Detection of finite frequency current moments with a dissipative resonant circuit

1. Detection of finite frequency current moments with a dissipative resonant circuit Sendai 07 Thierry Martin Centre de Physique Théorique & Université de la Méditerranée • With: • A. Zazunov (CPT, LPMMC) • M. Creux (CPT, thesis) • E. Paladino (Universita di Catania) • Crépieux (CPT) • cond-mat/0702247, PRB 74, 115323 2006

2. Outline: • Noise • Situations where finite frequencies are needed • Capacitive coupling schemes… • Inductive coupling scheme with dissipation • Noise correlations

3. The noise is the signal (R. Landauer) Ambiguity: symmerize or not-symmetrize noise? Not important at « low » frequencies Important at « high » frequencies

4. Test entanglement: Bell inequalities in NS Torres EPJB 99 Lesovik EPJB 2001 Chtchelkatchev PRB 2002 Diagnosis via a DC measurement. Energy filters +E -E on each arm Only split Cooper pairs in the two arms 2 spin filters with opposite directions on each arm

5. Number correlators in terms of noise: • - Assume local density matrix (LDM) • - Convert particle number into noise correlators • Derive corresponding inequality for zero • Frequency noise • THEN • - Compute noise correlations for an NS fork using QM • - Choose angles • RESULT: maximal violation of Bell inequality. On the one hand, τ should be large (ω=0 noise) On the other hand, it should be « small » (irreducible correlations)

6. Noise + noise cross-correlations Crépieux PRB03 in a nanotube: HERE, POSITIVE CORRELATIONS FOR AN INTERACTING FERMIONIC SYSTEM !!!

7. Nanotube with leads: finite frequency cross correlations are needed to measure charges (Lebedev PRB05) Several round trips No round trips Alternative: LL with leads with an impurity in the middle (Trauzettel et al. PRL04) High frequencies also needed

8. Noise measurement: Inductive coupling FIRST Without damping Lesovik + Loosen JETP97, Gavish…PRB2000 Repetitive Mesurement of the charge: histogram

9. Two unsymmetrized noise correlators: emission to the measuring circuit absorption from the measuring circuit Measured noise (from charge fluctuations on the capacitor) is a combination of emission and absorption term. X charge on capacitor, η adiabtic parameter Lesovik 97, Gavish 00 1) Symmetrized correlator does not happen here 2) Measured noise diverges with η=0

10. Capacitive coupling schemes Non-symmetrized noise, once again

11. Experimental implementation: Deblock et al. Also:

12. …. ALSO: Combination of inductive and capacitive coupling Paris (Glattli group 2004) Yale (Schoelkopf group 97) HBT experiment in GHz range for photons emitted by the conductor (noise of noise)

13. PRL05 Theoretical suggestion. Measure charge noise due to a nearby mesoscopic circuit? Use continuity equation to convert charge noise to current noise ?

14. THIS WORK: quantum LC circuit with dissipation • Need to address this problem from a microscopic • point of view: • What is the origin of η ? • Look at « old » literature: • Radiation Line width for Josephson effect • (Larkin+ Ovchinikov, JETP 60’s) • Line width occurs because of fluctuations in the neighboring circuit. • For noise measurement, add dissipation modeled by • a bath of oscillators. • Use Keldysh approach assuming bath+ LC decoupled • at t=-infinity

15. Noise measurement: Inductive coupling NOW With damping Propose to measure excess width and excess displacement

16. Free oscillator (LC circuit, coordinate q) Keldysh Resistance: coupling to a bath of oscillators Caldeira-Legett

17. LC Greens function is dressed by bath Add coupling to the mesoscopic circuit + η Integrate out LC circuit

18. Derivatives with respect to η to get charge and fluctuations (contains all higher moments of current time derivatives) NOW EXPAND in α !

19. Result for fluctuations: Noise correlators Generalized susceptibility Bath spectral function N(ω) Bose Einstein distribution Square of a Lorentzian flucuations diverge with zero damping !

20. Underdamped regime, low T (Sharp cusps are for no-damping) Finite temperature and overdamped regime

21. Average charge on the LC circuit first order term in inductive coupling α vanishes for stationary case Third moment vanishes for incoherent tranport No singular behavior for zero damping

22. Low temperature, under damped Fix T, vary γ/2<T or (inset) Fix γ, vary T (similar behavior, « LC is a bath »)

23. What about noise correlations? How to measure them with a LC circuit ? Two inductances are needed: in parallel or in series Then invert the wiring…

24. Hamiltonian for the circuit with two inductances Minimal coupling: For series circuit For parallel circuit Charge fluctuations with 2 possible wirings:

25. Subtract signals with two different wirings Define 2 noise cross correlators: Charge fluctuations on the capacitor: The result is of course real (properties of correlators)

26. Simple illustration: noise correlations at finite frequency Noise correlations display singularities at Chemical potential differences, as expected. Negative noise correlations if measuring circuit has « low enough » temperature.

27. CONCLUSION: • Inductive coupling scheme to measure the noise, • Using a dissipative LC circuit. • Dissipation included in Caldeira Legett model • Essential to get a finite result for the noise. • Yet dissipation blurs the noise measurement. • Measured third moment identified. • Temperature changes the sign of both noise and third moment • cond-mat/0702247, PRB 74, 115323 2006

28. CNRS POST DOC POSITION AVAILABLE: 24 months Equipe de Nanophysique du CPT, Marseille martin@cpt.univ-mrs.fr Theoretical mesoscopic physics/nanophysics Molecular electronics, QI,… Deadline April 30th

29. Photoassisted Andreev reflection as a probe to finite frequency noise (with Nguyen T. K. Thanh) DC current in detector circuit pairs of electrons can be emitted from/ absorbed in the Superconductor.

30. Model

31. Photo-assisted current 1 quasiparticle, 2quasiparticle, and Andreev current

32. Andreev current blowup