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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

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

outline
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
scattering approach
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)

slide5

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)

slide6

Adiabatic approximation: ћW  0

V(t) ~ VeiWt

stationary driving

?

S

SF

The zeroth order approximation, j = 0:

slide7

Quantities of interest

a pump set up:

a current:

a current-current correlation function:

slide8

Current generated

Ia,dc

w

5W

-5W

-4W

-3W

-2W

-W

0

W

2W

3W

4W

slide9

Current correlation function: Spectrum

stationary case ( l = 0 )

w

a zero frequency noise power:

( τ0 )

W

w

a two-time current

correlation function:

W

slide10

Current correlation function: Time domain

(we average over a time interval τ0 )

simplifications made:

Stationary case:

Driving case:

slide11

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 )

slide12

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

slide13

Current correlation coefficient

To make the effect of driving more sharp we consider

and introduce

stationary case (r is independent of S):

driving case:

slide14

Example: a resonant transmission pump

Large driving, close to the quantized pumping regime:

I1

I2

=/2

Idc 0

slide15

No dc currents ...

Large driving, close to the quantized pumping regime:

I1

I2

=

=0

Idc= 0

slide16

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)