Bruit de grenaille mesuré par comptage d'électrons dans une boîte quantique

Transcription

1 Bruit de grenaille mesuré par comptage d'électrons dans une boîte quantique GDR Physique Quantique Mésoscopique, Aussois, mars 2007 Simon Gustavsson Matthias Studer Renaud Leturcq Barbara Simovic Roland Schleser Thomas Ihn Paul Studerus Klaus Ensslin ETH Zurich collaborations: Eugene Shukorukov (Genève) Andrew Jordan (Rochester) D. C. Driscoll A. C. Gossard (UCSB) M. Reinwald W. Wegscheider (Regensburg)

2 Bruit de grenaille mesuré par comptage d'électrons dans une boîte quantique conductor A shot noise: SI = 2eI (Schottky, 1918) time

3 Bruit de grenaille mesuré par comptage d'électrons dans une boîte quantique conductor A time

4 Outline Introduction 1. Detection of single electron transport 2. Current fluctuations and full counting statistics in a semiconductor quantum dot 3. Tunneling through multiple states: bunching of electrons 4. Single photon detection with a double quantum dot Conclusion and outlook

5 Semiconductor quantum dots gate S source D dot drain tunnel barriers Electrostatic energy EC Quantum level spacing source S k BT quantum dot drain D EC

6 DC current measurement in a quantum dot Spectroscopy of electronic states source quantum dot drain EC k BT k B T E C GSD (10-3 e2/h) VPG (mv)

7 DC current measurement in a quantum dot Spectroscopy of electronic states source S k BT quantum dot k B T E C drain D EC GSD (10-3 e2/h) VPG (mv)

8 DC current measurement in a quantum dot Spectroscopy of electronic states source S k BT quantum dot k B T E C drain D EC N-1 GSD (10-3 e2/h) EC (+Δ) N N+1 VPG (mv)

9 Noise in quantum dots Early experiments in non-tunable quantum dots showed reduction of the shot noise: SI < 2eI Birk et al., PRL 75, 1610 (1995) scanning tunneling microscope Nauen et al., PRB 70, (2004) InAs self-assembled QDs Challenge in lateral quantum dots very low noise level: I 1 pa SI < A2/Hz! strongly non-linear systems

10 Quantum dots realized by AFM lithography AFM tip water film 34 nm 2DEG GaAs/AlGaAs heterostructure (UCSB) 300 nm mesa ohmic contact oxide line 10 Nanophysics µm group

11 part 1: Detection of single electron transport

12 Detection of single electron transport Quantum point contact as a charge detector GQPC 2e2/h N+1 electrons in the QD N electrons in the QD VP Te = 350 mk Field et al., PRL 70, 1311 (1993) Elzerman et al., Nature 430, 431 (2004) Petta et al., Science 309, 2180 (2005)

13 Detection of single electron transport Quantum point contact as a charge detector Low bias voltage on the quantum dot quantum source S dot drain D k BT Te = 350 mk Schleser et al., APL 85, 2005 (2004) Vandersypen et al., APL 85, 4394 (2004)

14 Detection of single electron transport Quantum point contact as a charge detector Large bias voltage on the quantum dot quantum dot source S drain D k BT Te = 350 mk

15 Detection of single electron transport N N+1 quantum dot source S drain D k BT Te = 350 mk

16 Detection of single electron transport N current N+1 previous experiments: Te = 350 mk time Lu et al., Nature 423, 422 (2003) Fujisawa et al., APL 84, 2343 (2004) Bylander et al., Nature 434, 361 (2005)

17 Measuring the current by counting electrons N N+1 Count number n of electron entering the dot within a time t0: I = e<n>/t0 Max. current = few fa (bandwidth = 30 khz) BUT no absolute limitation for low current and noise measurements we show here: I few aa, SI A2/Hz

18 Detection of double occupancy of the quantum dot

19 Determination of the individual tunneling rates Exponential distribution of waiting times for independent events S = < in>, D = < out> N N+1

20 part 2: Current fluctuations in a quantumdot Full counting statistics

21 Current fluctuations measured by electron counting More than noise: access to the full counting statistics (distribution function) I = eµ/t0, µ = <n> SI = 2e2µ2/t0, µ2 = <(n-<n>)2> SI3 = e3µ3/t0, µ3 = <(n-<n>)3> and many more... S. Gustavsson, RL et al., Phys. Rev. Lett. 96, (2006)

22 Histogram of current fluctuations Poisson distribution for asymmetric coupling Sub-Poisson distribution for symmetric coupling Theory: Hershfield et al., PRB 47, 1967 (1993) Bagrets & Nazarov, PRB 67, (2003)

23 Noise in a quantum dot Asymmetric coupling statistics dominated by the thicker barrier quantum dot source S k BT drain Symmetric coupling Coulomb blockade orders the electrons quantum dot source S D drain D k BT

24 Counting statistics in a single-level quantum dot Bagrets & Nazarov, PRB 67, (2003) d p0 =M p 0 dt p1 p1 S M = D i Se D quantum dot source S drain D k BT Generating function determined from the minimal eigenvalue of M(χ): S =t 0 min t 0 P n = d S i n e 2

25 Histogram of current fluctuations S. Gustavsson, RL et al., PRL 96, (2006) Poisson distribution for asymmetric coupling Sub-Poisson distribution for symmetric coupling Theory: Hershfield et al., PRB 47, 1967 (1993) Bagrets & Nazarov, PRB 67, (2003)

26 Adjustable asymmetry of the tunneling rates S D a= S D

27 Current fluctuations vs. asymmetry S. Gustavsson, RL et al., Phys. Rev. Lett. 96, (2006) Reduction of the second and third moments for symmetric coupling Theory: Hershfield et al., PRB 47, 1967 (1993) Bagrets & Nazarov, PRB 67, (2003)

28 Full counting statistics S. Gustavsson, RL et al., Phys. Rev. B 75, (2007) Reaching higher moments of the distribution T = 10 min

29 Full counting statistics Reaching higher moments of the distribution detector not perfect (finite band width) missing events: can be taken into account with an additional rate det QD detector A. Naaman and J. Omentado,PRL 96, (2006) out N N+1 det N P =M P N+1 N+1 in N det N+1 N out [ [ N, N P= N 1, N N, N 1 N 1, N 1 ] in out det in out det 0 M = 0 0 in det 0 0 out det e i out 0 in ]

30 Full counting statistics Reaching higher moments of the distribution detector not perfect (finite band width) missing events: can be taken into account with an additional rate det QD detector A. Naaman and J. Omentado,PRL 96, (2006) out N N+1 det N N+1 N+1 in N det N+1 N out

31 Full counting statistics Reaching higher moments of the distribution detector not perfect (finite band width) finite length of the time trace T = 10 min m = T / t0 e S n = q 0 p e t 0 n n q p 0 (finite t0) D.A. Bagrets & Y.V. Nazarov, PRB 67, (2003)

32 Full counting statistics S. Gustavsson, RL et al., Phys. Rev. B 75, (2007) Reaching higher moments of the distribution T = 10 min

33 part 3: Bunching of electrons Super-poissonian noise

34 Super-poissonian noise Bunching of photons Bose-Einstein statistics Anti-bunching of electrons anti-symmetrization of the wave function (Pauli principle) shown experimentally shown experimentally Handburry-Brown & Twiss, Nature 177, 27 (1956) Henny et al., Science 284, 296 (1999); Oliver et al., Science 284, 299 (1999) wire with T=1 noiseless electron source

35 Super-poissonian noise Anti-bunching of photons? light from single atom interaction between atom and electromagnetic field shown experimentally H. J. Kimble et al., PRL 39, 691 (1977) application: single photon source Bunching of electrons? entangled electrons Loss & Sukhorukov, PRL 84, 1035 (2000); Saraga & Loss, PRL 90, (2003) with interactions Sukhorukov et al., PRB 63, (2001); Cottet et al., PRB 70, (2004); Belzig, PRB 71, (R) (2005)

36 Super-poissonian noise: bunching of electrons source quantum dot S drain D k BT IQPC [na] Time [ms] S. Gustavsson, RL et al., Phys. Rev. B 74, (2006)

37 Super-poissonian noise: bunching of electrons Two time scales quantum dot S 1 ~ 20 khz, 0 ~ 1.5 khz Fast tunneling sometimes blocked by a slow tunneling drain D k BT 8 IQPC [na] source Time [ms] S. Gustavsson, RL et al., Phys. Rev. B 74, (2006)

38 Super-poissonian noise: bunching of electrons super-poissonian noise occurs at the edge of conductance steps Counts/s [khz] 15 µ 3 µ 2 10 µ Vbias [mv] 1.6 S. Gustavsson, RL et al., Phys. Rev. B 74, (2006)

39 Super-poissonian noise: the model Needs two states with different coupling to the leads Γ0 Γ1 kbt the slow state blocks the conduction, due to Coulomb blockade similar to Belzig, PRB 71, (R) (2005) 8 IQPC [na] Time [ms]

40 Super-poissonian noise: the model Master equation pa pa d pb = M p B dt p2 p2 M = ib 0 i B 1 T1 T1 ob rb e i 1 o i Ae T1 i o o r A A B B i A 2 B A Bagrets & Nazarov, PRB 67, (2003) Belzig, PRB 71, (R) (2995)

41 Super-poissonian noise: bunching of electrons Well described by our model S. Gustavsson, RL et al., Phys. Rev. B 74, (2006) µ T1 µ µ 0 But requires long relaxation time T1 > 1 ms (spin effects?) Vbias (V) 1.6

42 Conclusions Real-time detection of single electron traveling through a semiconductor quantum dot Measurement of current fluctuations (noise) and even the full counting statistics Bunching for interacting electrons Double quantum dot + quantum point contact = single photon detector

43 Outlook Electron counting statistics in the cotunneling regime? Kondo regime,... need for faster charge detector: RF-SET, RF-QPC,... Correlation measurement counting statistics of photons emitted by a quantum conductor probing entanglement of electrons