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Coherent exciton–plasmon interaction in the

hybrid semiconductor quantum dot and metal

nanoparticle complex

Mu-Tian Cheng, Shao-Ding Liu, Hui-Jun Zhou, Zhong-Hua Hao, and Qu-Quan Wang*

Department of Physics and Key Laboratory of Acoustic and Photonic Materials and Devices of Ministry of Education,

Wuhan University, Wuhan 430072, China

*Corresponding author: qqwang@whu.edu.cn

Received April 30, 2007; revised June 4, 2007; accepted June 8, 2007;

posted June 13, 2007 (Doc. ID 82588); published July 20, 2007

We studied theoretically the exciton coherent dynamics in the hybrid complex composed of CdTe quantum

dot (QDs) and rodlike Au nanoparticles (NPs) by the self-consistent approach. Through adjusting the aspect

ratio of the rodlike Au NPs, the radiative rate of the exciton and the nonradiative energy transfer rate from

the QD to the Au NP are tunable in the wide range 0.05–4 ns−1and 4.4?10−4to 2.6 ns−1, respectively; con-

sequently, the period of Rabi oscillations of exciton population is tunable in the range 0.6?–9?. © 2007

Optical Society of America

OCIS codes: 240.6680, 270.1670, 320.7130.

The exciton coherent dynamics in a single semicon-

ductor quantum dot (SQD), which has potential ap-

plications in solid quantum computation and quan-

tum information, has been studied widely in past

years [1,2]. With the development of modern nano-

science,SQDs[3–20], semiconductor

[21–23], and metal nanoparticles (MNPs) can be as-

sembled into complexes that exhibit many interest-

ing phenomena, such as energy transfer [3–23], en-

hanced emission[7–15],

wavelength shift [22], and the nonlinear Fano effect

[24].

The basic excitations in the MNPs are the surface

plasmons. When the exciton energy in a SQD lies in

the vicinity of the plasmon peak of the MNP, the cou-

pling of the plasmon and exciton becomes very strong

[24]. The exciton coherent dynamics are modified

strongly by the strong coherent interaction. In this

Letter, the exciton coherent dynamics in the com-

plexes composed of SQDs and rodlike MNPs are stud-

ied theoretically.

Figures 1(a) and 1(b) are schematic diagrams of

the SQD and the rodlike MNP with to-the-end and

by-the-side orientations, respectively. A reasonable

representation for the rodlike MNP is an ellipsoid

with semimajor axis a and semiminor axes b [25],

and the corresponding aspect ratio is q=a/b. Here d

and ? are the center-to-center and surface-to-surface

distance between the MNP and the SQD. The SQD

with exciton vacuum state ?0? and exciton state ?1? is

described by a density matrix and the MNP by clas-

sical electrodynamics. The polarized external field E

=E0cos??Lt? with circular frequency ?Lis parallel to

the semimajor axis. The total field felt by the SQD

andby the MNPcan

+gPMNP/??effd3? and EMNP=E+gPSQD/??effd3? [24,25].

?eff=?2?0+?s?/3, where ?0, and ?sare the dielectric

constants of the background medium and the SQD,

respectively. The constant g is 2 or −1 for the complex

with a to-the-end or a by-the-side orientation when E

is parallel to the long axis of the rodlike MNP. The

nanowires

luminescenceemission

begiven as

ESQD=E

dipole of the MNP PMNP=?MNPEMNPcomes from the

charge induced on the surface of MNP with the

dipole polarizability

?MNP=?0ab2??m−?0?/?3???m

−?0?Lx+?0???. The corresponding enhancement factor

inside the hybrid complex is f???=1+g?MNP/??effd3?

[26]. The dipole of the SQD is PSQD=?SQD??01+?10?

[24], where ?SQDis the dipole moment of the transi-

tion ?0?–?1? and ?01and ?10are the off-diagonal ele-

ments of the density matrix.

We first consider the exciton damping rate ?10,

which can be decomposed to the exciton radiative re-

combination rate ?radand an additional decay rate ?

[2]. ? accounts for all other processes that scatter the

exciton out of state ?1? and is assumed to be a con-

stant in our calculation, since it is independent of the

metal plasmon. ?radis modified strongly by the inter-

action of exciton and plasmon. By quantization of the

electromagnetic field felt by the SQD, ?radis obtained

Fig. 1.

complexes with (a) to-the-end orientation and (b) by-the-

side orientation.

(Color online) Schematic diagrams of the hybrid

August 1, 2007 / Vol. 32, No. 15 / OPTICS LETTERS

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0146-9592/07/152125-3/$15.00© 2007 Optical Society of America

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as ?rad=?f????2?rad

rate in the absence of the MNP, which can also be ob-

tained by using Govorov’s methods [20]. ?radcan be

enhanced or suppressed, since ?f????2can be larger or

smaller than 1, by adjusting the mutual orientation

and ?MNP. In the following calculation, we take the

CdTe quantum dot and Au nanoparticle (NP) for ex-

ample. The corresponding parameters are ?s=10, ?0

=2.25, and ?rad

=0.08 ns−1[27]. ?mis taken from [28];

b is assumed to be 6 nm. For the resonant excitation

of the SQD, r is taken as 3.2, 6.6, and 9.5 for the ex-

citation wavelength ?excof 600, 750, and 900 nm, re-

spectively [29].

The interaction of the exciton and plasmon is

weakened with increasing gap ?. Figures 2(a) and

2(b) exhibit ?radversus q with different gaps ?. When

? is fixed at 2 nm and q varies from 1 to 3.5, ?radis

tunable in the range 0.05–4 ns−1for the complex

with g=−1, which is much wider than that of the

complex with g=2, mainly because of the shorter d.

?radvaries with b, but it reaches the maximum with

almost the same q. The plasmon peak of the rodlike

Au NP is tunable by adjusting q [30]. Figures 2(c)

and 2(d) show ?radversus q with different ?excfor the

complexes with g=2 and g=−1. ?rad reaches the

maximum when q=1.7,3.1,4.2 for ?exc=600, 750,

900 nm, respectively.

Due to the long-range Coulomb interaction, the en-

ergy transfer from the SQD to the MNP occurs via

the Förster effect, a nonradiative process [20]. An-

other interesting effect of the exciton–plasmon inter-

action is the exciton frequency shift [21]. The com-

plex coupling factor G=2g2?SQD

quantitatively describe both the nonradiative energy

transfer and the exciton shift [24]. In the weak

excitation region, the real part of G is related

to the exciton shift, while the imaginary part of

G denotes the energy transfer rate from the SQD

to the MNP with the relationship ?non-rad=Im?G?

=2g2?SQD

/???eff

degenerates into a spherical one when q=1, and the

0, where ?rad

0

is the exciton radiative

0

2

?MNP/???eff

2d6? can

22d6?Im??MNP? [24]. The rodlike MNP

theoretical results are consistent with the experi-

mental data [5,6]. Figures 3(a) and 3(b) exhibit

?non-radversus q for the complexes with different ?

and different g. When ? is fixed at 2 nm and q varies

from 1 to 2.9, ?non-radis tunable in the range of 4.4

?10−4to 2.6 ns−1and 1.5?10−2to 0.8 ns−1for the

complex with g=−1,2, respectively. ?non-radalso in-

creases with decreasing ?. The calculations also re-

veal that ?non-radreaches the maximum with almost

the same q even though b is different. Figures 3(c)

and 3(d) show ?non-radversus q with different ?exc,

which reaches the maximum when q=1.6,2.9,3.8 for

?exc=600, 750, 900 nm, respectively.

We next turn to the exciton coherent dynamics

modulated by the plasmon. The Hamiltonian is given

by HˆSQD=?i=0,1??i? ˆii−?ESQD?? ˆ01+? ˆ10? [24], where ?i

is the eigenfrequency of the state ?i?. ? ˆ01and ? ˆ10are

the dipole transition operator between the states ?0?

and ?1?. With the rotation-wave approximation, the

motion equation of optical

=?10exp?i?Lt?+c.c.,

V=i?10exp?i?Lt?+c.c.

=?11−?00of the SQD are deduced as

1

Bloch vectors

and

U

W

U˙= −

2??10− Im?G?W?U +?? −

+ Im??eff?W,

2??10− Im?G?W?V −?? −

+ Re??eff?W,

1

2Re?G?W?V

?1?

V˙= −

1

1

2Re?G?W?U

?2?

W˙= − ?10?1 + W? − Re??eff?V − Im??eff?U

1

4Im?G??U2+ V2?,

−

?3?

where ?eff=?0f???, ?0=?SQDE/?, and ?=?L−??1

−?0?. Equations (1) and (2) clearly indicate that the

Fig. 2.

plexes with (a) g=2 and (b) g=−1 when ?=2, 4, 6 nm. ?rad

versus q for the complexes with (c) g=2 and (d) g=−1 when

?exc=600, 750, 900 nm.

(Color online) ?radversus q for the hybrid com- Fig. 3.

plexes with (a) g=2 and (b) g=−1 when ?=2, 4, 6 nm.

?non-radversus q for the hybrid complexes with (c) g=2 and

(d) g=−1 when ?exc=600, 750, 900 nm.

(Color online) ?non-radversus q for the hybrid com-

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OPTICS LETTERS / Vol. 32, No. 15 / August 1, 2007

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Re?G? is related to the exciton shift and that Im?G? is

the energy transfer rate ?non-radin the weak excita-

tion region W?−1 [24].

The calculated excitonic population in the state ?1?

versus the input pulse area ??t?=?−?

Figs. 4(a) and 4(b) for the two kinds of complex. In

the calculation, ?=10 ns−1. The periods of Rabi oscil-

lation (RO) are about 1.9?, 0.9?, and 3? for q

=1,3,4 in the complex with g=2, which changes to

2.1?, ?, 0.86? for the complex with g=−1. When the

exciton energy lies in the vicinity of the plasmon

peak of the Au NP, the RO period of the complex with

g=−1 is tunable in the range 0.6?–9? as q varies

from 2.6 to 3.3, and that of the complex with g=2 is

tunable in the range 0.8?–5? as q varies from 3.1

to 3.7.

In summary, when the exciton energy of the CdTe

QD lies in the vicinity of the plasmon peak of the Au

NP, ?radand ?non-radare tunable in the large range of

0.05–4 ns−1and 4.4?10−4to 2.6 ns−1, and the corre-

sponding RO period in the range of 0.6?–9?, by ad-

justing q for the complex with by-the-side orienta-

tion. The tunable ranges of ?rad, ?non-rad, and the

period of RO of the complex with to-the-end orienta-

tion are narrower than those of the complex with by-

the-side orientation mainly because of the larger d.

t?0dt is shown in

This research was supported by the Natural Sci-

ence Foundation of China (10534030) and the

NationalProgramon

(2006CB921900).

KeyScienceResearch

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Fig. 4.

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(Color online) Exciton dynamics in the hybrid com-

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