1. Dynamic response of a mesoscopic capacitor in the presence of strong electron interactions Yuji Hamamoto*, Thibaut Jonckheere, Takeo Kato*, Thierry Martin * University of Tokyo, Kashiwa Obergurgl 05/06/2010 (Phys. Rev. B 81, 153305 (2010)) (PHC Sakura) Phys. Rev. B 2010 Quantum RC circuit

2. Perspectives: quantum optics with electrons Hambury Brown and Twiss experiment with single electrons Hong –Ou-Mandel experiment with single electrons

3. Electrochemical capacitance Charge relaxation resistance Experimental verification, LPA ENS (Science 06)

4. OUTLINE This work: beyond the single electron model and its mean field generalizations How can one include Coulomb Blockade exactly How to account for the existence of electronic correlations in the reservoir ? (STRONG ELECTRONIC CORRELATIONS) Strong coupling between dot and reservoir Monte Carlo calculations Weak coupling: instantons and scaling equations

5. MODEL Our setup: a semi-infinite Luttiger Liquid with a Barrier reservoir Quantum point contact: backscattering Quantum dot AC modulated gate

6. Full Hamiltonian: bosonization Charging energy backscattering Gate voltage

7. Linear response calculation: Kubo type formula (Matsubara formalism: imaginary time)

8. No drastic modification of the relaxation resistance for the case of WEAK backscattering SCALE ! Perturbation theory Monte Carlo data

9. Scaling equations: Tunneling strength Grows Tunneling reduced RG flow towards weak coupling with specified charge. strong coupling between dot and reservoir Tunneling amplitude Dilute instanton gas description

10. Justifies Define low frequency resistance instead as: extrapolate

11. Coherent transport (Thermal time=1/T) Decoherence before charge relaxation is achieved Quantum dot acts like a « reservoir » Furusaki Matveev PRL02

12. CONCLUSION: Relaxation resistance (renormalized by interactions) well defined, as long as interaction are sufficiently weak KT phase transition dot acts like an incoherent reservoir low frequency resitence exceeds RC time diverges, and the relaxation resistance cannot be defined anymore. Interactions in a 1D mesoscopic capacitor drastically modify its finite frequency behavior compared to single electron model Phys. Rev. B 81, 153305 (2010)