The noise spectrum of a quantum dot Eitan Rothstein Netanel Gabdank Ora Entin-Wohlman* Amnon Aharony* Physics Department, Ben Gurion University of the Negev * Also at Tel Aviv University

Mesoscopic Physics 2/10 Meso = Intermidiate, in the middle. Mesoscopic physics = A mesoscopic system is really like a large molecule, but it is always, at least weakly, coupled to a much larger, essentially infinite, system – via phonos, many body excitation, and so on. (Y. Imry, Introduction to mesoscopic physics) A naïve definition: Something very small coupled to something very large. 2/10

Mesoscopic Physics 3/10

Quantum dot 4/10 There are different types of quantum dots. A large atom connecting to two ledas A metallic grain on a surface Voltage gates on 2DEG 4/10

The model 5/10 The model DC conductance Noise spectrum Quantum-Dot (QD) N∆ Left (L) electronic reservoir Right (R) electronic reservoir … ∆ -N∆ DC conductance Noise spectrum No interaction Hartree Fock 5/10

The model 6/10 The Hamiltonian Hartree Fock approximation electronic states on QD charging energy momentum states in R/L reservoirs coupling R/L reservoir-QD Hartree Fock approximation Hartree Fock Self-consistent calculation 6/10

Level Occupancy and Effective Hamiltonian The effective Hamiltonian * energy scaled with Level Occupancy Effective single-e energies (Hartree) (Hartree) (Hartree Fock) (Hartree Fock) Hartree terms Fock terms Hartree terms Fock terms 7/10

The Scattering Formalism Treating the problem in the Landauer Büttiker formalism Tight-Binding model Current and correlations S(E) scattering region states (Landauer) (Büttiker) 8/10

The noise spectrum 9/10 Noise spectrum * energy scaled with Calculations performed for and , so the noise given by symmetric symmetric Hartree No interaction Hartree Hartree Fock symmetric asymmetric Hartree Fock No interaction Hartree Hartree Fock 9/10

Thanks Summary 10/10 “The noise is the signal” - R. Landauer The noise spectrum exhibits steps and dips The steps quantum dot resonances The dips energy difference between the resonances contain information on the coupling asymmetry The interaction effect Shifts levels to preserves neutrality Shifts noise steps and dips Fock effect Small quantitative effect – modifies the width of the levels Thanks 10/10