Coherent exciton-plasmon interaction in the hybrid semiconductor quantum dot and metal nanoparticle complex.

Abstract

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(-1) and 4.4 x 10(-4) to 2.6 ns(-1), respectively; consequently, the period of Rabi oscillations of exciton population is tunable in the range 0.6 pi-9 pi.

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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-
hancedemission[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
and bytheMNPcan
+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
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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
motionequationof 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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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
National Program on
(2006CB921900).
KeyScience Research
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Fig. 4.
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(Color online) Exciton dynamics in the hybrid com-
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