et al., PRB 80, 241307(R) (2009) D.L. Kovrizhin et al., PRB 81, 155318 (2010) Neder et al., PRL 96 016804 (2006) decoupled propagation in ch. 1 & 2 2 new eigenmodes : - slow neutral mode - fast charge mode Capacitive coupling between channels GDR méso Aussois 2013 – vincent.freulon@ens.fr

6. In frequency domain: edge magneto-plasmons (EMP) Edge magneto-plasmons In the "frequency domain": charge oscillations Sine wave induced in outer edge channel GDR méso Aussois 2013 – vincent.freulon@ens.fr

7. In frequency domain: edge magneto-plasmons (EMP) Edge magneto-plasmons In the "frequency domain": charge oscillations Sine wave induced in outer edge channel Phase shift between both modes: GDR méso Aussois 2013 – vincent.freulon@ens.fr

8. In frequency domain: edge magneto-plasmons (EMP) Edge magneto-plasmons In the "frequency domain": charge oscillations Sine wave induced in outer edge channel Phase shift between both modes: GDR méso Aussois 2013 – vincent.freulon@ens.fr

9. Scattering of EMP over propagation length between source and QPC Experimental realisation Sine excitation. No tunneling (capacitive coupling). 1 2 GDR méso Aussois 2013 – vincent.freulon@ens.fr

10. QPC completely closed QPC partially open Experimental realisation GDR méso Aussois 2013 – vincent.freulon@ens.fr

11. Experimental results Points spiraling in the complex plane ( damping ). Charge oscillations. E. Bocquillon et al., Nature Comm. 4, 1839 (2013). GDR méso Aussois 2013 – vincent.freulon@ens.fr

12. 2 non-dispersive regimes. non-zero imaginary part reveals damping. Dispersion relation Dispersion relation of the neutral mode E. Bocquillon et al., Nature Comm. 4, 1839 (2013). Short range Long range GDR méso Aussois 2013 – vincent.freulon@ens.fr

13. Short-range model Low-frequency regime: well reproduced Oscillations: 1 timescale not enough Local (zero-range) density-density interactions distributed capacitance between channels No characteristic length 1 timescale constant velocity Short-range model I.P. Levkivskyi et al., PRB 78, 045322 (2008) P. Degiovanni et al., PRB 80, 241307(R) (2009) D.L. Kovrizhin et al., PRB 81, 155318 (2010) Also in non-chiral Lüttinger liquids: I. Safi et al., PRB 52, R17040 (1995) GDR méso Aussois 2013 – vincent.freulon@ens.fr

14. Long-range model Low-frequency regime: well reproduced Oscillations: 2 timescales sufficient Dissipation: well reproduced, origin unknown ? Long-range charge-charge interactions capacitance between channels Range propagation length 2 time-scales 2 different velocities Dissipation: compatible with RC circuit description Long-range model GDR méso Aussois 2013 – vincent.freulon@ens.fr

15. Conclusion Perspectives: -Understand the effect of coupling probed using EMP (collective modes) in term of two particle interferences (HOM). GDR méso Aussois 2013 – vincent.freulon@ens.fr

16. G. Fève former members : E. Bocquillon, J. Gabelli, A. Mahé, F. D. Parmentier, J.-M. Berroir B. Plaçais Mesoscopic Physics group, LPA ENS, pièce L175 Samples Fab, LPN Marcoussis A. Cavanna Y. Jin V. Freulon A. Marguerite Theory, ENS Lyon P. Degiovanni C. Grenier D. Ferraro E. Thibierge People involved GDR méso Aussois 2013 – vincent.freulon@ens.fr