High Frequency Third Cumulant of Quantum Noise

Transcription

1 Hgh Frequency Thrd Cumulant of Quantum Nose Julen Gabell, Bertrand eulet Laboratore de Physque des Soldes Orsay (France) Lafe Spetz NIST Boulder, CO (USA)

2 DC Transport n Dsordered Systems 1-p Temperature T= p Despte ther quantum nature, electrons behave as classcal partcules Levtov, Lee & Lesovk, 96 What about fnte frequences?

3 Experment (ω=,t=4.k) Tunnel juncton made by L. Spetz at Yale (na) f δi / e x crossover ev = T = 4. K f ~ 1 GHz x1-6 k B T < Ι > (µa) Equlbrum nose δi = 4k B TG ) (na f δi / e x T = 4. K f ~ 1 GHz x1-6 < Ι > (µa) Temperature ndependent! Sgnal to nose: S 1 / ( S ) I

4 Quantum mechancs: orderng of operators? Average current: Nose S : S ( ω) = dte ωt 1 I DC = Iˆ Iˆ() Iˆ( t) Iˆ( t) Iˆ() ( ) Iˆ() Iˆ( t) + Iˆ( t) Iˆ() Absorpton Emsson Classcal But for smple systems: S sym abs em S ( ω) = S ( ω) em 1 ( ω) = S ( ω) + Ghω

5 How to measure S (ω)? 1) «Classcal» detecton wth a lnear amplfer δv(t) band pass ω ) «Quantum» detecton wth a photo-detector δv(t) band pass ω Photo-multpler: absorbs photons

6 S n the quantum regme ħω>k B T,eV Tunnel juncton =5Ω T phonons = mk T electrons = 7 mk f = GHz hf/k B = 9 mk Ghf/e =.5µA It s not possble to separate the nose of the amplfer from the ZPF! S (K) No photon emtted: Zero pont fluctuatons ev=ħω current (µa)

7 The thrd cumulant S? S ( ω1, ω) = I( ω1) I( ω ω1) I( ) ω Measures phase correlatons at dfferent frequences! * Classcal result: n a Drac peak, all the Fourer components are IN PHASE * Quantum regme: correlatons nvolvng zero pont fluctuatons? We have measured: S (, ω) = I() I( ω) I( ω ) low freq. current fluctuatons ZPF

8 How to calculate S? ) )( (1 ) ( ˆ L L L L a a a a p p a a a a p I = For ω=, r and t energy ndependent: To leadng order n p: ) ˆ (1 p p I WONG!! eason: causalty s not respected Beenakker & Schomerus, 1 Salo, Hekkng & Pekola, 6

9 S and Q mechancs: orderng??? ( ωt+ ω t ) S (, ) = ˆ(,,?) ˆ(,,?) ˆ(,, ω ω dtdt e I t t I t t I t t?) The result depends on ODEING: S e p(1 p)(1 (,) = V h p (1 p) p) Keldysh orderng Fully symmetrzed At fnte frequency, Keldysh orderng, for a tunnel juncton: S ω e I Independent of frequency!! 1 (, ω ) = Galaktonov, Golubev & Zakn, 8

10 How to measure S (,ω)? low pass S () I(ε) δv(t) S (,f) band pass ω S (ω) I(ω-ε) I(-ω) ω ω ω ω

11 S (,ω): a frst experment n the Quantum regme =44 Ω

12 ( ) ( ) ( ) ( ) V V t V // // ) )( // ( ) ( + = + = = δ δ δ Envronmental effects I(t) V (t) (t) V(t) The probablty dstrbuton P() depends on V(t)

13 Feedback and nose of the envronment Kndermann Nazarov Beenakker * The nose of the sample s modulated by external voltage fluctuatons: ds ds = S ( V ( t)) δv ( t) = ( // ) dv dv Nose of the envronment: T env Nose susceptblty * The nose of the sample s modulated by ts own current fluctuatons through the external mpedance: = = V + S ( V ( t)) V ( // Feedback (even for T env =) ) ds dv

14 The same mechansm leads to Dynamcal Coulomb Blockade h δi = K( ω) ωχω ( ω) dω e Correlaton functon of the envronment Nose susceptblty for ω =ω χ ω (ω) χ ( ω)

15 Expermental setup Low frequency current fluctuatons Zero pont fluctuatons of the sample amplfed 1 GHz 4 8 GHz Hgh frequency envronment: 5 Ω at the sample s temperature Dplexer, not spltter Envronmental effects: only the low freq. envronmental nose temp. s not well known.

16 Thrd cumulant of VOLTAGE x1-6 S V (a.u.) ev=ħω T = 7 mk 1 4 current (µa)

17 Thrd cumulant of CUENT x1-6 5 S (a.u.) 15 1 ev=ħω e I current (µa)

18 Another way to measure S (,f)? low pass S () δv(t) S (,f) band pass f S em (f) Photo-multpler: absorbs photons Gves zero for ev<hf: another orderng of the operators?

19 Thrd cumulant of CUENT wth lnear amp. (experment) S (a.u.) x1-6 wth a photo-detector (expected) -4-4 current (µa)

20 Conclusons * A lnear amplfer amplfes the zero pont current fluctuatons * There s a correlaton between low frequency current fluctuatons and hgh frequency, zero pont current fluctuatons * The thrd cumulant of current fluctuatons measured wth lnear amplfers s well descrbed by the Keldysh order S (, ω) = I() I( ω) I( ω) = e I

21 Some open questons * What order of operators for a gven expermental setup? What experment to perform to probe a gven correlator? * We detect electromagnetc feld: how correlators nvolvng electrc feld (.e., photons) n a coax cable are related to correlators of the current (.e., electrons) n the samples? What s the photon densty matrx?