- Email: [email protected]
Quantum beats of confined excitons in CuCl nanocrystals
JOURNAL
OF
LUMINESCENCE .lournal of Luminescence 76&77 ( 1998) 125 129
ELSEVIER
Abstract We have performed femtosecond degenerate four-wave-mixing (DFWM) to investigate coherent transient phenomena in CuCl nanocrystals. We present observation of quantum coherence of weakly confined excitons in nanocrystals through quantum beats in the spectrally resolved signal of DFWM. In large nanocrystals with a mean radius R of 220 tk the quantum beat between the sublevels of confined excitons is observed. In small nanocrystals with R = 40 A, WC observe the quantum beat between the confined exciton and its optical phonon side band. These results suggest that the coupling of confined excitons to optical phonons becomes stronger for the smaller sizes. In the decay behavior of coherence, the two-component decay is observed. and the fast and slow components are attributed to the homogeneous width of the phonon side band and that of zero-phonon band of the confined exciton transition. respectively. c 1998 Elsevicr Science B.V. All rights reserved. Kqwotds:
Coherent
phenomena:
Quantum
beats; Nanocrystals
1. Introduction
quantum
Ultrafast coherent phenomena of excitons in solids have been widely studied with the development of femtosecond laser techniques. In a transient degenerate four-wave-mixing (DFWM) spectroscopy. we can measure not only optical dephasing of excited states but also quantum interference between two or more levels in a multi-level system. When we excite simultaneously two optical transitions by coherent light pulses, we observe an oscillating modulation of the signal with a time corresponding to the inverse of their energy splitting. Such beating phenomena have been observed not only in the DFWM but also in the fluorescence for various semiconductors such as GaAsiAlGaAs
In semiconductor nanocrystals. the size quantization of exciton states has been extensively investigated. Their density of state is transformed from a continuum of bulk semiconductor to a series of discrete levels by quantum confinement [5,6]. Because of the size quantization effect, the oscillator strength is concentrated on a discrete level, and nanocrystals show a large optical nonlinearity [7 -91. In CuCl, the exciton Bohr radius is so small (6.8 A) that translational motion of excitons is confined in a nanometer sized crystallite (weak confincment). In nanocrystals. lattice vibrations and their interactions with electronic states are also affected by the restricted geometry. Recently, some groups have reported that exciton- LO phonon interaction in the weak confinement regime is increased with decreasing crystallite size [ 10,111. The size dependence of the exciton-phonon interaction may modify
*Corresponding
author.
Fax:
+ 81 57 789 3724:
nak~lrnurafrc,nuap.n~~(~~~-u.ac,lp.
0021-2313 PII
9X 519.00
C’ 1998
s00”-231?(97l00191-9
Elscvier
e-mail
Science B.V. All rights reserved
well structures,
AgBr,
Bi13 and
so on
phonon-mediated optical transitions and dephasing processes of excitons In this paper, we present observation of quantum coherence of weakly confined excitons in nanocrystals through quantum beats in the spectrally resolved degenerate four-wave-mixing (SR-DFWM). We have performed conventional DFWM and SR-DFWM experiments in the self-diffraction geometry with two incident beams using CuCl nanocrystals with mean radii of R = 40 and 220 A.
1.5
(a) R = 220 A
(b) R = 40 A
2. Experimental
T = 4.2 K
1
23
t CuCl nanocrystals embedded in glass were prepared by the double heat treatment procedure of glass containing CuCl. The crystallite radius can be altered by changing temperatures of heat treatment between 450°C and 520°C [12]. The mean radii of nanocrystallites were determined using X-ray diffraction data and Scherrer’s formula. Experiments of DFWM with two-beam configuration were carried out using second harmonic of a femtosecond mode-locked Ti : sapphire laser. The pulse duration and the spectral width were 200 fs and 15 meV. respectively. The excitation fluence was 0.1 uJ cme2 and the pulse repetition rate was 1 kHz. The self-diffracted signal due to the third-order nonlinear polarization was observed in the directions of 2k2 - kl, and 2k, - kz, where kl and k2 are the wave vectors of two incident beams. In the case of the SR-DFWM, the self-diffracted signal light was analyzed using a monochromator with a band width of 2 meV. The decay of the diffracted signal with increasing the delay time between the incident pulses is a measure of the phase relaxation of excitons [13].
3. Results and discussion Fig. 1 shows the absorption spectrum of CuCl nanOocrystals with mean radii of R = 220 A (a) and 40 A (b) at 4.2 K. The Z3 exciton band is shifted to higher-energy side compared to the exciton energy of a bulk crystal shown by the arrow due to quantum confinement. The confinement energies are 4 meV for R = 220 A and 33 meV for R = 40 A.
0.5
0 3.20
3.25
PHOTON ENERGY [eV] Fig. I. Absorption spectra of CuCl nanocrystals with radii of 220 A (a) and 40 A (b) at 4.2 K (solid line). The arrow indicates the exciton energy of bulk crystal. The spectrum of excitation light pulse is also shown (dashed line).
According to the infinite spherical potential model for the exciton confinement, the energy splitting between the first ( 1s) and second ( 1p) confined levels is 4 meV, and the first and third (2s) level is 16 meV for R = 220 A. Those for R = 40 A are 33 and 132 meV, respectively. In the absorption spectra. however, we cannot observe splitting of absorption band because of the crystallite size distribution. The dashed line shows spectrum of the excitation pulse which is tuned to the high-energy side of Z3 exciton peak to excite simultaneously optical transitions of confined sublevels in DFWM experiments. Fig. 2a shows the correlation trace of the spectrally integrated DFWM (SI-DFWM) signal for R = 220 A, which exhibits a two-component decay. The time constants of fast and slow components are 0.6 and 20 ps, respectively, and corresponding homogeneous widths are 0.5 meV and 17 ueV, respectively. The latter width is much narrower than the spectral width (6 120 ueV) of photoluminescence
(a) SI-DFWM
(b) SR-DFWM 1.0
a
z
z 1
I
0.5 y I L.,.l....l 0
t
50 100 FREQUENCY km-‘1
0 0
1 TIME
2
DELAY Ipsl
Fig. 2. (a) C’orrelatbon traces of spectrally integrated DFWM signal for R = 210 A. The inset shows the signal on a logarlthmic scale in a time range of 20 ps. (b) Correlation trace of spectrally resolved DFWM for R = X0 A. The inset shows the Fourier transform of the SK-DFWM signal.
from single CdSe nanocrystals 1141. The ratio of fast and slow components depends on the incident laser power density, and the slow component relatively increases with decreasing laser power density. We measured temperature dependence of decay behaviors at temperatures between 4.2 and 2.5 K. and the fast and slow components showed different temperature dependences [15]. Considering these results. we may tentatively attribute the fast component to the homogeneous width of the phononside band and the slow one to the zero-phonon band of confined excitons. No oscillatory structure corresponding to the quantum beat could be observed in SI-DFWM. Fig. 2b shows the correlation trace of SRDFWM signal measured at photon energy of 3.310 eV for R = 220 A. An oscillatory structure superimposed onto the exponential decay is clearly observed. When there exists an inhomogeneous broadening due to the size distribution. the signal measured by SI-DFW M consists of various periods
of quantum beats. Consequently. even if the quantum interference of excitons in the nanocrystals with different sizes occurs, oscillatory structures disappear as a result of destructive interference effects of the electromagnetic waves with various periods of quantum beats [ 161. The model calculations of the three-level system with the inhomogeneous broadening have shown that although the signal of the SI-DFWM does not exhibit an oscillation. that of SR-DFWM demonstrates quantum beats. This means that we can pick up a certain beat structure within the size distribution by resolving spectrally DFWM signal. The advantage of the SR-DFWM has been also demonstrated by Pantke et al. 1171: the quantum beat between the exciton and biexciton states was nbserved when the signal light was detected at the two-photon transition of biexcitons. Shown in the inset of Fig. 2b is a Fourier transform of the SR-DFWM for R = 320 A. The beat consists of a single oscillation and the frequency is 43 cm-i corresponding to the energy of 5.3 mcV. This energy is close to the energy splitting between the confined 1s and Ip sublevels assuming that nanocrystal shape is a sphere and an exciton is confined by the infinite spherical potential. Optical transition from ground state to confined Ip sublevel is forbidden for spherical CuCI nanocrystals. but if the shape of CuCl nanocrystals embedded in the glass matrix is not spherical. the transition to the confined lp sublevel becomes allowed. In CdSe nanocrystals. confined p-like transition becomes allowed due to a Stark effect induced by trapped carriers [lg]. Therefore. we attribute this oscillation to the quantum beat between the Is and lp sublevels of confined excitons. When the crystallite size is decreased, a different beating behavior is observed. Fig. 3a and Fig. 3b show the correlation trace of the SI-DFWM signal and SR-DFWM signal detected at 3.235 eV foi R = 40 A. respectively. WC see a two-component decay in the SI-DFWM signal and the SR-DFWM signal exhibits the oscillation with a period shortei than that for R = 330 r\. As shown in the inset ol Fig. 3b. Fourier analysis yields the frequency of 169 cm- ‘. The corresponding energy splitting is 21.0 meV. and is not equal to the energy splitting between the confined Is and Ip sublevels (33 meVl
128
H. Ohmura, A. Nakamura J Journal qf‘luminescence
(a) SI-DFWM
76& 77 (1998) 125-129
nanocrystals to the quantum beat between the confined 1s and its TO phonon side band. Here, it is worthy to note that the quantum beat associated with optical phonons can be observed only in small nanocrystals with R = 40 A. This suggests that the coupling of confined excitons to optical phonons becomes stronger for the smaller size, which is consistent with the hybridization of optical phonons with Ip transitions observed by photoluminescence experiments [lo].
4. Summary
FREQUENCY [cm-‘1 0
1 TIME DELAY [psi
I I I 2
Fig. 3. Correlation traces of spectrally integrated DFWM signal (a) and spectrally resolved DFWM (b) for R = 40 A. The inset shows the Fourier transform of the SR-DFWM signal.
for this crystallite size. Instead, the energy corresponds to TO phonon energy. The similar oscillating behaviors associated with optical phonons have been observed in the transient DFWM experiments for bulk GaAs [ 191 and CdSe nanocrystals [20]. In bulk GaAs, the oscillation with a time period slightly shorter than LO phonon frequencies was observed, and for this reason the oscillation was interpreted in terms of non-Markovian effect. In CdSe nanocrystals, on the other hand, the oscillation was explained by the quantum beat between the confined lowest state of exciton and its LO phonon side band. In the non-Markovian process, the deviation from the exponential decay of the DFWM signal depends on a correlation time ~~ of reservoir as well as a strength of interaction between the relevant system and the reservoir. As a result, the decay behavior does not necessarily exhibit an oscillatory ,behavior corresponding to the characteristic time. In line with the interpretation for the results of CdSe nanocrystals, we attribute the oscillatory behavior observed in CuCl
We have investigated the quantum coherence of weakly confined excitons in CuCl nanocrystals through quantum beat in the transient DFWM. We observed the quantum beat between the confined 1s and lp sublevels for large nanocrystals. The transition to the lp sublevel may be partially allowed because of the deviation from the spherical shape of CuCl nanocrystals in glass. In small nanocrystals, the quantum beat between the confined exciton and its optical phonon side band was observed. The different beat behaviors depending on the size suggest that the confined excitonoptical phonon coupling is stronger for the smaller size.
Acknowledgements We thank Y. Kondo and Y. Kuroiwa for providing us glass samples. This work was supported by the New Energy and Industrial Technology Development Organization (NEDO).
References Cl1 E.O. Gobel, K. Leo, T.C. Damen, J. Shah, S. Schmitt-Rink. W. Schafer, J.F. Miiller, K. Kiihler. Phys. Rev. Lett. 64 (1990) 1801. PI V. Langer, H. Stoltz. W. von der Osten. Phys. Rev. Lett. 64 (1990) 854. c31T. Tokizaki, A. Nakamura. Y. Ishida. T. Yajima. I. Akai. T. Karasawa, in: C.B. Harris, E.P. Ippen. G.A. Mourou. A.H. Zewail (Eds.), Ultrafast Phenomena VII, Springer. Berlin, 1990. p. 253.
[4]
M. Koch. G. von Plessen. .I. Feldmann.
E.O. Ghbel.
Chem.
Ph>s. 120 (1996) 367. Efros. A.L. Efros. Sov. Phys. Semicond.
[I31
T. Yajimn.
[I41
S.A. Empedocles.
.I. Phys. Sot. Japan 47 (197’)) 1620.
D...
Norrls.
[5]
A.I.
[6]
Y. Kayanuma.
Phys. Reb. B 38 (1988) 9797.
[I 51 H. Ohmura.
A. Nakamura.
[7]
E. Hanamura.
Phys. Rc\.
[lh]
A. Naknmura.
[X]
T. Kataoka. (IYY?I
[Y]
T. Tokiraki.
T. K.
A. Nakamura.
Phys. Rev. B 1X
Itoh. Inoue.
S. Iwai. T. Itoh. S. Yano, T. Goto.
M. Rosen. A.V.
A.I.
Ekimov.
C.
Gourdon.
K. Toba. A.V.
F-cdoro\.
Phys.
Rev.
Baranov.
[ I97
A.A.
f 10X2)
775
r\.A. Onushchenko.
So\.
Phqs. Semicond.
16
Phps. Rev.
D.M.
Colv~n.
unpublished. 2nd
Int. C‘onf. on The Ph\\~c\
vol. I. lYY4, p. 2OIY.
II. Oberhau\er.
V.C. Lywnho.
.1.M H\am.
,A. Sacra. C.B. Murra!.
h1.C; Ba~cndl.
l’hks.
72 (1994) 2612.
1.. Banqal. W. Stab.
[20]
A.I. Ekimo\.
Lett.
D.B.
II. Stelnhach.
B 54 (1996)
RX32l.
Ba\\cndl.
Phys. Re\. B 47 I I YY?) 21 I .?
[)..I. Norri\. Re\.
Phya. Rev. Lett. 74 (19951 1645.
Pantke.
G. Warnann. [IX]
Nishljima.
A. Yamanaka.
Onuahchenho. [I’]
T. Tokiraki.
of Semiconductors.
Phys. Rev.
11205. M.
M.G.
Lett. 77 (1096) 3X7?.
1171 K.-H.
AI.1.. Efrw. [I I]
B 37 (198X) 1273.
2x1s.
K. Edamntsu. B .il (19Y5)
[IO]
16 (1982) 771.
Y. Talra.
Tran
Phys. Re\.
Mittlemnn.
E. Reit\amer. hl. Wegcncl-. T
H.
Iiaug.
hlarschncr.
Lett. 75 (lY951 21Xx. R.b’.
.A.P. .Alixi\at~~~.
(10911 13435.
Thoal.
h1.U. Wehnw.
Schocnle~n. CL’.
Shank.
.I _I. Shian:. Php
Kc\.
\‘.L. B 3’)
OF
LUMINESCENCE .lournal of Luminescence 76&77 ( 1998) 125 129
ELSEVIER
Abstract We have performed femtosecond degenerate four-wave-mixing (DFWM) to investigate coherent transient phenomena in CuCl nanocrystals. We present observation of quantum coherence of weakly confined excitons in nanocrystals through quantum beats in the spectrally resolved signal of DFWM. In large nanocrystals with a mean radius R of 220 tk the quantum beat between the sublevels of confined excitons is observed. In small nanocrystals with R = 40 A, WC observe the quantum beat between the confined exciton and its optical phonon side band. These results suggest that the coupling of confined excitons to optical phonons becomes stronger for the smaller sizes. In the decay behavior of coherence, the two-component decay is observed. and the fast and slow components are attributed to the homogeneous width of the phonon side band and that of zero-phonon band of the confined exciton transition. respectively. c 1998 Elsevicr Science B.V. All rights reserved. Kqwotds:
Coherent
phenomena:
Quantum
beats; Nanocrystals
1. Introduction
quantum
Ultrafast coherent phenomena of excitons in solids have been widely studied with the development of femtosecond laser techniques. In a transient degenerate four-wave-mixing (DFWM) spectroscopy. we can measure not only optical dephasing of excited states but also quantum interference between two or more levels in a multi-level system. When we excite simultaneously two optical transitions by coherent light pulses, we observe an oscillating modulation of the signal with a time corresponding to the inverse of their energy splitting. Such beating phenomena have been observed not only in the DFWM but also in the fluorescence for various semiconductors such as GaAsiAlGaAs
In semiconductor nanocrystals. the size quantization of exciton states has been extensively investigated. Their density of state is transformed from a continuum of bulk semiconductor to a series of discrete levels by quantum confinement [5,6]. Because of the size quantization effect, the oscillator strength is concentrated on a discrete level, and nanocrystals show a large optical nonlinearity [7 -91. In CuCl, the exciton Bohr radius is so small (6.8 A) that translational motion of excitons is confined in a nanometer sized crystallite (weak confincment). In nanocrystals. lattice vibrations and their interactions with electronic states are also affected by the restricted geometry. Recently, some groups have reported that exciton- LO phonon interaction in the weak confinement regime is increased with decreasing crystallite size [ 10,111. The size dependence of the exciton-phonon interaction may modify
*Corresponding
author.
Fax:
+ 81 57 789 3724:
nak~lrnurafrc,nuap.n~~(~~~-u.ac,lp.
0021-2313 PII
9X 519.00
C’ 1998
s00”-231?(97l00191-9
Elscvier
Science B.V. All rights reserved
well structures,
AgBr,
Bi13 and
so on
phonon-mediated optical transitions and dephasing processes of excitons In this paper, we present observation of quantum coherence of weakly confined excitons in nanocrystals through quantum beats in the spectrally resolved degenerate four-wave-mixing (SR-DFWM). We have performed conventional DFWM and SR-DFWM experiments in the self-diffraction geometry with two incident beams using CuCl nanocrystals with mean radii of R = 40 and 220 A.
1.5
(a) R = 220 A
(b) R = 40 A
2. Experimental
T = 4.2 K
1
23
t CuCl nanocrystals embedded in glass were prepared by the double heat treatment procedure of glass containing CuCl. The crystallite radius can be altered by changing temperatures of heat treatment between 450°C and 520°C [12]. The mean radii of nanocrystallites were determined using X-ray diffraction data and Scherrer’s formula. Experiments of DFWM with two-beam configuration were carried out using second harmonic of a femtosecond mode-locked Ti : sapphire laser. The pulse duration and the spectral width were 200 fs and 15 meV. respectively. The excitation fluence was 0.1 uJ cme2 and the pulse repetition rate was 1 kHz. The self-diffracted signal due to the third-order nonlinear polarization was observed in the directions of 2k2 - kl, and 2k, - kz, where kl and k2 are the wave vectors of two incident beams. In the case of the SR-DFWM, the self-diffracted signal light was analyzed using a monochromator with a band width of 2 meV. The decay of the diffracted signal with increasing the delay time between the incident pulses is a measure of the phase relaxation of excitons [13].
3. Results and discussion Fig. 1 shows the absorption spectrum of CuCl nanOocrystals with mean radii of R = 220 A (a) and 40 A (b) at 4.2 K. The Z3 exciton band is shifted to higher-energy side compared to the exciton energy of a bulk crystal shown by the arrow due to quantum confinement. The confinement energies are 4 meV for R = 220 A and 33 meV for R = 40 A.
0.5
0 3.20
3.25
PHOTON ENERGY [eV] Fig. I. Absorption spectra of CuCl nanocrystals with radii of 220 A (a) and 40 A (b) at 4.2 K (solid line). The arrow indicates the exciton energy of bulk crystal. The spectrum of excitation light pulse is also shown (dashed line).
According to the infinite spherical potential model for the exciton confinement, the energy splitting between the first ( 1s) and second ( 1p) confined levels is 4 meV, and the first and third (2s) level is 16 meV for R = 220 A. Those for R = 40 A are 33 and 132 meV, respectively. In the absorption spectra. however, we cannot observe splitting of absorption band because of the crystallite size distribution. The dashed line shows spectrum of the excitation pulse which is tuned to the high-energy side of Z3 exciton peak to excite simultaneously optical transitions of confined sublevels in DFWM experiments. Fig. 2a shows the correlation trace of the spectrally integrated DFWM (SI-DFWM) signal for R = 220 A, which exhibits a two-component decay. The time constants of fast and slow components are 0.6 and 20 ps, respectively, and corresponding homogeneous widths are 0.5 meV and 17 ueV, respectively. The latter width is much narrower than the spectral width (6 120 ueV) of photoluminescence
(a) SI-DFWM
(b) SR-DFWM 1.0
a
z
z 1
I
0.5 y I L.,.l....l 0
t
50 100 FREQUENCY km-‘1
0 0
1 TIME
2
DELAY Ipsl
Fig. 2. (a) C’orrelatbon traces of spectrally integrated DFWM signal for R = 210 A. The inset shows the signal on a logarlthmic scale in a time range of 20 ps. (b) Correlation trace of spectrally resolved DFWM for R = X0 A. The inset shows the Fourier transform of the SK-DFWM signal.
from single CdSe nanocrystals 1141. The ratio of fast and slow components depends on the incident laser power density, and the slow component relatively increases with decreasing laser power density. We measured temperature dependence of decay behaviors at temperatures between 4.2 and 2.5 K. and the fast and slow components showed different temperature dependences [15]. Considering these results. we may tentatively attribute the fast component to the homogeneous width of the phononside band and the slow one to the zero-phonon band of confined excitons. No oscillatory structure corresponding to the quantum beat could be observed in SI-DFWM. Fig. 2b shows the correlation trace of SRDFWM signal measured at photon energy of 3.310 eV for R = 220 A. An oscillatory structure superimposed onto the exponential decay is clearly observed. When there exists an inhomogeneous broadening due to the size distribution. the signal measured by SI-DFW M consists of various periods
of quantum beats. Consequently. even if the quantum interference of excitons in the nanocrystals with different sizes occurs, oscillatory structures disappear as a result of destructive interference effects of the electromagnetic waves with various periods of quantum beats [ 161. The model calculations of the three-level system with the inhomogeneous broadening have shown that although the signal of the SI-DFWM does not exhibit an oscillation. that of SR-DFWM demonstrates quantum beats. This means that we can pick up a certain beat structure within the size distribution by resolving spectrally DFWM signal. The advantage of the SR-DFWM has been also demonstrated by Pantke et al. 1171: the quantum beat between the exciton and biexciton states was nbserved when the signal light was detected at the two-photon transition of biexcitons. Shown in the inset of Fig. 2b is a Fourier transform of the SR-DFWM for R = 320 A. The beat consists of a single oscillation and the frequency is 43 cm-i corresponding to the energy of 5.3 mcV. This energy is close to the energy splitting between the confined 1s and Ip sublevels assuming that nanocrystal shape is a sphere and an exciton is confined by the infinite spherical potential. Optical transition from ground state to confined Ip sublevel is forbidden for spherical CuCI nanocrystals. but if the shape of CuCl nanocrystals embedded in the glass matrix is not spherical. the transition to the confined lp sublevel becomes allowed. In CdSe nanocrystals. confined p-like transition becomes allowed due to a Stark effect induced by trapped carriers [lg]. Therefore. we attribute this oscillation to the quantum beat between the Is and lp sublevels of confined excitons. When the crystallite size is decreased, a different beating behavior is observed. Fig. 3a and Fig. 3b show the correlation trace of the SI-DFWM signal and SR-DFWM signal detected at 3.235 eV foi R = 40 A. respectively. WC see a two-component decay in the SI-DFWM signal and the SR-DFWM signal exhibits the oscillation with a period shortei than that for R = 330 r\. As shown in the inset ol Fig. 3b. Fourier analysis yields the frequency of 169 cm- ‘. The corresponding energy splitting is 21.0 meV. and is not equal to the energy splitting between the confined Is and Ip sublevels (33 meVl
128
H. Ohmura, A. Nakamura J Journal qf‘luminescence
(a) SI-DFWM
76& 77 (1998) 125-129
nanocrystals to the quantum beat between the confined 1s and its TO phonon side band. Here, it is worthy to note that the quantum beat associated with optical phonons can be observed only in small nanocrystals with R = 40 A. This suggests that the coupling of confined excitons to optical phonons becomes stronger for the smaller size, which is consistent with the hybridization of optical phonons with Ip transitions observed by photoluminescence experiments [lo].
4. Summary
FREQUENCY [cm-‘1 0
1 TIME DELAY [psi
I I I 2
Fig. 3. Correlation traces of spectrally integrated DFWM signal (a) and spectrally resolved DFWM (b) for R = 40 A. The inset shows the Fourier transform of the SR-DFWM signal.
for this crystallite size. Instead, the energy corresponds to TO phonon energy. The similar oscillating behaviors associated with optical phonons have been observed in the transient DFWM experiments for bulk GaAs [ 191 and CdSe nanocrystals [20]. In bulk GaAs, the oscillation with a time period slightly shorter than LO phonon frequencies was observed, and for this reason the oscillation was interpreted in terms of non-Markovian effect. In CdSe nanocrystals, on the other hand, the oscillation was explained by the quantum beat between the confined lowest state of exciton and its LO phonon side band. In the non-Markovian process, the deviation from the exponential decay of the DFWM signal depends on a correlation time ~~ of reservoir as well as a strength of interaction between the relevant system and the reservoir. As a result, the decay behavior does not necessarily exhibit an oscillatory ,behavior corresponding to the characteristic time. In line with the interpretation for the results of CdSe nanocrystals, we attribute the oscillatory behavior observed in CuCl
We have investigated the quantum coherence of weakly confined excitons in CuCl nanocrystals through quantum beat in the transient DFWM. We observed the quantum beat between the confined 1s and lp sublevels for large nanocrystals. The transition to the lp sublevel may be partially allowed because of the deviation from the spherical shape of CuCl nanocrystals in glass. In small nanocrystals, the quantum beat between the confined exciton and its optical phonon side band was observed. The different beat behaviors depending on the size suggest that the confined excitonoptical phonon coupling is stronger for the smaller size.
Acknowledgements We thank Y. Kondo and Y. Kuroiwa for providing us glass samples. This work was supported by the New Energy and Industrial Technology Development Organization (NEDO).
References Cl1 E.O. Gobel, K. Leo, T.C. Damen, J. Shah, S. Schmitt-Rink. W. Schafer, J.F. Miiller, K. Kiihler. Phys. Rev. Lett. 64 (1990) 1801. PI V. Langer, H. Stoltz. W. von der Osten. Phys. Rev. Lett. 64 (1990) 854. c31T. Tokizaki, A. Nakamura. Y. Ishida. T. Yajima. I. Akai. T. Karasawa, in: C.B. Harris, E.P. Ippen. G.A. Mourou. A.H. Zewail (Eds.), Ultrafast Phenomena VII, Springer. Berlin, 1990. p. 253.
[4]
M. Koch. G. von Plessen. .I. Feldmann.
E.O. Ghbel.
Chem.
Ph>s. 120 (1996) 367. Efros. A.L. Efros. Sov. Phys. Semicond.
[I31
T. Yajimn.
[I41
S.A. Empedocles.
.I. Phys. Sot. Japan 47 (197’)) 1620.
D...
Norrls.
[5]
A.I.
[6]
Y. Kayanuma.
Phys. Reb. B 38 (1988) 9797.
[I 51 H. Ohmura.
A. Nakamura.
[7]
E. Hanamura.
Phys. Rc\.
[lh]
A. Naknmura.
[X]
T. Kataoka. (IYY?I
[Y]
T. Tokiraki.
T. K.
A. Nakamura.
Phys. Rev. B 1X
Itoh. Inoue.
S. Iwai. T. Itoh. S. Yano, T. Goto.
M. Rosen. A.V.
A.I.
Ekimov.
C.
Gourdon.
K. Toba. A.V.
F-cdoro\.
Phys.
Rev.
Baranov.
[ I97
A.A.
f 10X2)
775
r\.A. Onushchenko.
So\.
Phqs. Semicond.
16
Phps. Rev.
D.M.
Colv~n.
unpublished. 2nd
Int. C‘onf. on The Ph\\~c\
vol. I. lYY4, p. 2OIY.
II. Oberhau\er.
V.C. Lywnho.
.1.M H\am.
,A. Sacra. C.B. Murra!.
h1.C; Ba~cndl.
l’hks.
72 (1994) 2612.
1.. Banqal. W. Stab.
[20]
A.I. Ekimo\.
Lett.
D.B.
II. Stelnhach.
B 54 (1996)
RX32l.
Ba\\cndl.
Phys. Re\. B 47 I I YY?) 21 I .?
[)..I. Norri\. Re\.
Phya. Rev. Lett. 74 (19951 1645.
Pantke.
G. Warnann. [IX]
Nishljima.
A. Yamanaka.
Onuahchenho. [I’]
T. Tokiraki.
of Semiconductors.
Phys. Rev.
11205. M.
M.G.
Lett. 77 (1096) 3X7?.
1171 K.-H.
AI.1.. Efrw. [I I]
B 37 (198X) 1273.
2x1s.
K. Edamntsu. B .il (19Y5)
[IO]
16 (1982) 771.
Y. Talra.
Tran
Phys. Re\.
Mittlemnn.
E. Reit\amer. hl. Wegcncl-. T
H.
Iiaug.
hlarschncr.
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