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Time-resolved noise of adiabatic quantum pumps

Time-resolved noise of adiabatic quantum pumps. M. Moskalets Dpt. of Metal and Semiconductor Physics, NTU " Kharkiv Polytechnical Institute ", Ukraine. in collaboration with M. Büttiker

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Time-resolved noise of adiabatic quantum pumps

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  1. Time-resolved noise of adiabatic quantum pumps M. Moskalets Dpt. of Metal and Semiconductor Physics, NTU "Kharkiv Polytechnical Institute", Ukraine in collaboration with M. Büttiker Dpt. de Physique Théorique, Université de Genève, Switzerland 2006

  2. Outline • Introduction • Scattering approach, • Adiabatic approximation • Current and noise generated by the pump: • Frequency and time domains • Two-particle scattering matrix • Current correlation coefficient • Example: resonant transmission pump • Summary

  3. Scattering approach g b ba = Saeae S Sgd aa SS† = S†S = I a ba d incoming particles: outgoing particles: [aa†(E), ab(E)] = da,b d(E- E) [ba†(E), bb(E)] = da,b d(E- E) ba†(E)bb(E) = da,b d(E- E)fa(out)(E) aa†(E)ab(E) = da,b d(E- E)f0,a(E)

  4. Periodic driving V(t) ~ VeiWt g b En = E + nћW n = … -2,-1,0,1,2,... SF SF,gd(En,E) aa(E) a ba(En) d ba(E) = SF,ae(E ,En) ae (En)

  5. Adiabatic approximation: ћW  0 V(t) ~ VeiWt stationary driving ? S SF The zeroth order approximation, j = 0:

  6. Quantities of interest a pump set up: a current: a current-current correlation function:

  7. Current generated Ia,dc w 5W -5W -4W -3W -2W -W 0 W 2W 3W 4W

  8. Current correlation function: Spectrum stationary case ( l = 0 ) w a zero frequency noise power: ( τ0 ) W w a two-time current correlation function: W

  9. Current correlation function: Time domain (we average over a time interval τ0 ) simplifications made: Stationary case: Driving case:

  10. Current correlation function:Decomposition (2) Pab(in, out) ~  a†aaab†b bb; t1 t2 a Pab(in, in) ~  a†aaa a†b ab; b dbb ~ aa t2 Sba(t2) t1 t2 a I = I(out) - I(in); I(out) ~ b† b; I(in) ~ a† a; ba = Sg Sagag Pab ~  IaIb + IbIa   Pab= Pab (in, in)+Pab (in, out)+Pab (out, in)+Pab (out, out) (1) Pab(in, in) ~  Ia(in)Ib(in)+ Ib(in)Ia(in) - 2  Ia(in)  Ib(in); Pab(in, in)(t1,t2) ~ da,bha(t1- t2); ( auto-correlator: > 0 ) Pab(in, out)(t1,t2) ~ -|Sba(t2)|2ha(t1- t2); ( cross-correlator: < 0 ) (3) Pab(out, in)(t1,t2) ~ -|Sab (t1)|2hb(t1- t2); ( cross-correlator: < 0 )

  11. Two-particle scattering matrix ( )* ( )* ( )* ( )* stationary case: t2 driving case: t1 (4) a pump set up: fa,0 = f0 Pab(out, out)(t1,t2) ~ |Sab (t1,t2)|2h (t1- t2) ( auto-correlator: > 0 ) g b a d

  12. Current correlation coefficient  To make the effect of driving more sharp we consider and introduce  stationary case (r is independent of S): driving case:

  13. Example: a resonant transmission pump Large driving, close to the quantized pumping regime: I1 I2 =/2 Idc 0

  14. No dc currents ... Large driving, close to the quantized pumping regime: I1 I2 = =0 Idc= 0

  15. Summary • Two-time current correlation function of an adiabatic quantum pump is calculated • Oscillatory pump changes the sign of a current correlation function • Current auto-correlation is an indicator of current pulses (arising at the same or at another lead)

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