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(1)

Optical Nonlinearties due to the Dipole-dipole Interactions in Two Coupled Quantum Dots

Koo-Chul Je

Department of Physics, College of Liberal Arts and Sciences, Anyang University, Anyang 14028, Korea (Received 15 May 2015 : revised 8 July 2015 : accepted 10 July 2015)

We investigate a cooperative optical nonlinearity due to the dipole-dipole interactions between two coupled quantum-dots systems, which are excited by using a pump pulse with a different strength to generate the lowest excitonic state and a probe pulse to couple to the excited state, as a function of the excitonic density and the distance to the neighboring quantum dot. We find that the local field of the neighboring dipoles can make the exciton state transparent, causing suppression of the absorption on resonance, which results from the phases of the polarizations between the two quantum dots.

PACS numbers: 72.15.Eb, 72.20.Pa, 85.80.Fi

Keywords: Cooperative optical nonlinearity, Dipole-dipole interactions, F¨orster energy transfer, The coupled quantum dots

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PACS numbers: 72.15.Eb, 72.20.Pa, 85.80.Fi

Keywords: až4&hF gÆ&<†h q+þA, Š©œFG-Š©œFG ©œ ñŒ•6 x, F¨orster\-t ú5Åx, +˝)a€ªœ&h

E-mail: je [email protected]

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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HQDH K” YUs4R `OÛ¼–Ð “ôÇ F g†<Æ&h“ Š©œFG (dipole) ©œ ñŒ•6 x`¦ Ÿí†<Ê H ¿º €ªœ&h\"f_ "lor—:r [

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λ1Pλ1λ1+X

λ2

λ2Pλ2λ2

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− E0(t)X

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(2)

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 YUs4R `OÛ¼s“¦, dλ1(2) =< 0|r|αλ1(2) >H¿º €ªœ&h

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+ X

λ



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(3)

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δλ0δi,j @/yŒ•oü< ¢-a„›'a>(the completeness relation) P

λ011λ01 >< αλ1| = 1\¦ëߖ7á¤ôÇ.

¿

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HDD = X

λ1λ012λ02

e2ρλ1λ0

1ρλ2λ0

2

4πε0R3D Pλ1λ01Pλ2λ02

= X

λ12



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.

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&h“ Ùüt2Ÿx©œ ñŒ•6 xܼ–Ð ³ð‰&³)a.

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ƒ

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 כ¹™è[þt\ @/ôÇ Liouville ~½Ó&dñ”ܼ–ÐÂÒ' ÅÒ#QtHX<, s

כ `¦ ìøÍ•¸^‰_ ^¦!3~½Ó&ñd” (the semiconductor Bloch equations)s ÂҏÉr.

i~∂

∂t∆ =h H, ∆i

(6)

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dtpλ,A(B)(t) = −i

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~ X

λ0

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pλ,A(B)

+ i

~



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λ0

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×

n0,A(B)− nλ,A(B)

 (7)

d

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~Im

dλ,A(B)E0(t)pλ,A(B) +X

λ0

VFpλ,A(B)pλ0,B(A) . (8)

1The electric dipole potential is φd= κ~p·~r

r3 and the electric dipole field is obtained with ~p = e ~d as follow:

E~d= −∇φd= κ r3 h

3(~p · ~r r )~r

r− ~p i

(5)

Fig. 1. (Color online) Linear absorption spectra of the two A and B coupled CdSe-quantum dots with their ra- dius of 30 and 35 ˚A, respectively. (The red and dark lines are the pump and probe pulses with their widths of 1 ps, respectively.)



õ&hܼ–Ð Ér €ªœ&h_ Š©œFG\ _K Ä»•¸÷&H €ªœ



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&

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>

úH€ªœ&h_ ¼#FG P (t) =P

λdpλ(t)–Ð ÂÒ' 6£§

›'

a>d” α(ω) ∝ Im[EP (ω)

t(ω)]ܼ–Ð %3#Q”.

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s

Ö© H Ér €ªœ&h\ yœô©Ç FGœíéߖ `ÛO¼\¦ 6 x 

#

Œ Š©œFG[þt`¦ +þA$í #Œ, s Š©œFG[þts lïr€ªœ&h\ p

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¼ Et(t)–Ð ¾º#Q ìøÍ•¸^‰ ^¦!3~½Ó&ñd”`¦ úu&hܼ–Ð > í

ߖ #Œ ”'Ÿ½+É כ s. ¿º €ªœ&h“Ér CdSe–Ð ìøÍâ_ ß¼ l

H 30õ 35 ˚As. *3içõ ›¸ `OÛ¼Hĺۼ +þAI–Ð

”

;Ÿ¤ìøÍ_ rçߖ ;Ÿ¤s 1ps s.

Fig. 1“Ér ìøÍâ RAü< RB\¦ ú°H ¿º €ªœ&h_ ‚+þA&h

“

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

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

H bright "lor—:r©œI[þts. ìøÍâs H€ªœ&h (B-QD)

\

 ]j{9 ±ú“Ér ïr0A_ "lor—:r[þt`¦*3áÔ `ÛO¼–Ð Òqt$ír&, s

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Fig. 2. (Color online) (a) Nonlinear absorption spec- tra of the A-QD with the radius of 35 ˚A for different generated excitonic densities by the pump pulses in the B-QD. (b) Coherent polarizations of the A-QD for dif- ferent strengths of the pump pulses as function of real time.

—

:r ïr0A |1L>Bü< |1L>A /\BN"îr(l\, ĺo ƒ½¨

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Ér "lor—:r[þt–Ðëߖ ½¨$íH†d`¦·ú˜ ú e”.

Fig. 2(a)H B-QD\"f ]j{9 ±ú“Ér "lor—:r ïr0A\ *3áÔ

`O

Û¼_ [jl\¦˨#Q Š©œFG\¦+þA$íôÇ Êê\, s Š©œFG [

þ

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s. A-QD\"f ›¸ H ›¸ `OÛ¼_ [jlH Bĺ

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Œ

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€

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 Ä»•¸)a „l©œ“Ér f¨Ãº Û¼&7˜àÔ!3_ [jl\¦€•çߖ 7£x r

vH כ `¦ ^¦ ú e”. sכ “Ér Ös© H•ô€Ç Š©œFG _

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² ú

˜ € "lor—r:_ f¨Ãº Œ•t€"f €ªœAá¤\ Dh–Ðîr Œ•

“ É

r 4Ÿxĺo[þt–Ð  > a). nB = 0.84_ *3iç_ â Ä

ºH sp *3iç `OÛ¼ {9÷&H îrX< B-QD_ ]j{9

± ú

“Ér "lor—:rs ¢-a„y G0>” 6£§\ {Œ•©œI–Ð b#Q t

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s

 ‰&³©œ`¦ 7á§8 [j > ¶ú˜(R˜Ðl 0AK"f, A-QD_ ]j {9

 ±ú“Ér "lor—r:\ Ä»•¸)a ´ú“rɼ#FG`¦Û`O¼ rçߖ\ 



 Fig. 2(b)\  ÍÇx. sÖ© Hœ€ª&h\"f €•ôÇ *3

Fig. 3. (Color online) Absorption spectra of the A-QD for different distances RSbetween both edges of the QDs.

Strength of the pump pulse corresponds to the excitonic density of 0.90 in the B-QD. (Rs increases along the ar- row.)

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수치

Fig. 3. (Color online) Absorption spectra of the A-QD for different distances R S between both edges of the QDs.

참조

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