Quantum Noise of a Carbon Nanotube Quantum Dot in the Kondo Regime Exp : J. Basset, A.Yu. Kasumov, H. Bouchiat and R. Deblock Laboratoire de Physique des Solides – Orsay (France) Theory : P. Simon ( LPS ), C.P. Moca and G. Zarand ( Budapest ) Chernogolovka - June 2012

Kondo effect : - model system for electronic correlations - screening of a localized magnetic moment in a conductor - nanophysics (quantum dots ( Goldhaber-Gordon et al. Nature (1998), Cronenwett et al. Science (1998); carbon nanotube ( Nygard et al. Nature (2000)) Kondo effect on a single spin In situ control of the parameters new situation (out of equilibrium, orbital Kondo effect) Many body problem Kondo effect and Mesoscopic physics supra normal kondo Increase of the resistance (T<T K )

3 Kondo effect in quantum dots U : charging energy;  0 : energy level;  L  R : coupling to the reservoirs Under specific conditions: - Odd number of electrons in the dot - Intermediate transparency of the contacts - Temperature below Kondo temperature T K Kondo effect : dynamical screening of the dot’s spin LL RR reservoir Quantum dot VSVS A VGVG gate

4 Kondo resonance in quantum dots T K = (U  ) 1/2 exp (-1/ J eff ) - Transport through second order spin flip events - Formation of a many body spin singlet (spin of the dot + conduction electrons) - Peak in the DOS of the dot at the Fermi energy of the leads  Kondo resonance virtual H eff = J eff .Swith J eff =  / U : DOS

5 2T K T < T K T > T K TKTK Signature of the Kondo effect on conductance What about Kondo dynamics? Increase of conductance at low temperature

What about noise? A ? VSVS VGVG Out-of-equilibrium Kondo dynamics at frequencies h ~k B T K ? T K = 1K, >20GHz

Noise detection in the Kondo regime Low frequency regime (h << k B T K ) and low bias voltage (eV sd < k B T K ) : - semiconductor quantum dots (SU2) : Influence of Kondo correlations on the Fano factor O. Zarchin et al. Phys. Rev. B (2008) Y. Yamauchi et al., Phys.Rev.Lett. (2011) - carbon nanotube quantum dots : Signature of orbital and spin effect T. Delattre et al., Nature Phys. (2009)

Theoretical predictions C.P. Moca et al., PRB (2011) Signature of the Kondo effect on noise : Logarithmic singularity at V=h /e RG calculation eV=h =5k B T K - RG calculations at high frequency h >k B T K and out-of-equilibrium - Prediction of a logarithmic singularity at eV=h  even when h >>k B T K High frequency quantum noise detection at frequencies ≥ k B T K /h

Outline - Introduction to noise measurement in the quantum regime - Resonant coupling circuit and SIS detector : - Emission noise of a Josephson junction - High frequency noise detection of a carbon nanotube in the Kondo regime System Detector Emission <0 >0 Absorption ? ? VSVS VGVG A

What is electronic noise? Introduction to electronic noise I(t)= +  I(t) V sd I(t) Conducting system Why measure noise? Electronic correlations, effective charge, characteristic energy scale, …

Noise in the quantum regime energy scales (eV,  …  and characteristic times quantum noise : zero point fluctuations System mesoscopic device Detector Amplifier, Quantum dot, SIS junction,… Emission <0 >0 Absorption h >> k B T, h > eV

Source Detector Mesoscopic system S S I Noise measurement in the quantum regime Josephson Junction - Carbon nanotube in the Kondo regime Superconductor / Insulator / Superconductor (SIS) junction Noise detection with SIS junction : Kouwenhoven’s group, Science (2003) P.M. Billangeon et al.,PRL (2006) Resonant Circuit T=20 mK

Quantum Noise Detection with a SIS Junction EMISSION ABSORPTION Photo-assisted tunneling current (PAT) =30GHz S S I Ingold & Nazarov (1992)

Source/detector coupling with a resonant circuit  ¼ wavelength resonant circuit as in T.Holst et al. PRL(1994)  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 (Q~10) L=1mm a=5µm b=100µm L=n /4 n odd integer

Source and detector coupled via the resonant circuit Source = Josephson Junction AC Josephson effect : « on-chip » calibration of the coupling Measurement of the quasi-particle high frequency noise

PAT current due to the tunneling of quasiparticles I PAT measurement as a function of V source Detector bias voltage (V D1 or V D2 ) : selection of frequency range V D <2  /e

Direct measurement of HF emission noise of a Josephson junction DC current but No emission Noise while eV S <2  +h i Josephson junction emitting a photon h =eV S -2  2Δ/e Calculated ( =0) Theory at Theory at & finite bandwidth

Quantum noise measurement with SIS detector Detection of emission and absorption noise Quantitative measurement of the HF Emission Noise of a Josephson Junction J. Basset et al. PRL 105, (2010) J. Basset et al. PRB 85, (2012) Sensitivity : 2 fA² /Hz (1.5mK on 20k  ) at 28 GHz, 8 fA² /Hz (5.8mK on 20k  ) at 80 GHz Powerful tool to measure HF noise of mesoscopic systems : carbon nanotube quantum dot in the Kondo regime

What about emission noise? A ? VSVS VGVG Out-of-equilibrium Kondo dynamics at frequencies h ~k B T K ?

20 L L VGVG A VDVD R A VSVS R source drain gate NT 500nm 1m1m junctions Carbon nanotube coupled to the SIS detector Detector biased for emission noise detection

21 Kondo effect in the measured carbon nanotube Kondo ridge Center of the ridge  T K =1.4K  =30GHz 2T K V G =3.12V Zero bias peak What about noise?

Recent theoretical predictions C.P. Moca et al., PRB (2011) Signature of the Kondo effect on noise : Logarithmic singularity at V=h /e RG calculation eV=h =5k B T K - RG calculations at high frequency h >k B T K and out-of-equilibrium - Prediction of a logarithmic singularity at eV=h  even when h >>k B T K

23 High frequency noise in the Kondo regime 30 GHz h ~k B T K 2h 1 /e 2h 3 /e No emission noise if |eV S | < h Small singularity related to the Kondo resonance at h ~k B T K h ~k B T K : - Absence of emission noise if |eV S | < h - Singularity at |eV S | = h qualitatively consistent with predictions V S (mV)

24 High frequency noise in the Kondo regime 30 GHz h ~k B T K 80 GHz h ~ 2.5 k B T K ANY EXPLANATIONS??  Dynamics of the Kondo effect ? Not predicted by theory C.P. Moca et al. PRB 10 2h 1 /e 2h 3 /e Singularity related to the Kondo resonance at h ~k B T K  Qualitatively consistent but not quantitatively Coll. with C.P.Moca, G.Zarand and P.Simon - Theoretical comparison takes into account experimental data with no fitting parameter! - Kondo temperature T K =1.4K  T K RG =0.38K - asymmetry a= U=2.5meV,  =0.51meV - Theoretical predictions approximately 2 times higher than experimental result

25 High frequency noise in the Kondo regime 30 GHz h ~k B T K 80 GHz h ~ 2.5 k B T K Singularity related to the Kondo resonance at h ~k B T K  Qualitatively consistent but not quantitatively 2h 1 /e 2h 3 /e No singularity at h ~2.5 k B T K !  Not consistent with theory

26 High frequency noise in the Kondo regime 30 GHz h ~k B T K 80 GHz h ~ 2.5 k B T K Singularity related to the Kondo resonance at h ~k B T K  Qualitatively consistent but not quantitatively 2h 1 /e 2h 3 /e No singularity at h ~2.5 k B T K !  Not consistent with theory ANY EXPLANATIONS??  Decoherence at high V S ? Monreal et al. PRB 05 Van Roermund et al. PRB 10 De Franceschi et al. PRL 02 Fit with additional spin decoherence rate

27 Decoherence due to voltage bias - External decoherence rate  Form similar to the intrinsic rate (C.P. Moca et al. PRB 11)  Consistent with the differential conductance  Consistent with the noise power for both frequencies Spin lifetime in the dot reduces with applied voltage bias V S Coll. with C.P.Moca, G.Zarand and P.Simon ,  : fitting parameters

28 Single decoherence rate function reproduce the data 30 GHz h ~k B T K 80 GHz h ~ 2.5 k B T K Fits OK using a single bias dependent spin decoherence rate function with  =14,  =0.15

29 Logarithmic singularity and decoherence effects eV increases  Kondo peaks in the density of states (attached to the leads) split and vanish due to decoherence Decoherence already pointed out Exp. : De Franceschi et al. PRL 02, Leturcq et al. PRL 05 Th. : Monreal et al. PRB 05, Van Roermund et al. PRB 10 Many photons emitted at eV=h 1 Few photons emitted at eV=h 3

Real time Renormalization Group technique Systematic expansion in the reservoir-system coupling S. Andergassen et al., Nanotechnology (2010) Kondo system out of equilibrium Relaxation and decoherence included Other theoretical approach Good agreement with experiment with no fit parameter S. Mülher and S. Andergassen

31 High frequency Fano like factor in the Kondo regime 30 GHz 80 GHz Subpoissonian Noise F  1 F decreases when conductance increases  Consistent with a highly transmitted channel 0 1 N.B. : Energy independent transmission  Fano factor

Conclusions High frequency noise in the Kondo regime Singularity due to Kondo effect for h ~ k B T K No singularity for h ~ 2.5 k B T K Consistent with theory with decoherence due to the bias voltage J. Basset et al. Phys. Rev. Lett. 108, (2012).

Quantum Noise of the resonant circuit No source bias Detector only sensitive to Quantum Noise of the resonator at equilibrium

Real part of the impedance seen by the detector  Low quality factor due to direct connection  Even peaks due to finite value of impedance mismatch AC Josephson effect : calibration I C : critical current Dynamical Coulomb blockade Ingold et Nazarov (1992)

T~0.9K Resonator Photons exchange Resonator T~0.02K T~0.5K S S S I S S I S S I Signal due to the resonant circuit Voltage Noise

Real part of the impedance of the resonant circuit. Extracted from calibration. T=0 : No Emission noise but Absorption  Zero Point fluctuations T increases : Emission appears & Absorption increases Crossover from Quantum to thermal Noise crossover from quantum to thermal noise 1 =28 GHz

38 T=0 : No Emission noise but Absorption  Zero Point fluctuations T increases : Emission appears & Absorption increases Thermal Noise T=0 (ZPF) Noise spectrum of a resistor R

Josephson junction as signal source 2 operating modes : Cooper pairs tunneling : AC Josepshon effect Quasiparticle tunneling : and Symmetric spectrum with peaks at frequencies Only absorption noise Singularities at Emission and absorption noise Singularity in emission at Singularity in absorption at emission absorption