Article Cite This: J. Phys. Chem. C 2017, 121, 27751−27757
pubs.acs.org/JPCC
Ultrashort Radiation of Biexcitonic Superfluorescence from HighDensity Assembly of Semiconductor Quantum Dots Kensuke Miyajima,*,† Yuki Kumagai,† and Akira Ishikawa‡ †
Department of Applied Physics, Graduate School of Science, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, Japan ‡ Department of Science for Advanced Materials, University of Yamanashi, 4-3-11 Takeda, Kofu, Yamanashi 400-8511, Japan ABSTRACT: High-density semiconductor quantum dot (QD) assembly is a promising system to generate ultrashort radiation of superfluorescence (SF) which is a cooperative emission of many coherent excited particles induced by an interaction with a resonant radiation field. In this paper, we report the superfluorescent spectra and time profiles of biexcitons in CuCl QDs where a complete population inversion between the biexciton and exciton states was achieved by resonant two-photon excitation of biexcitons. A spontaneous emission at low excitation density changed to SF by increasing the excitation density. For a high excitation density, superfluorescent characteristics, i.e., narrowing of the pulse width and shortening of the delay time, were observed. Furthermore, broadening of the spectral width was observed, resulting from the enhancement of radiative rate of QD assembly. On the other hand, the SF at low temperature changed to an amplified spontaneous emission with the increase in temperature due to the increase in the dephasing rate. The critical temperature to generate the SF was approximately 75 K, which was considerably higher than that of other materials. We believed that the short radiative time of the biexciton caused ultrafast formation of coherence for the excited QDs. Thus, ultrashort pulsed emission from the QDs and high critical temperature in generating the SF can be realized. Considering the QD density, we expect achieve generation of short pulsed coherent emission of less than 1 ps. We conclude that the ultrashort radiation and high-temperature performance are expected SF characteristics of semiconductor QDs.
■
superfluorescence (SF).2−5 SF generation requires the following conditions. First, high-density of the isolated two-level systems (where the distances between them are sufficiently shorter than the emission wavelength) is required to realize coherent coupling between them. Second, the dephasing rate of the excited two-level system must be smaller than the enhanced radiative rate of the assembly. Third, a complete population inversion in the assembly is necessary to generate pulsed SR. Until today, SF has been mainly observed in gaseous atoms,6−9 molecules,10 and molecules embedded in solid states.11−14 For some organic materials, appearances of SF have been reported, where the narrow spectral widths or the fast decays of the emissions were claimed as evidence of the SF. However, the pulsed emission with a delay, which is a typical property of SF, was not observed.15−18 On the other hand, few reports for semiconductors are available. Dai et al. reported the SF of bound excitons in ZnTe bulk crystal.19 In addition, Kono and his group reported the SF of an electron−hole plasma in InGaAs quantum wells (QWs) with the application of an external magnetic field.20−22 On the other hand, the assembly of semiconductor quantum dots (QDs) is a promising system to generate SF because a QD can possibly be identified as an
INTRODUCTION Optical properties of semiconductor or metal nanoparticles have been investigated extensively until now. Particularly, those of single particle have been focused on mainly. On the contrary, a cooperative phenomenon of particles assembly has become a challenging and significant theme in physics and chemistry with a progress of nanofabrication techniques. A cooperative radiation from the assembly of coherent two-level systems was first reported as superradiance (SR) by Dicke in 1954.1 Dicke predicted the appearance of a pulsed radiation from the assembly by calculating the time evolution of radiative rate under the condition that all the two-level systems are excited, i.e., a complete population inversion. On the other hand, Dicke’s theory resulted in another suggestion: when only one level in the assembly is excited, the radiative rate of the coherent assembly increases in proportion to the number of two-level systems and that of an isolated one. Experimentally, the pulsed SR under complete population inversion originated from the following process. Many two-level systems are optically excited in which they are initially incoherent. Then, coherence between the excited two-level systems spontaneously occurs through interaction with a radiation field of spontaneous emission in the assembly. Therefore, the generation process of pulsed SR involves a delay from the moment when all the twolevels are excited due to the occurrence of coherence. Because of this mechanism, this pulsed SR is referred to as © 2017 American Chemical Society
Received: October 3, 2017 Revised: November 21, 2017 Published: November 21, 2017 27751
DOI: 10.1021/acs.jpcc.7b09795 J. Phys. Chem. C 2017, 121, 27751−27757
Article
The Journal of Physical Chemistry C
inhomogeneously broadened spectral width.28 In addition, this ultrashort pulsed SF exhibited a blue shift in the peak energy with the increase an excitation density.29 From these results, we suggest that the SF generation efficiency is related to the dot-size-dependent properties, e.g., radiative time. The subpicosecond excitation pulse resulted in short pulsed SF, but the influence of a large spectral width on SF generation has not yet been revealed. On the other hand, a picosecond excitation pulse is available to clarify the size-dependent properties of biexcitons and to investigate the influence of inhomogeneous broadening because the narrow spectral width of an excitation light results in the resonant excitation of the biexciton confined in a QD. The size-selective excitation of the biexciton in CuCl QDs was realized using resonant two-photon excitation,31 and the presence of appropriate photon energy to efficiently generate biexcitons for the QDs assembly was reported. In the current paper, we will report the clear characteristics of SF using picosecond excitation pulses. The excitation density dependence showed two regimes related to the change in the PL: one is for the transition from spontaneous emission to SF and the other is for the SF characteristics. The spectral width of biexciton PL was predominantly determined by not only the size distribution but also the SF radiative time. As a result, the generation of subpicosecond pulsed SF is proposed. Furthermore, the temperature dependence of SF generation was investigated. The critical temperature for SF generation was high compared with that of other materials.
isolated quantum system due to the quantization of exciton energy. Preparation of high-density assembly of QDs is possible, and a long dephasing time can be achieved from the quantization of exciton energy. SR occurrence of semiconductor QDs was reported in CdSe QDs23 and (In,Ga)As/ GaAs QDs24 where the radiative time of the assembly increased with the number of QDs. These reports correspond to the SR in the case where only one level is excited in a coherent assembly. In addition, because this mechanism of the SR is available for a metal nanoparticle assembly, the plasmonic SRs have been reported.25,26 In contrast, the present study focuses on the SF of a QD assembly, which is pulsed SR when all twolevel systems are excited. Achievement of complete population inversion between two levels in the QDs appears to be difficult because the number of excitons generated in a QD obeys a Poisson distribution when the excitons are optically excited under conventional band-to-band excitation. Therefore, controlling the population of excitons or excitonic complexes is necessary. We expect an ultrashort pulsed time profile as the SF characteristic of semiconductor QDs. Because the coherence of an assembly is triggered by spontaneous emission of two-level systems, the formation time of coherence depends on the spontaneous radiative time. The radiative time of an exciton or excitonic complexes in an isolated QD is shorter than that associated with optical transitions between electronic levels in an atom or a molecule, which results in a fast formation of coherence among QDs. Subsequently, ultrafast generation and ultrashort pulse of the SF are expected. Furthermore, the influence of inhomogeneous spectral width due to the size distribution of the QD assembly should be considered. The inhomogeneous spectral width of the QD assembly degrades the coupling of the QDs due to the increase in the dephasing rate of the assembly. However, because a shorter time width of a coherent pulse results in a wider spectral width due to the Fourier transfer limit, a large QD assembly spectral width can possibly be advantageous for generation of an ultrashort coherent pulse. Ishikawa et al. indicated that the inhomogeneous broadening of an assembly accelerates the generation of ultrashort SF when the cooperative numbers of excited dots are more than the critical value.27 The SF from biexcitons, which are bound two-exciton pairs, in CuCl QDs was reported in our previous papers.28−30 On the contrary, for the excitons, the SF was not observed because of a reabsorption process. The resonant two-photon excitation of biexcitons is useful for establishing complete population inversion between the biexciton and exciton states as an initial population state because the excitation photon energy is lower than the exciton energy. A transition process from a spontaneous emission of biexcitons to SF with the increase in excitation density was reported30 where CuCl QDs were excited using a picosecond pulse (pulse width of ∼2 ps, and spectral width of ∼3 meV). On the other hand, by using a subpicosecond pulse (pulse width of 120 fs and spectral width of 12 meV), short pulsed emission (denoted as FM28) occurred before the increase in ordinal biexciton PL (PL). This emission was also concluded to be SF because of the excitation-density dependence on the peak intensity. In this case, the large spectral width of the subpicosecond excitation light resulted in resonant excitation of the biexcitons in many QDs with a large size distribution. As a result, we suggest that ultrashort pulsed SF appeared only under two conditions: initial complete population inversion between the biexciton and exciton states and simultaneous excitation of the QD assembly with
■
EXPERIMENTAL METHODS We fabricated a sample of CuCl QDs embedded in a NaCl single crystal using the transverse Bridgman method and the succeeding heat treatment.32 The CuCl concentration prepared for the Bridgman method was 5 mol %, and the heat treatment was performed at 580 °C for 48 h. During the heat treatment, the CuCl density decreased. According to the X-ray fluorescence measurement, the actual concentration of CuCl was ∼0.2%. The average radius of the QDs was 7.4 nm, which was estimated using the peak energy of the PL excitation spectrum. The NaCl crystal, including the CuCl QDs, was cleaved to a thickness of 1.01 mm, and it was fixed in a cryostat. The time-resolved PL spectra were obtained by the optical Kerr gate method using a narrow-width pulse laser based on a regenerative amplifier (wavelength, 800 nm; time width, ∼ 3 ps; repetition time, 1 kHz). The light from the regenerative amplifier was divided into two: one for the gate light for Kerr gate spectroscopy and the other for the pump light for an optical parametric amplifier (OPA). The excitation light was obtained from the fourth-harmonic light of a signal beam from the OPA using two β-BaB2O4 crystals. The excitation light was irradiated on the sample using a cylindrical lens where the excitation area had a stripe shape with a length of 995 μm and a width of 75 μm. Then, the PL along the stripe was collected from the edge of the sample. The spectra were analyzed using a 50 cm spectrometer (2400 grating/mm) and a charge-coupled device. The time-integrated PL and time-resolved PL were obtained using the same optical paths. For the time-resolved measurement, toluene was used as Kerr medium, and the time resolution of the system was ∼4.9 ps.
■
RESULTS AND DISCUSSION The excitation density dependence of the PL spectra at 3 K is shown in Figure 1a. The excitation photon energy was 3.186 27752
DOI: 10.1021/acs.jpcc.7b09795 J. Phys. Chem. C 2017, 121, 27751−27757
Article
The Journal of Physical Chemistry C
Figure 2. (a) Excitation-density dependence of the PL intensities of the M band in the time-integrated PL spectra (TI intensity: solid squares) and peak intensities in the PL time profiles (TR intensity: solid circles), together with delay times in the PL time profiles (open circles). The delay times are indicated in the right axis, and the PL intensities are indicated in the left axis. (b) Excitation-density dependence of the spectral width of the M band in the time-integrated PL spectra (solid circles) and delay times in the PL time profiles (open circles).
Figure 1. (a) Excitation-density dependence of the time-integrated PL spectra at 3 K. The PL band denoted by M is caused by the biexcitons. The strong signal indicated by the arrow is due to the scattered excitation light, whose photon energy is 3.185 eV. The PL line denoted by I1 is due to the exciton trapped in the neutral acceptors. The BM band is caused by the bound biexcitons. (b) Excitationdensity dependence of the PL time profiles at the peak of the M band. At the lowest trace, the profile of the excitation light is also shown. The excitation densities of all results are indicated at the right-hand side.
inhomogeneous width of the excited QD assembly) to 3.5 meV. These changes indicate a transition from spontaneous emission to SF. The coherent coupling among the QDs with equivalent transition energy resulted in narrowing the spectral width. Simultaneously, in the time profiles, the increase in the SF component resulted in the pulsed profile with a long delay time, which reached 25 ps. In contrast, in the high-excitationdensity regime of over 2.4 mJ/cm2, the delay time deceased. Then, it reached 10 ps, and the spectral width slightly increased up to 4.0 meV. From these results, we concluded that the SF component was dominant in the observed PL band. The decrease in the delay time with the increase in the number of excited QDs is one of the typical features of the SF3,5. In addition, we can reasonably conclude that broadening of the spectral width was induced by narrowing of the time width of the time profile, although it did not completely obey the Fourier transfer limit. This classification of the excitation density regime is supported by the excitation-density dependence of the PL intensities. Because of the resonant two-photon absorption process of biexcitons, the density of the biexcitons increased in proportion with the square of the excitation density. At low excitation density, the PL intensities nonlinearly increased with the excitation density to the power of 2.4 for the time-integrated intensity and to the power of 4.0 for the peak intensity of the time profiles. This result indicates that the increase in the SF component emitted along the excitation length enhanced the nonlinearity. In particular, because the PL intensities dramatically increased (to the power of 4.4 for the integrated intensity and ∼10 for the peak intensity) when the excitation density crossed over the border between the two regimes, we found that the SF components increased. In the high excitation density, the time-integrated intensity and the peak intensity of the time profile obeyed the power of 2.3 and 3.2, respectively. This dependence is almost 2.0 and 4.0 for ideal SF profiles when all the excited QDs are related to the observed PL intensities. Above 4.0 mJ/cm2, the PL intensities became saturated. It is suggested that this saturation originates from a limitation of the number of the QDs in the excited volume. From the results of the excitation-density dependence, we concluded that the biexciton’s PL changed from spontaneous emission to SF. Subsequently, we examined the influence of the dephasing rate of the QDs on the SF generation according to
eV, which corresponds to the resonant energy of two-photon absorption of biexcitons.31 The excitation density was increased from 0.4 to 6.4 mJ/cm2. The PL band at 3.160 eV, which is denoted as M, was caused by the biexcitons. The peak at 3.186 eV represented the excitation light. In the low excitationdensity case, the PL of the bound biexciton (BM) and the exciton bound to a neutral acceptor (I1) were observed at 3.169 and 3.177 eV, respectively.33 Moreover, a broad band around 3.170 eV was also observed due to the other impurity levels. Although the M band overlapped with the tails due to the PL band impurity at the lowest excitation density (0.4 mJ/cm2), it became clear with the increase in the excitation density due to the superlinear increase. The PL peak energy was almost constant, but the spectral width became narrow up to 2.4 mJ/ cm2. Then, it broadened under a high excitation-density range. Figure 1b shows the time profiles at 3.160 eV corresponding to the peak energy of the M band. At the lowest excitation density, the time profile showed an exponential decay with a decay time of 70 ps, which is almost consistent with the reported spontaneous lifetime of the biexciton, i.e., ∼80 ps.30 The rise time to the peak was determined by the propagation time of light in the excited length. With the increase in the excitation density, the time profile gradually changed to a pulsed profile with a long delay to the peak. For an excitation density of over 2.4 mJ/cm2, the pulsed profile changed with the decrease in the delay time and time width. The intensities and spectral widths of the PL band were derived from the PL spectra shown in Figure 1a, and the delay times to the peak and the peak intensities were obtained from the time profiles shown in Figure 1b. Figure 2a shows the PL intensities of the PL spectra, the peak intensities of the time profiles and the delay times to the peaks as a function of the excitation density. Figure 2b shows the spectral width of the M band and the delay times to the peaks as a function of the excitation density. Figure 2b shows that the features of the M band were classified into two excitation-density regimes. In the low-excitation-density regime of up to 2.4 mJ/cm2, the spectral width decreased from 15 meV (which reflected the 27753
DOI: 10.1021/acs.jpcc.7b09795 J. Phys. Chem. C 2017, 121, 27751−27757
Article
The Journal of Physical Chemistry C
classified into three temperature regions. In the low-temperature region (T < 50 K), the delay time was 5 ps at 3 K, which was the lowest value, and gradually increased with the increase in the temperature. In the middle-temperature region (50 K < T < 75 K), the delay time steeply increased and reached the maximum value of 25 ps at 75 K. In the high-temperature region (T > 75 K), the delay time decreased. These changes can be explained by the transition from the SF to amplified spontaneous emission (ASE), similar to that reported for O2−:KCl.12,13 The change in the spectral width in the same temperature regions was also analyzed. In the low-temperature region, the spectral width at 3 K was 4.9 meV, and it gradually decreased with the increase in temperature and then reached the minimum value of 4.0 meV at 50 K. The spectral width slightly increased in the middle-temperature region, and it started to dramatically increase in the high-temperature region. From these results, the transition process from SF to ASE can be described as follows. At the lowest temperature, a pulsed SF with the shortest delay time and shortest time width was observed. The spectral width was mainly determined by the pulse width. With the increase in temperature, the formation time of the coherence in the excited QDs became longer due to the increase in the dephasing rate, which resulted in longer delay and longer time width of the SF. These events occurred in the low-temperature region (T < 50 K). We suggest that the decrease in the spectral width was induced from broadening of the time width of the SF, which was described above, as a typical feature of the SF in the high-excitation density regime. In the middle-temperature region, the ASE components started to mix with the dominant SF components in the observed PL. In the time profile, the rapid increase in the delay time resulted from the increase in the dephasing rate. The delay time reached a maximum of 25 ps at 75 K. On the other hand, the increase in the spectral width was not due to the time width of the SF but to the onset of the contribution of the inhomogeneous width. In the high-temperature region, because the SF component was eliminated and the ASE component became dominant, the delay time decreased. The steep increase in the spectral width indicated inhomogeneous broadening of the PL band of the biexcitons although it did not reflect the size distribution completely because of the high excitation density. Consequently, in this temperature region, the ASE components became predominant. We will discuss the temperature dependence of the PL intensity shown in Figure 4a. A noticeable change in the PL intensity was observed in the low-temperature region. The PL intensity from 3 to 20 K decreased and was almost constant up to approximately 60 K. In general, the PL intensity decreased with the increase in the temperature because of the nonradiative rate due to the exciton−phonon interaction. However, because this mechanism did not agree with the existence of a plateau from 20 to 60 K, another mechanism was inferred. The experimental results showed that the inhomogeneous width of the QD assembly was larger than the radiative width of the SF. In other words, a partial assembly was associated with the SF among all QDs. When the radiative width increased with narrowing of the time width, the size-distribution of the QDs, which involved the SF, was extended. Consequently, cooperative number N was enhanced with the increase in the radiative width. As a result, the PL intensity of the SF from 20 to 3 K increased when the spectral width gradually increased. On the other hand, the PL intensity sharply decreased around 75 K. In this case, we suggest that the disappearance of the SF
the temperature dependence. The temperature dependence of the PL spectra and the time profiles at the PL peak energy are shown in Figure 3, parts a and b, respectively. The excitation
Figure 3. (a) Temperature-dependence of the PL spectra. The PL band denoted by M is due to the biexcitons. The downward arrows show the excitation photon energy, which is tuned by considering the change in the bandgap energy. The excitation density is fixed at 6.0 mJ/cm2. (b) Temperature dependence of the time profiles at the peak of the M band. All temperatures are indicated at the right-hand side.
density was fixed at 6.0 mJ/cm2, which was sufficiently high to generate the SF at low temperature. Because the bandgap energy depends on the temperature,34 the excitation photon energy was tuned to correspond to the resonant two-photon excitation energy of the biexcitons when the temperature changed. The PL peak energy of the M band also shifted to higher energy following the change in the bandgap energy. The time profile of the SF at low temperature changed to a longer pulsed profile with the increase in the delay time up to 75 K. Then, it changed to an ordinal exponential-decay profile at higher temperature. At 90 K, the PL decay time was obtained to be 20 ps from the fitting using the exponential function. Figure 4a shows the temperature dependence of the PL intensities obtained from the time-integrated band and the peak intensity of the time profile. Figure 4b shows the temperature dependence of the delay times on the peaks obtained from the time profile and the spectral widths of the time-integrated PL band. The change in the delay time shown in Figure 4b is
Figure 4. (a) Temperature-dependence of the PL intensities of the M band in the time-integrated PL spectra (TI intensity: solid squares) and peak intensities in the PL time-profiles (TR intensity; solid circles). (b) Temperature dependence of the delay time in the PL profiles (open circles) and the spectral width of the M band (solid circles). 27754
DOI: 10.1021/acs.jpcc.7b09795 J. Phys. Chem. C 2017, 121, 27751−27757
Article
The Journal of Physical Chemistry C
reflected the decrease in the time width of the coherent pulse. Further, in the temperature-dependence case, the spectral width is associated with the time width of the pulsed emission in the low-temperature region. We supposed that if the SF were a Fourier-limited pulse, the shortest time width of the SF could be ∼350 fs at 3 K, where the SF time profile obeys the squared hyperbolic second function. On the other hand, from the relationship between cooperative lifetime τr and time width Δt, namely, Δt = τr × [ln(2πN)1/2],40 the pulse width was calculated to be 1.96 ps, which was inconsistent with the value expected from the spectral width. However, considering that the actual cooperative number increased with the broadening of the homogeneous width, the pulse width could be narrow at low temperature and high excitation density. We can expect that the pulse width of the SF would be less than a picosecond. Detailed discussion of the change in the time width or PL intensity requires higher time resolution of the time-resolved or single-shot measurement in the future.
component mainly contributed to this steep decrease in the intensity. The change in the PL intensity did not follow the change in the nonradiative rate of the biexcitons. In the SF generation mechanism, the nonradiative rate results in reducing cooperative number N. According to previous reports, from 2 to 77 K, the decay time of the biexciton decreased by several tens of percentage.33,35 Both the decrease in cooperative number N and increase in the dephasing rate resulted in the disappearance of the SF and steep decrease in the PL intensity. In this paper, we discuss the possibility of ultrashort pulsed emission of the SF in semiconductor QDs. Cooperative lifetime τr is a key parameter for SF generation, which is defined as τr = 8πτsp/3ρλ2l,3,5 where τsp is the radiative time due to spontaneous emission, ρ is the dot density, λ is the wavelength, and l is the excited length of the medium. In this experiment, τsp = 80 ps, λ = 263 nm in the matrix, and l = 955 μm. Here, dot density ρ is approximately 2 × 1015 cm−3 from the actual density of CuCl of ∼0.2 mol % and average dot radius of 7.4 nm. As a result, τr was calculated to be 2.6 fs. In addition, we need to consider the actual cooperative number by considering the inhomogeneous width of the QDs. Because no report is available on the dephasing rate of the biexcitons in CuCl QDs, we used the homogeneous width of the biexciton in CuCl bulk crystal at 5 K, which is 0.1 meV.36 The inhomogeneous width due to the size distribution was determined as 15 meV from the spectral width at 0.4 mJ/cm2. Hence, the cooperative lifetime of the SF in the CuCl QDs system was estimated to be 420 fs, which is shorter than that of KCl:O2− reported as 2.7 ps.12 We can conclude that the shorter cooperative lifetime results in a fast formation time of the coherence and short pulsed emission. Furthermore, the short cooperative lifetime results in high critical temperature for SF generation. Our experimental result, namely 75 K, in the CuCl QDs is quite high compared with that of KCl:O2−, which was reported as 23 K.12 The distinction between ASE and SF is associated with dephasing time T2, delay time τD, and cooperative lifetime τr. In other words, the emission is attributed to ASE if τr ≪ T2 ≪ (τrτD)1/213 and it is an SF characteristic if T2 ≫ (τrτD)1/2. Figure 4b shows that the critical temperature for generating the SF was 75 K. (τrτD)1/2 was calculated to be 3.2 ps at 75 K using the values τr = 420 fs and τD = 25 ps, which were obtained from the experimental result shown in Figure 4b. On the other hand, at this temperature, the dephasing time of the biexciton in the CuCl bulk was T2 = 0.6 ps, calculated at 75 K.31 Because T2 was shorter than (τrτD)1/2, the observation of the SF was contradictory. However, considering the suppression of the dephasing rate due to the quantum effects, this value is probable even if SF was generated. Therefore, we consider that this QDs system can be sufficient in observing SF at high temperature. Finally, we discuss the time width of the SF. The time resolution of our experimental setup was 4.9 ps; thus, estimating a time width of less than a picosecond was difficult. In addition, the excitation length of 995 μm affected the SF time profile. The normalized time profile of the scattered excitation light is shown in Figure 1b. The time width of the PL is comparable to that of the excitation light. In addition, the SF showed fluctuation of its time profile in every event because it was triggered by spontaneous emission.11,37−39 Unfortunately, this fluctuation is impossible to obtain because of the limitation of our experimental procedure using the optical Kerr gate method. However, in the excitation-density dependence, the spectral width increased with high excitation density, which
■
CONCLUSION In conclusion, the generation of SF from the biexcitons in CuCl QDs has been studied using the excitation-density dependence associated with the number of excited QDs. The transition process from spontaneous emission to SF was clearly observed. In particular, the changes in the pulsed time profiles and spectral width in the integrated spectra were remarkable. Simultaneous observations of the shortening of the time width and broadening of the spectral width implied the generation of SF following the Fourier transfer limit. In addition, the transition from SF to ASE was observed with the increase in temperature corresponding to the increase in the dephasing rate. The critical temperature of 75 K was high. In the case of organic materials, the generation of the SF at room temperature has been claimed but the pulsed profile with the delay was unclear and the critical temperature has not been shown.15−18 The SF generation at 125 K was reported for InGaAs QWs by applying an external magnetic field of 10 T.22 However, the SF of the CuCl QDs occurred without any external field. One of the reasons in realizing such high critical temperature is the fast formation of macro coherence due to the short spontaneous emission time of the biexciton. In addition, suppression of the dephasing rate due to quantum confinement effect in the QDs supports an increase in the critical temperature. The spectral width of the SF and the estimation from the QD density indicate the possibility of generating SF pulsed emission with a time width of less than 1 ps. Our findings will open a new paradigm in optical phenomena of semiconductor QDs, which is related to the coherent behavior of a QD assembly.
■
AUTHOR INFORMATION
Corresponding Author
*(K.M.) E-mail:
[email protected]. Telephone: +81-3-58761717. ORCID
Kensuke Miyajima: 0000-0002-7586-1409 Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS The work was supported by JSPS KAKENHI Grant Number 26400320. 27755
DOI: 10.1021/acs.jpcc.7b09795 J. Phys. Chem. C 2017, 121, 27751−27757
Article
The Journal of Physical Chemistry C
■
(21) Noe, G. T., II; Kim, J.; Lee, J.; Wang, Y.; Wójcik, A. K.; McGill, S. A.; Reitze, D. H.; Belyanin, A. A.; Kono, J. Giant superfluorescent bursts from a semiconductor magneto-plasma. Nat. Phys. 2012, 8, 219−224. (22) Cong, K.; Wang, Y.; Kim, J.; Noe, G. T., II; McGill, S. A.; Belyanin, A.; Kono, J. Superfluorescence from photoexcited semiconductor quantum wells: Magnetic field, temperature, and excitation power dependence. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 235448. (23) Scheibner, M.; Schmidt, T.; Worschech, L.; Forchel, A.; Bacher, G.; Passow, T.; Hommel, D. Superradiance in quantum dots. Nat. Phys. 2007, 3, 106−110. (24) Mazur, Y. I.; Dorogan, V. G.; Marega, E., Jr; Cesar, D. F.; LopezRichard, V.; Marques, G. E.; Zhuchenko, Z. Y.; Tarasov, G. G.; Salamo, G. J. Cooperative Effects in the Photoluminescence of (In,Ga)As/ GaAs Quantum Dot Chain Structures. Nanoscale Res. Lett. 2010, 5, 991−1001. (25) Iida, T. Control of Plasmonic Superradiance in Metallic Nanoperticle Assembly by Light-Induced Force and Fluctuations. J. Phys. Chem. Lett. 2012, 3, 332−336. (26) Tokonami, S.; Hidaka, S.; Nishida, K.; Yamamoto, Y.; Nakao, H.; Iida, T. Multipole Superradiance from Densely Assembled Metallic Nanoparticles. J. Phys. Chem. C 2013, 117, 15247−15252. (27) Ishikawa, A.; Miyajima, K.; Ashida, M.; Itoh, T.; Ishihara, H. Theory of Superfluorescence in Highly Inhomogeneous Quantum Systems. J. Phys. Soc. Jpn. 2016, 85, 034703. (28) Miyajima, K.; Kagotani, Y.; Saito, S.; Ashida, M.; Itoh, T. Superfluorescent pulsed emission from biexcitons in an ensemble of semiconductor quantum dots. J. Phys.: Condens. Matter 2009, 21, 195802. (29) Miyajima, K.; Maeno, K.; Saito, S.; Ashida, M.; Itoh, T. Biexcitonic superfluorescence from CuCl quantum dots under resonant two-photon excitation. Phys. Status Solidi C 2011, 8, 209− 212. (30) Phuong, L. Q.; Miyajima, K.; Maeno, K.; Itoh, T.; Ashida, M. Transitions from spontaneous emission to stimulated emission and superfluorescence of biexcitons confined in CuCl quantum dots. J. Lumin. 2013, 133, 77−80. (31) Sato, G.; Akatsu, T.; Miyajima, K. Biexciton generation processes for CuCl quantum dot ensembles. Mater. Res. Express 2016, 3, 025002. (32) Itoh, T.; Iwabuchi, Y.; Kataoka, M. Study on the Size and Shape of CuCl Microcrystals Embedded in Alkali-Chloride Matrices and Their Correlation with Exciton Confinement. Phys. Status Solidi B 1988, 145, 567−577. (33) Yano, S.; Goto, T.; Itoh, T.; Kasuya, A. Dynamics of excitons and biexcitons in CuCl nanocrystals embedded in NaCl at 2 K. Phys. Rev. B: Condens. Matter Mater. Phys. 1997, 55, 1667−1672. (34) Göbel, A.; Ruf, T.; Cardona, M.; Lin, C. T.; Wrzesinski, J.; Steube, M.; Reimann, K.; Merle, J.-C.; Joucla, M. Effects of the isotopic composition on the fundamental gap of CuCl. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 15183−15190. (35) Yano, S.; Yamamoto, A.; Goto, T.; Kasuya, A. Relaxation processes of photoexcited carriers in CuCl nanocrystals embedded in NaCl. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 7203−7207. (36) Vanagas, E.; Kudrna, J.; Brinkmann, D.; Gilliot, P.; Hönerlage, B. Phase relaxation dynamics of excitons and biexcitons in CuCl studied by femtosecond and picosecond degenerate four-wave mixing. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 63, 153201. (37) Polder, D.; Schuurmans, M. F. H.; Vrehen, Q. H. F. Superfluorescence: Quantum-mechanical derivation of MaxwellBloch description with fluctuating field source. Phys. Rev. A: At., Mol., Opt. Phys. 1979, 19, 1192−1203. (38) Haake, F.; King, H.; Schröder, G.; Haus, J.; Glauber, R. Fluctuations in superfluorescence. Phys. Rev. A: At., Mol., Opt. Phys. 1979, 20, 2047−2063. (39) Haake, F.; Haus, J. W.; King, H.; Schröder, G.; Glauber, R. Delay-time statistics of superfluorescent pulses. Phys. Rev. A: At., Mol., Opt. Phys. 1981, 23, 1322−1333.
REFERENCES
(1) Dicke, R. H. Coherence in Spontaneous Radiation Processes. Phys. Rev. 1954, 93, 99−110. (2) Rehler, N. E.; Eberly, J. H. Supperradiance. Phys. Rev. A: At., Mol., Opt. Phys. 1971, 3, 1735−1751. (3) Bonifacio, R.; Lugiato, L. A. Cooperative radiation processes in two-level systems: Superfluorescence. Phys. Rev. A: At., Mol., Opt. Phys. 1975, 11, 1507−1521. (4) Bonifacio, R.; Lugiato, L. A. Cooperative radiation processes in two-level systems: Superfluorescence II. Phys. Rev. A: At., Mol., Opt. Phys. 1975, 12, 587−598. (5) MacGillivray, J. C.; Feld, M. S. Theory of superradiance in an extended, optically thick medium. Phys. Rev. A: At., Mol., Opt. Phys. 1976, 14, 1169−1189. (6) Gibbs, H. M.; Vrehen, Q. H. F.; Hikspoors, H. M. J. Single-Pulse Superfluorescence in Cesuim. Phys. Rev. Lett. 1977, 39, 547−550. (7) Gross, M.; Fabre, C.; Pillet, P.; Haroche, S. Observation of NearInfrared Dicke Superradiance on Cascading Transitions in Atomic Sodium. Phys. Rev. Lett. 1976, 36, 1035−1038. (8) Flusberg, A.; Mossberg, T.; Hartmann, S. R. Observation of Dicke Superradiance at 1.30 μm in Atomic Tl Vapor. Phys. Lett. A 1976, 58A, 373−374. (9) Paradis, E.; Barrett, B.; Kumarakrishnan, A.; Zhang, R.; Raithel, G. Observation of superfluorescent emissions from laser-cooled atoms. Phys. Rev. A: At., Mol., Opt. Phys. 2008, 77, 043419. (10) Skribanowitz, N.; Herman, I. P.; MacGillivray, J. C.; Feld, M. S. Observation of Dicke Superradiance in Optically Pumped HF Gas. Phys. Rev. Lett. 1973, 30, 309−312. (11) Florian, R.; Schwan, L. O.; Schmid, D. Time-resolving experiments on Dicke superfluorescence of O2− centers in KCl. Two-color superfluorescence. Phys. Rev. A: At., Mol., Opt. Phys. 1984, 29, 2709−2715. (12) Malcuit, M. S.; Maki, J. J.; Simkin, D. J.; Boyd, R. W. Transition from Superfluorescence to Amplified Spontaneous Emission. Phys. Rev. Lett. 1987, 59, 1189−1192. (13) Maki, J. J.; Malcuit, M. S.; Raymer, M. G.; Boyd, R. W.; Drummond, P. D. Influence of collisional dephasing process on superfluorescence. Phys. Rev. A: At., Mol., Opt. Phys. 1989, 40, 5135− 1542. (14) Ashida, M.; Arai, H.; Morikawa, O.; Kato, R. Luminescence and superfluorescence-like emission from a thin layer of O2− centers in KBr crystal. J. Lumin. 1997, 72−74, 624−625. (15) Frolov, S. V.; Vardeny, Z. V.; Yoshino, K. Cooperative and stimulated emission in poly(p-phenylene-vinylene) thin films and solutions. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 9141− 9147. (16) Hiramatsu, T.; Matsuoka, N.; Yanagi, H.; Sasaki, F.; Hotta, S. Gain-narrowed emissions of thiophene/phenylene co-oligomer single crystals. Phys. Status Solidi C 2009, 6, 338−341. (17) Belfield, K. D.; Bondar, M. V.; Yao, S.; Mikhailov, I. A.; Polikanov, V. S.; Przhonska, O. V. Femtosecond Spectroscopy of Superfluorescent Fluorenyl Bensothiadiazoles with Large Two-Photon and Excited-State Absorption. J. Phys. Chem. C 2014, 118, 13790− 13800. (18) Shang, H.; Shimotani, H.; Ikeda, S.; Kanagasekaran, T.; Oniwa, K.; Jin, T.; Asao, N.; Yamamoto, Y.; Tamura, H.; Abe, K.; Kanno, M.; Yoshizawa, M.; Tanigaki, K. Comparative Study of Single and Dual Gain-Narrowed Emission in Thiophene/Furan/Phenylene CoOligomer Single Crystal. J. Phys. Chem. C 2017, 121, 2364−2368. (19) Dai, D. C.; Monkman, A. P. Observation of superfluorescence from a quantum ensemble of coherent excitons a ZnTe crystal: Evidence for spontaneous Bose−Einstein condensation of excitons. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 115206. (20) Jho, Y. D.; Wang, X.; Kono, J.; Reitze, D. H.; Wei, X.; Belyanin, A. A.; Kocharovsky, V. V.; Kocharovsky, Vl. V.; Solomon, G. S. Cooperative Recombination of a Quantized High-Density ElectronHole Plasma in Semiconductor Quantum Wells. Phys. Rev. Lett. 2006, 96, 237401. 27756
DOI: 10.1021/acs.jpcc.7b09795 J. Phys. Chem. C 2017, 121, 27751−27757
Article
The Journal of Physical Chemistry C (40) MacGillivray, J. C.; Feld, M. S. Limits of superradiance as a process for achieving short pulses of high energy. Phys. Rev. A: At., Mol., Opt. Phys. 1981, 23, 1334−1349.
27757
DOI: 10.1021/acs.jpcc.7b09795 J. Phys. Chem. C 2017, 121, 27751−27757
