Cavity-coupled strongly correlated nanodevices

1. Cavity-coupled strongly correlated nanodevices Quantum noise through a nanotube quantum dot: Experiment: J. Basset, A.Yu. Kasumov, H. Bouchiat, and R. Deblock(Orsay) Theory: P. Simon (Orsay), C.P. Moca(TU Budapest) , C.H. Chung (Taiwan) Gergely Zaránd TU Budapest Cavity-coupled dots: T. Kontos (Ecole Normale) C.P. Moca and CsabaTőke(TU Budapest) Chernogolovka, September 2012

2. Motivation Technological pressure to integrate nanocircuits into rf cavities (quantum computation) • High frequency noise/conductance measurements! Access new regions of non-equilibrium physics • New correlated states / structures ?

3. Quantum noise througha carbon nanotube Carbon naontube = Quantum dot Electron spin Schöneberger group

4. Shot noise Cathode ray tube: Assume independent events: Autocorrelation of a single pulse „white noise”

5. Classical versus quantum region... Structure of pulses is visible ! Point-like pulses (white noise) This is what we look for (v = 50-100 GHz)

6. Symmetrized noise of a biased tunnel junction (V≠0 ) Non-equilibrium spectrum: ( symmetrized noise ) Tunnel junction „quantum noise” oxide Shot noise

7. Functional RG theory Carbon naontube = Quantum dot Electron spin

8. Nanotube with single electron KondoHamiltonian : Dot spin Usepseudofermions (Abrikosov) Do perturbative RG for !?

9. Difficulties Kondoeffect Logarithmic singularities with „fine structure” Standard RG is not accurate enough Paaske, Rosch, Kroha, Wölfle: Scaling equations (heuristic) for the vertex function: Retardedinteractions ! Currentconservation??? What is???

10. Real time path integral on the Keldysh contour Action: quadratic Keldyshlabel Interaction part: Interactioninitially local: Keldyshsign:

11. Generating RG equations 1. Expandin 2. Rescale Cut-offfunction „Standard” RG:

12. Renormalizedvertex Kroha, Wölfle, Rosch, Paaske

13. Currentvertex Current operator fromequation of motion: Current conservation Generatingfunctional: RG: 1. Expand in and in 2. Rescale and

14. Currentvertexrenormalization Currentnecessarilybecomes non-local time of the measurement! Initially:

15. RG equations Current vertex scaling: Current conservation: Automatically satisfied at the functional level !

16. Renormalizedcurrentvertex

17. Symmetrizednoisespectra Non-equilibrium Kondo effect

18. Non-equilibriumaclinearconductivity Non-equlibriumac-conductance Safi:

19. Emission noise of quantum dot

20. How to measure (quantum) noise at 70 GHz ???

21. The experimentalsetup

22. Resonant coupling betwen a Carbon nanotube and a SIS detector ¼ wavelength resonant circuit Independent DC polarisations of the source and the detector Coupling at eigen frequencies of the resonator (30 GHz and harmonics) Coupling proportional to the quality factor (J. Basset et al. PRL 2010)

23. Kondoeffectinnanotube dI/dV Noise ???

24. Back toexperiment…

25. Noise data • Additional source of decoherence??? (Monreal et al. PRB 05; Van Roermund et al. PRB 10; De Franceschi et al. PRL 02) • Independent flow of spin relaxation ???

26. Coupling quantum dots through cavities

27. Double dot structures Cavity mode Dot 1 Dot 2 Quantum fluctuations of cavity • Sign and size of U can be designed • Couplings up to

28. Stability diagram for attractive U Conductance (NRG) Stability diagram Spinless case Charge Kondo effect (negative U Anderson model !)

29. Summary Quantum noise in the Kondo regime: • Current-conserving functional RG scheme • Noise anomalies predicted and observed • Spin relaxation ? Moca, Simon, Chung, and G.Z., PRB 83, (RC)201303 (2011); Basset, Kasumov, Moca, G.Z., Simon, Bouchiat, Deblock, PRL 108, 046802 (2012) Cavity-coupled quantum dots: • First controlled realization of negative U Anderson model • New quantum states (spinful case) Moca, Tőke, Kontos, G.Z. (to be submitted)

30. Taiwan mini-workshop, January 2009

31. Fitted thecoherencerate… • Additional source of decoherence??? (Monreal et al. PRB 05; Van Roermund et al. PRB 10; De Franceschi et al. PRL 02) • Self-consistent treatment of spin relaxation ???

32. Conclusions • Real time functional RG formalism • showsstronganomaliesat • showssplitKondoresonance Current-conservingscheme Theory: Experiment: • Non-equilibriumquantumnoisemeasurment • Logarithmicanomaliesobserved • Additional spin relaxation must be assumedtoagreewiththeory J. Basset et al, arXiv:1110.1570

33. Whatdoweknowaboutcurrentnoise of a quantumdot? • Shotnoise Theory : Meir and Golub, PRL (2002) Experiments: Delattre et al., Nature Physics (2009) • Noisespectrum ? Toulouse Limit: Schiller and Herschfield (1998) Sindel et al, PRL (2005) Perturbative calculations: Korb et al, PRB (2007) Ourquestions ? (non-equilibriumlinearconducatence) Explore only regime

34. Computingthenoise Functional RG noise formula:

35. Perturbationtheory

36. Noisespectra fixed frequency

37. Quantumnoisedetectionwith SIS junction Ingold and Nazarov (1992)

38. Back toexperiment…

39. Back toexperiment… • Theory:no free fittingparameter! • Kondo temperature TK=1.4K TKRG=0.38K • asymmetry a=0.67 Additional decoherence ??? (Monreal et al. PRB 05; Van Roermund et al. PRB 10; De Franceschi et al. PRL 02)

40. Motivation, introduction to noise Correlations and Quantumnoise ?

41. Emission noise of a tunnel junction ( V=0 ) Equilibrium (V=0) Tunnel junction oxide “Emission” noise emission absorbtion

42. Noise of tunnel junction (V≠0 ) Non-equilibrium spectrum: Symmetrized noise Emission noise Shot noise

43. Symmetrized equilibrium noise of a tunnel junction ( V=0 ) Equilibrum spectrum (V=0) Tunnel junction ( symmetrized noise ) oxide „quantum” noise Thermal noise („white”)