1
Equilibrium Noise Suppression by Modulating Contact Transparency Y. B. Sherkunov, Jin Zhang, N. d'Ambrumenil, B. Muzykantskii Department of Physics, University of Warwick, Coventry, CV4 7AL, U.K . ABSTRACT Controlled injection of single electrons into a ballistic conductor is essential for ``moving- electron-based'' quantum computation. We obtain the full counting statistics (FCS) of a quantum point contact (QPC) for the case when the contact transparency is modulated in time, which is shown to be equivalent to a system with a time- dependent bias voltage applied between the leads. We demonstrate two optimal contact opening schemes with the equilibrium noise largely suppressed. The potential applications includes an optimal electronic entangler and on-demand single electron source. Scattering Matrix Approach R L t i t i R L a a S t B e t A e t A t B b b ) ( ) ( ) ( ) ( ) ( ) ( Minimal Excitation States (MES) F k F k 2 2 2 () Vt t Lorentzian Pulse (L.P.) () i t t i e t i t dt t V t ' ) ' ( ) ( 0 2 / ) ( F a e h i t i Faraday Flux: Mapping Method for Modulating Contact Transparency Noise Minimization for QPC? ) ( ) ( ) ( ) ( t B t A t A t B S No bias-voltage Real Transmission and Reflection Amplitudes A(t) and B(t) ) ( ) ( 0 0 ~ t i t i e e S ) ( ) ( ) ( t iA t B e t i R L R L ib b b ia a a 2 1 ~ 2 1 ~ 2 , 1 2 , 1 a S b ~ ~ ~ , 2 independent channels with For , (Direct analog to MES, see grey box) i t i t e t i ) ( , (electro ~ ~ ~ 1 1 1 e i b a e b (hole ~ ~ ~ 2 2 2 h i b a e b 0 2 1 0 ~ ~ Re Re 2 1 Rh Lh Le Rh Le Lh h e b b b b b ib b ib b b Optimal Electronic Entangler 2 1 2 eq Q () Im t i At t i ), ε log(t F f 2 2 A eq Q Arbitrary Switching: Spin Entanglement: Useful Not Useful 2 1 Q 2 Q 0 Q Single Electron Source 1 1 1 1 1 1 1 1 2 2 2 2 Im ) ( i t t i t t i t t i t t t A 1 1 1 1 ( ) 0.8, 2 2 t when (0) 1 A 4 1 2 eq Q Probability Total noise due to MES: Non-Optimal Opening Extra noise due to finite time cut-off tf Entangler Source 1 0 0 ) ( i t t i t t i t i t e t i References: Ivanov, Lee, Levitov, Phys. Rev. B 56, 6839 (1997) Keeling, Klich, Levitov, Phys. Rev. Lett. 97, 116403 (2006) Abanov and Ivanov, Phys. Rev. Lett. 100, 086602 (2008) YS, JZ, NdA, BM, arXiv:0812.4433v3 JZ, YS, NdA, BM, in preparation F k F k Arbitrary Pulse ) ( ) ( t V t V Arb 1,2 0 A t f t

Equilibrium Noise Suppression by Modulating Contact Transparency

  • Upload
    elyse

  • View
    30

  • Download
    0

Embed Size (px)

DESCRIPTION

Equilibrium Noise Suppression by Modulating Contact Transparency Y. B. Sherkunov, Jin Zhang, N. d'Ambrumenil, B. Muzykantskii Department of Physics, University of Warwick, Coventry, CV4 7AL, U.K . A. when. 0. t. ABSTRACT - PowerPoint PPT Presentation

Citation preview

Page 1: Equilibrium  Noise  Suppression by Modulating Contact Transparency

Equilibrium Noise Suppression by Modulating Contact TransparencyY. B. Sherkunov, Jin Zhang, N. d'Ambrumenil, B. Muzykantskii

Department of Physics, University of Warwick, Coventry, CV4 7AL, U.K.

ABSTRACTControlled injection of single electrons into a ballistic conductor is essential for ``moving-electron-based'' quantum computation. We obtain the full counting statistics (FCS) of a quantum point contact (QPC) for the case when the contact transparency is modulated in time, which is shown to be equivalent to a system with a time-dependent bias voltage applied between the leads. We demonstrate two optimal contact opening schemes with the equilibrium noise largely suppressed. The potential applications includes an optimal electronic entangler and on-demand single electron source.

Scattering Matrix Approach

R

Lti

ti

R

L

aa

S

tBetAetAtB

bb

)()()()(

)(

)(

Minimal Excitation States (MES)

FkFk

2 2

2( )V tt

Lorentzian Pulse (L.P.)( )i t t ie

t i

t

dttVt ')'()( 02 /)(

F

ae hiti

Faraday Flux:

Mapping Method for Modulating Contact Transparency

Noise Minimization for QPC?

)()()()(tBtAtAtB

S

No bias-voltageReal Transmission and Reflection Amplitudes A(t) and B(t)

)(

)(

00~ti

ti

ee

S

)()()( tiAtBe ti

RL

RL

ibbb

iaaa

21~2

1~

2,1

2,1aSb ~~~ , 2 independent channels with

For , (Direct analog to MES, see grey box)

itite ti

)(

,(electron) ~~~111 e

i baeb (hole) ~~~222 h

i baeb

0210~~

ReRe21 RhLhLeRhLeLhhe bbbbbibbibbb

Optimal Electronic Entangler

212

eqQ( ) Im t iA t

t i

),εlog(t Ff22 A

eqQ

Arbitrary Switching:

Spin Entanglement:

Useful Not Useful

2

1Q 2Q 0Q

Single Electron Source

11

11

11

11

22

22Im)(

ittitt

ittitttA

1

1

1 1( ) 0.8,2 2t

when (0) 1A

412

eqQ

Probability

Total noise due to MES:

Non-Optimal Opening

Extra noise due to finite time cut-off tf

Entangler Source

1

0

0)(

ittitt

itite ti

References:Ivanov, Lee, Levitov, Phys. Rev. B 56, 6839 (1997)Keeling, Klich, Levitov, Phys. Rev. Lett. 97, 116403 (2006)Abanov and Ivanov, Phys. Rev. Lett. 100, 086602 (2008)YS, JZ, NdA, BM, arXiv:0812.4433v3JZ, YS, NdA, BM, in preparation

FkFk

Arbitrary Pulse)()( tVtV Arb

1,2

0

A

tft