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Polariton-condensation effects on photoluminescence dynamics in a CuBr microcavity
Journal of Luminescence 191 (2017) 68–72
Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Polariton-condensation effects on photoluminescence dynamics in a CuBr microcavity Masaaki Nakayama n, Katsuya Murakami, Yoshiaki Furukawa Department of Applied Physics, Graduate School of Engineering, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 3 August 2016 Received in revised form 17 February 2017 Accepted 21 February 2017 Available online 22 February 2017
Temporal profiles of photoluminescence (PL) from the cavity polariton at the ground state in a CuBr microcavity at 10 K have been investigated from the viewpoint of the cavity-polariton condensation. We measured angle-resolved reflectance spectra to characterize the cavity-polariton dispersions, cavityphoton dispersion, and quality factor from which the intrinsic cavity-polariton lifetime was estimated. The threshold-like changes of the PL intensity, band width, and energy of the lower polariton as a function of excitation power are consistent with previously reported experimental results for the cavitypolariton condensation. It was found that the PL rise and decay times are markedly decreased by the cavity-polariton condensation, which can be attributed to the appearance of the bosonic final state stimulation and intrinsic lifetime of polaritons in the relaxation and decay processes, respectively. & 2017 Elsevier B.V. All rights reserved.
Keywords: Microcavity CuBr Cavity-polariton condensation Photoluminescence dynamics
1. Introduction In a semiconductor microcavity, exciton polaritons, the socalled cavity polaritons, are formed by strong coupling between excitons and cavity photons [1]. For the past decade, much attention has been paid to Bose-Einstein condensation and polariton lasing from nonequilibrium condensates in microcavities owing to the bosonic nature of the cavity polariton [2–16]. The effective mass of the cavity polariton is very light relative to that of a bare exciton: typically of the order of 10 4, which is a great merit for cavity-polariton condensation because achieving unity for the occupancy at the ground state is considerably easy. From the viewpoint of thermal stability of the cavity polariton, wide-gap semiconductors such as GaN and ZnO were used as an active layer in the microcavities because of the large exciton binding energies: Eb ¼ 26 (63) meV for GaN (ZnO) [17]. In fact, room-temperature condensation was realized in GaN [4,7,9,10,15] and ZnO microcavities [14,15]. The exciton binding energies of cuprous halides such as CuBr, CuCl, and CuI are large: Eb ¼108, 190, and 58 meV, respectively [17]. We showed that the Rabi splitting energy, which is also called normal mode splitting, in CuBr and CuCl microcavities is of the order of 100 meV [18,19]. Such a large Rabi splitting energy leads to the high stability of strong coupling in cavity-polariton condensation because of the following reason. With an increase in excitation power, the energy of a lower polariton (LP) usually exhibits a blueshift owing to cavity-polariton n
Corresponding author. E-mail address: [email protected] (M. Nakayama).
http://dx.doi.org/10.1016/j.jlumin.2017.02.045 0022-2313/& 2017 Elsevier B.V. All rights reserved.
renormalization [2–16]. When the blueshifted LP energy at an inplane wave vector k// ¼0 approaches the bottom of the cavityphoton dispersion, the strong coupling becomes unstable and turns to a weak coupling regime [20]. Therefore, the large Rabi splitting prevents the strong coupling from turning to weak coupling in relatively high density excitation. In our recent work [16], we demonstrated the cavity-polariton condensation at 77 K in a CuBr microcavity. Furthermore, we showed that the dispersion relation of condensates is flat around k// ¼0, which is possibly attributed to the diffusive Goldstone mode peculiar to nonequilibrium condensation [21]. In the present work, we have investigated the cavity-polariton condensation effect on the photoluminescence (PL) dynamics in a CuBr microcavity with HfO2/SiO2 distributed Bragg reflectors (DBRs). The experimental data of angle-resolved reflectance spectra were used to analyze the fundamental characteristics of the cavity polaritons in the CuBr microcavity using a phenomenological Hamiltonian for the strong coupling. The cavity-polariton condensation was examined by the excitation power dependence of steady-state PL spectra of the LP at the ground state from the viewpoint of threshold-like changes of the intensity, band width, and energy. Our finding is the fact that the PL rise and decay times are dramatically shortened by the cavity-polariton condensation.
2. Experimental details We prepared a CuBr microcavity with HfO2/SiO2 DBRs on a (0001) Al2O3 substrate. The CuBr active layer thickness was λ = λEX / εb [22]; namely, the sample belongs to a bulk microcavity.
M. Nakayama et al. / Journal of Luminescence 191 (2017) 68–72
The symbols, λEX and εb, are the resonant wavelength of the lowest-lying exciton and background dielectric constant, respectively: λ ¼ 208 nm for λEX ¼418.5 nm and εb ¼4.062 in CuBr [17]. The bottom and top DBRs, which were fabricated at room temperature by rf magnetron sputtering, consisted of 15.5 and 12.5 periods, respectively. Each DBR was terminated by a HfO2 layer. Commercially supplied plates of HfO2 with a purity of 99.9% and SiO2 with a purity of 99.99% were used as the targets in sputtering. The sputtering gas was Ar under a pressure of 0.5 Pa. The CuBr active layer was grown at 60 °C by vacuum deposition using CuBr powders with a purity of 99.999% in 5 10 6 Pa. The growth rates of HfO2, SiO2, and CuBr were monitored during the deposition process using a crystal oscillator. It was confirmed from X-ray diffraction patterns that the crystalline CuBr layer is oriented in the [111] direction. The excitation light source in PL measurements was a modelocked Ti:sapphire laser with a pulse duration of 140 fs and a repetition rate of 76 MHz. The excitation energy was 3.351 eV that was the second harmonic generation light of the fundamental laser. Note that the excitation energy is far above the stop band of the DBR. An objective lens was used for both excitation and detection of the PL. The angles of excitation and detection were perpendicular to the sample surface, θ ¼0°, corresponding to k// ¼0. The diameter of the excitation light on the sample surface was 40 μm. The excitation light and PL were separated by a beam splitter and a pin hole, which determined the angular resolution, was set after the beam splitter for the PL detection. The angular resolution was 75°. Steady-state PL spectra were detected using a cooled charge coupled device attached to a 32 cm single monochromator with a resolution of 0.15 nm. The PL decay profiles were measured using a streak camera system with a time resolution of 15 ps and a spectral resolution of 0.2 nm. Moreover, angle-resolved reflectance spectra were measured to evaluate the characteristics of the cavity-polariton dispersions. The probe light was a Xe lamp and a collimator attached to a goniometer was used to control the incident angle: The angular resolution was 72°. The reflectance spectrum was analyzed with the same monochromator system used in the steady-state PL measurement. All of the optical measurements were performed at 10 K.
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3. Results and discussion We first describe the characteristics of the cavity polariton in the CuBr microcavity. The excitonic system in a CuBr crystal with a zincblende structure consists of the Zf, Z1,2, and Z3 excitons at the Γ point. The Zf exciton corresponds to a triplet exciton; however, its oscillator strength is considerably increased by mixing between the triplet and singlet excitons [23]. The Z1,2 (Z3) exciton is assigned to the degenerate heavy-hole and light-hole excitons (splitoff-hole exciton). Therefore, it is expected that the strong coupling between the three excitons and the cavity photon produces four cavity polaritons: the LP, middle polariton 1 (MP1), MP2, and upper polariton (UP) [18]. Fig. 1(a) shows angle-resolved reflectance spectra at various incident angles from 0° to 50° in the CuBr microcavity. Three kinds of reflectance dip indicated by solid circles, open circles, and solid squares are attributed to the LP, MP1, and MP2, respectively [18]. We could not observe a reflectance signal from the UP because of strong absorption by the exciton continuum state, the energy region of which overlaps with that of the UP [24]. The apparent quality factor was estimated to be Qa ¼ ELP/ ΔEdip ¼7.5 102, where ELP and ΔEdip are the LP energy and full width at half maximum (FWHM) of the reflectance dip at θ ¼0°, respectively. Fig. 1(b) shows the dispersion relations of the cavity polaritons (solid curves) and cavity photon (dashed curve) estimated from the analysis of the incident angle dependence of reflectance dip energies indicated by the solid circles, open circles, and solid squares, where the horizontal dashed lines depict the energies of the Zf, Z1,2, and Z3 excitons obtained from an absorption spectrum [18]. The analysis was based on a phenomenological Hamiltonian for the strong coupling between the three excitons and cavity photon. The details of the analysis method are described in Ref. [18]. The Rabi splitting energies obtained from the analysis are 33, 114, and 89 meV for the Zf, Z1,2, and Z3 excitons, respectively. The energy of the cavity photon at θ ¼0° is Eph(0)¼2.978 eV and the detuning from the Zf exciton is þ 14 meV. Here, we discuss the intrinsic LP lifetime, τLP, at θ ¼0°, which is given by 1/τLP ¼ |XZ(f)|2/τZ(f) þ |XZ(1,2)|2/τZ(1,2) þ|XZ(3)|2/τZ(3) þ|C|2/τph [11,16], where |XZ(f)|2 (τZ(f)), |XZ(1,2)|2 (τZ(1,2)), and |XZ(3)|2 (τZ(3)) are the relative fractions (lifetimes) of the Zf, Z1,2, and Z3 excitons, respectively, and |C|2 and τph are the relative fraction and lifetime
Fig. 1. (a) Angle-resolved reflectance spectra at various incident angles from 0° to 50° in the CuBr microcavity. (b) Dispersion relations of the cavity polaritons (solid curves) and cavity photon (dashed curve) estimated from the analysis of the incident angle dependence of reflectance dip energies using a phenomenological Hamiltonian for the strong coupling, where the horizontal dashed lines depict the energies of the Zf, Z1,2, and Z3 excitons.
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M. Nakayama et al. / Journal of Luminescence 191 (2017) 68–72
Fig. 2. Relative fractions of the Zf, Z1,2, and Z3 excitons and cavity photon in the LP as a function of incident angle.
of the cavity photon, respectively. The relative fraction, which is also called the Hopfield coefficient, corresponds to the square of the eigenvector of the phenomenological Hamiltonian used in the analysis of the cavity-polariton dispersions. Fig. 2 shows the
relative fractions of the Zf, Z1,2, and Z3 excitons and cavity photon in the LP as a function of incident angle. The values of |XZ(f)|2, |XZ 2 2 2 (1,2)| , |XZ(3)| , and |C| at θ ¼ 0° are 0.05, 0.44, 0.03, and 0.48, respectively: The sum of the relative fractions is unity. The major relative fractions are |XZ(1,2)|2 and |C|2. The cavity-photon lifetime is given by τph ¼Q/(2πEph(0)/h) [25]. Here, we have to correct the apparent quality factor Qa using the relative fractions because the LP consists of the excitons and cavity photon. The corrected quality factor is Q¼Qa/|C|2 ¼1.6 103. Thus, the cavity-photon lifetime is calculated to be τph ¼ 0.35 ps. The lifetime of the Z1,2 exciton, which is the major exciton component of the LP, was reported to be 150 ps [26]. The exciton lifetime is much longer than τph. As a result, the intrinsic LP lifetime is approximately calculated to be τLP E τph/|C|2 ¼0.73 ps, which will be compared with PL decay times later. This very short lifetime suggests the occurrence of nonequilibrium cavity-polariton condensation in this sample because thermalization by acoustic phonon scattering is usually longer than the lifetime. Fig. 3(a) shows the excitation power dependence of the PL spectrum in the CuBr microcavity, where the vertical dashed line indicates the LP energy obtained from the angle-resolved reflectance spectrum at θ ¼0°. Note that the excitation power was corrected with the transmittance of the top DBR, 74%, at the
Fig. 3. (a) Excitation power dependence of the PL spectrum in the CuBr microcavity, where the vertical dashed line indicates the LP energy obtained from the angle-resolved reflectance spectrum at θ¼ 0°. (b) Integrated intensity, (c) FWHM, and (d) peak energy of the LP-PL band as a function of excitation power. The dashed line in (b) indicates the fitted excitation power dependence of the PL intensity below the threshold: IPL∝P1.2. The solid lines are guides for the eye.
M. Nakayama et al. / Journal of Luminescence 191 (2017) 68–72
excitation energy far above the stop band. An excitation power of 1.0 mW corresponds to excitation fluence of 1.0 μJ/cm2. The PL peak energy at the lowest excitation power, 1.0 mW, is in agreement with the LP energy. This reveals the fact that the PL band originates from the LP at θ ¼0°, i.e. the ground state. The PL peak energy shifts to high energy side with an increase in excitation power, which reflects the cavity-polariton renormalization due to many-body effects. Figs. 3(b), 3(c), and 3(d) show the integrated intensity, FWHM, and peak energy of the LP-PL band, respectively, as a function of excitation power. It is evident that the excitation power dependence of the PL characteristics exhibits a thresholdlike change at 15 mW indicated by the vertical dashed line. The dashed green line in Fig. 3(b) indicates the fitted excitation power dependence of the integrated PL intensity below the threshold: IPL∝P1.2. The excitation power dependence exceeds the linear dependence. This suggests that polariton-polariton scattering, which exhibits the square dependence in principle, slightly contributes to the relaxation process of the LP. Note that the peak energy at 25 mW, 2.925 eV, is much lower than Eph(0) ¼2.978 eV, which clearly means that the strong coupling for the cavity polariton is fully stable above the threshold. Consequently, the threshold-like changes of the PL characteristics at 15 mW are consistent with the previous reports for the cavity-polariton condensation [2–4,7,12]. The photogenerated carrier density n at the threshold excitation power (fluence, F¼ 15 μJ/cm2) was estimated to be 1.1 1018 cm 3 using n ¼F/(eEexc) [1–exp(–αL)]/L because the excitation pulse duration is shorter than the cavity-photon lifetime, where e is the electron charge, Eexc ¼ 3.351 eV is the excitation energy, L ¼208 nm is the active layer thickness of CuBr, and α ¼8.2 104 cm 1 [27] is the absorption coefficient at Eexc. The Mott transition density was estimated to be 2.7 1019 cm 3 in the framework of random phase approximation [16]; therefore, the stability of the excitonic system completely holds in the cavitypolariton condensation regime. Hereafter, we describe the cavity-polariton condensation effect on the LP-PL dynamics. The temporal LP-PL profiles (open circles) at 10, 15, and 20 mW are shown in Fig. 4, where the system response is depicted by solid blue circles. The detection energy was fixed at the PL peak energy. Because the temporal PL profile
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obviously consists of rise, fast decay, and slow decay components, it is phenomenologically expressed as IPL(t)¼ –Ir exp(–t/τr)þ If exp (–t/τf) þIs exp(–t/τs), where τr, τf, and τs are the rise, fast decay, and slow decay times, respectively, and Ir ¼If þIs. The solid curves in Fig. 4 indicate the fitted results using a convolution method for the system response and IPL(t). The rise and decay times at 10 mW below the condensation threshold were estimated to be τr ¼16, τf ¼ 64, and τs ¼4.1 102 ps. The error in the fitting was 78%. The slow decay component can be assigned to donor-acceptor pair (DAP) recombination because the LP-PL band locates at the energy region of a broad DAP-PL band in CuBr [28]. As described above, the estimated LP lifetime is 0.73 ps. Thus, the fast decay component does not originate from the intrinsic LP decay process. Trapping processes of excitons at defects and impurities in the exciton reservoir may elongate the decay time [4]. It should be noted that the rise and decay times of the LP PL are markedly shortened by the cavity-polariton condensation. As shown in Fig. 4, the rise and fast decay components fully overlap with the system response at 15 and 20 mW. Therefore, the rise and decay times are estimated to be shorter than 2 ps that is the sampling time interval in the streak camera system. The very short rise time indicates that the LP relaxation process is dramatically accelerated by the cavity-polariton condensation. This can be explained by bosonic final state stimulation leading to non-equilibrium condensation [11,29]. The bosonic final state stimulation corresponds to stimulated scattering of the LP into the ground state under the condition that the occupancy at k// ¼0 is of the order of unity owing to the bosonic nature of the cavity polariton. We believe that the very short decay time reflects the intrinsic LP lifetime, 0.73 ps, because the bosonic final state stimulation eliminates the exciton trapping process elongating the decay time. The slow decay times estimated from fitting the temporal PL profiles, 60 and 61 ps, at 15 and 20 mW are almost equal to the fast decay time below the condensation threshold. This fact suggests that non-condensates of the cavity polariton remain in the condensation regime, which may be due to spatial inhomogeneity of the CuBr microcavity.
4. Conclusions We have investigated the PL dynamics of the LP at the ground state in the CuBr microcavity from the viewpoint of the cavitypolariton condensation examined by the excitation power dependence of the intensity, FWHM, and peak energy of the LP PL. The threshold-like changes of the PL characteristics as a function of excitation power are consistent with the previously reported experimental results for the cavity-polariton condensation. The decay time of the LP PL below the condensation threshold, 64 ps, is much longer than the estimated intrinsic cavity-polariton lifetime, 0.73 ps. In addition, the PL rise time is relatively long: 16 ps. The prominent finding is that the PL rise and decay times are markedly decreased by the cavity-polariton condensation, less than 2 ps. The possible origins of dramatically shortening the rise and decay times are the acceleration of the cavity-polariton relaxation process by the bosonic final state stimulation peculiar to nonequilibrium condensation and appearance of the intrinsic LP lifetime in the decay process.
Acknowledgement Fig. 4. Temporal LP-PL profiles (open circles) at 10, 15, and 20 mW, where the system response is depicted by solid blue circles. The solid curves indicate the fitted results using a convolution method for the system response and IPL(t).
This work was supported by a KAKENHI Grant Number 15H03678 from Japan Society for the Promotion of Science.
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Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Polariton-condensation effects on photoluminescence dynamics in a CuBr microcavity Masaaki Nakayama n, Katsuya Murakami, Yoshiaki Furukawa Department of Applied Physics, Graduate School of Engineering, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 3 August 2016 Received in revised form 17 February 2017 Accepted 21 February 2017 Available online 22 February 2017
Temporal profiles of photoluminescence (PL) from the cavity polariton at the ground state in a CuBr microcavity at 10 K have been investigated from the viewpoint of the cavity-polariton condensation. We measured angle-resolved reflectance spectra to characterize the cavity-polariton dispersions, cavityphoton dispersion, and quality factor from which the intrinsic cavity-polariton lifetime was estimated. The threshold-like changes of the PL intensity, band width, and energy of the lower polariton as a function of excitation power are consistent with previously reported experimental results for the cavitypolariton condensation. It was found that the PL rise and decay times are markedly decreased by the cavity-polariton condensation, which can be attributed to the appearance of the bosonic final state stimulation and intrinsic lifetime of polaritons in the relaxation and decay processes, respectively. & 2017 Elsevier B.V. All rights reserved.
Keywords: Microcavity CuBr Cavity-polariton condensation Photoluminescence dynamics
1. Introduction In a semiconductor microcavity, exciton polaritons, the socalled cavity polaritons, are formed by strong coupling between excitons and cavity photons [1]. For the past decade, much attention has been paid to Bose-Einstein condensation and polariton lasing from nonequilibrium condensates in microcavities owing to the bosonic nature of the cavity polariton [2–16]. The effective mass of the cavity polariton is very light relative to that of a bare exciton: typically of the order of 10 4, which is a great merit for cavity-polariton condensation because achieving unity for the occupancy at the ground state is considerably easy. From the viewpoint of thermal stability of the cavity polariton, wide-gap semiconductors such as GaN and ZnO were used as an active layer in the microcavities because of the large exciton binding energies: Eb ¼ 26 (63) meV for GaN (ZnO) [17]. In fact, room-temperature condensation was realized in GaN [4,7,9,10,15] and ZnO microcavities [14,15]. The exciton binding energies of cuprous halides such as CuBr, CuCl, and CuI are large: Eb ¼108, 190, and 58 meV, respectively [17]. We showed that the Rabi splitting energy, which is also called normal mode splitting, in CuBr and CuCl microcavities is of the order of 100 meV [18,19]. Such a large Rabi splitting energy leads to the high stability of strong coupling in cavity-polariton condensation because of the following reason. With an increase in excitation power, the energy of a lower polariton (LP) usually exhibits a blueshift owing to cavity-polariton n
Corresponding author. E-mail address: [email protected] (M. Nakayama).
http://dx.doi.org/10.1016/j.jlumin.2017.02.045 0022-2313/& 2017 Elsevier B.V. All rights reserved.
renormalization [2–16]. When the blueshifted LP energy at an inplane wave vector k// ¼0 approaches the bottom of the cavityphoton dispersion, the strong coupling becomes unstable and turns to a weak coupling regime [20]. Therefore, the large Rabi splitting prevents the strong coupling from turning to weak coupling in relatively high density excitation. In our recent work [16], we demonstrated the cavity-polariton condensation at 77 K in a CuBr microcavity. Furthermore, we showed that the dispersion relation of condensates is flat around k// ¼0, which is possibly attributed to the diffusive Goldstone mode peculiar to nonequilibrium condensation [21]. In the present work, we have investigated the cavity-polariton condensation effect on the photoluminescence (PL) dynamics in a CuBr microcavity with HfO2/SiO2 distributed Bragg reflectors (DBRs). The experimental data of angle-resolved reflectance spectra were used to analyze the fundamental characteristics of the cavity polaritons in the CuBr microcavity using a phenomenological Hamiltonian for the strong coupling. The cavity-polariton condensation was examined by the excitation power dependence of steady-state PL spectra of the LP at the ground state from the viewpoint of threshold-like changes of the intensity, band width, and energy. Our finding is the fact that the PL rise and decay times are dramatically shortened by the cavity-polariton condensation.
2. Experimental details We prepared a CuBr microcavity with HfO2/SiO2 DBRs on a (0001) Al2O3 substrate. The CuBr active layer thickness was λ = λEX / εb [22]; namely, the sample belongs to a bulk microcavity.
M. Nakayama et al. / Journal of Luminescence 191 (2017) 68–72
The symbols, λEX and εb, are the resonant wavelength of the lowest-lying exciton and background dielectric constant, respectively: λ ¼ 208 nm for λEX ¼418.5 nm and εb ¼4.062 in CuBr [17]. The bottom and top DBRs, which were fabricated at room temperature by rf magnetron sputtering, consisted of 15.5 and 12.5 periods, respectively. Each DBR was terminated by a HfO2 layer. Commercially supplied plates of HfO2 with a purity of 99.9% and SiO2 with a purity of 99.99% were used as the targets in sputtering. The sputtering gas was Ar under a pressure of 0.5 Pa. The CuBr active layer was grown at 60 °C by vacuum deposition using CuBr powders with a purity of 99.999% in 5 10 6 Pa. The growth rates of HfO2, SiO2, and CuBr were monitored during the deposition process using a crystal oscillator. It was confirmed from X-ray diffraction patterns that the crystalline CuBr layer is oriented in the [111] direction. The excitation light source in PL measurements was a modelocked Ti:sapphire laser with a pulse duration of 140 fs and a repetition rate of 76 MHz. The excitation energy was 3.351 eV that was the second harmonic generation light of the fundamental laser. Note that the excitation energy is far above the stop band of the DBR. An objective lens was used for both excitation and detection of the PL. The angles of excitation and detection were perpendicular to the sample surface, θ ¼0°, corresponding to k// ¼0. The diameter of the excitation light on the sample surface was 40 μm. The excitation light and PL were separated by a beam splitter and a pin hole, which determined the angular resolution, was set after the beam splitter for the PL detection. The angular resolution was 75°. Steady-state PL spectra were detected using a cooled charge coupled device attached to a 32 cm single monochromator with a resolution of 0.15 nm. The PL decay profiles were measured using a streak camera system with a time resolution of 15 ps and a spectral resolution of 0.2 nm. Moreover, angle-resolved reflectance spectra were measured to evaluate the characteristics of the cavity-polariton dispersions. The probe light was a Xe lamp and a collimator attached to a goniometer was used to control the incident angle: The angular resolution was 72°. The reflectance spectrum was analyzed with the same monochromator system used in the steady-state PL measurement. All of the optical measurements were performed at 10 K.
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3. Results and discussion We first describe the characteristics of the cavity polariton in the CuBr microcavity. The excitonic system in a CuBr crystal with a zincblende structure consists of the Zf, Z1,2, and Z3 excitons at the Γ point. The Zf exciton corresponds to a triplet exciton; however, its oscillator strength is considerably increased by mixing between the triplet and singlet excitons [23]. The Z1,2 (Z3) exciton is assigned to the degenerate heavy-hole and light-hole excitons (splitoff-hole exciton). Therefore, it is expected that the strong coupling between the three excitons and the cavity photon produces four cavity polaritons: the LP, middle polariton 1 (MP1), MP2, and upper polariton (UP) [18]. Fig. 1(a) shows angle-resolved reflectance spectra at various incident angles from 0° to 50° in the CuBr microcavity. Three kinds of reflectance dip indicated by solid circles, open circles, and solid squares are attributed to the LP, MP1, and MP2, respectively [18]. We could not observe a reflectance signal from the UP because of strong absorption by the exciton continuum state, the energy region of which overlaps with that of the UP [24]. The apparent quality factor was estimated to be Qa ¼ ELP/ ΔEdip ¼7.5 102, where ELP and ΔEdip are the LP energy and full width at half maximum (FWHM) of the reflectance dip at θ ¼0°, respectively. Fig. 1(b) shows the dispersion relations of the cavity polaritons (solid curves) and cavity photon (dashed curve) estimated from the analysis of the incident angle dependence of reflectance dip energies indicated by the solid circles, open circles, and solid squares, where the horizontal dashed lines depict the energies of the Zf, Z1,2, and Z3 excitons obtained from an absorption spectrum [18]. The analysis was based on a phenomenological Hamiltonian for the strong coupling between the three excitons and cavity photon. The details of the analysis method are described in Ref. [18]. The Rabi splitting energies obtained from the analysis are 33, 114, and 89 meV for the Zf, Z1,2, and Z3 excitons, respectively. The energy of the cavity photon at θ ¼0° is Eph(0)¼2.978 eV and the detuning from the Zf exciton is þ 14 meV. Here, we discuss the intrinsic LP lifetime, τLP, at θ ¼0°, which is given by 1/τLP ¼ |XZ(f)|2/τZ(f) þ |XZ(1,2)|2/τZ(1,2) þ|XZ(3)|2/τZ(3) þ|C|2/τph [11,16], where |XZ(f)|2 (τZ(f)), |XZ(1,2)|2 (τZ(1,2)), and |XZ(3)|2 (τZ(3)) are the relative fractions (lifetimes) of the Zf, Z1,2, and Z3 excitons, respectively, and |C|2 and τph are the relative fraction and lifetime
Fig. 1. (a) Angle-resolved reflectance spectra at various incident angles from 0° to 50° in the CuBr microcavity. (b) Dispersion relations of the cavity polaritons (solid curves) and cavity photon (dashed curve) estimated from the analysis of the incident angle dependence of reflectance dip energies using a phenomenological Hamiltonian for the strong coupling, where the horizontal dashed lines depict the energies of the Zf, Z1,2, and Z3 excitons.
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Fig. 2. Relative fractions of the Zf, Z1,2, and Z3 excitons and cavity photon in the LP as a function of incident angle.
of the cavity photon, respectively. The relative fraction, which is also called the Hopfield coefficient, corresponds to the square of the eigenvector of the phenomenological Hamiltonian used in the analysis of the cavity-polariton dispersions. Fig. 2 shows the
relative fractions of the Zf, Z1,2, and Z3 excitons and cavity photon in the LP as a function of incident angle. The values of |XZ(f)|2, |XZ 2 2 2 (1,2)| , |XZ(3)| , and |C| at θ ¼ 0° are 0.05, 0.44, 0.03, and 0.48, respectively: The sum of the relative fractions is unity. The major relative fractions are |XZ(1,2)|2 and |C|2. The cavity-photon lifetime is given by τph ¼Q/(2πEph(0)/h) [25]. Here, we have to correct the apparent quality factor Qa using the relative fractions because the LP consists of the excitons and cavity photon. The corrected quality factor is Q¼Qa/|C|2 ¼1.6 103. Thus, the cavity-photon lifetime is calculated to be τph ¼ 0.35 ps. The lifetime of the Z1,2 exciton, which is the major exciton component of the LP, was reported to be 150 ps [26]. The exciton lifetime is much longer than τph. As a result, the intrinsic LP lifetime is approximately calculated to be τLP E τph/|C|2 ¼0.73 ps, which will be compared with PL decay times later. This very short lifetime suggests the occurrence of nonequilibrium cavity-polariton condensation in this sample because thermalization by acoustic phonon scattering is usually longer than the lifetime. Fig. 3(a) shows the excitation power dependence of the PL spectrum in the CuBr microcavity, where the vertical dashed line indicates the LP energy obtained from the angle-resolved reflectance spectrum at θ ¼0°. Note that the excitation power was corrected with the transmittance of the top DBR, 74%, at the
Fig. 3. (a) Excitation power dependence of the PL spectrum in the CuBr microcavity, where the vertical dashed line indicates the LP energy obtained from the angle-resolved reflectance spectrum at θ¼ 0°. (b) Integrated intensity, (c) FWHM, and (d) peak energy of the LP-PL band as a function of excitation power. The dashed line in (b) indicates the fitted excitation power dependence of the PL intensity below the threshold: IPL∝P1.2. The solid lines are guides for the eye.
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excitation energy far above the stop band. An excitation power of 1.0 mW corresponds to excitation fluence of 1.0 μJ/cm2. The PL peak energy at the lowest excitation power, 1.0 mW, is in agreement with the LP energy. This reveals the fact that the PL band originates from the LP at θ ¼0°, i.e. the ground state. The PL peak energy shifts to high energy side with an increase in excitation power, which reflects the cavity-polariton renormalization due to many-body effects. Figs. 3(b), 3(c), and 3(d) show the integrated intensity, FWHM, and peak energy of the LP-PL band, respectively, as a function of excitation power. It is evident that the excitation power dependence of the PL characteristics exhibits a thresholdlike change at 15 mW indicated by the vertical dashed line. The dashed green line in Fig. 3(b) indicates the fitted excitation power dependence of the integrated PL intensity below the threshold: IPL∝P1.2. The excitation power dependence exceeds the linear dependence. This suggests that polariton-polariton scattering, which exhibits the square dependence in principle, slightly contributes to the relaxation process of the LP. Note that the peak energy at 25 mW, 2.925 eV, is much lower than Eph(0) ¼2.978 eV, which clearly means that the strong coupling for the cavity polariton is fully stable above the threshold. Consequently, the threshold-like changes of the PL characteristics at 15 mW are consistent with the previous reports for the cavity-polariton condensation [2–4,7,12]. The photogenerated carrier density n at the threshold excitation power (fluence, F¼ 15 μJ/cm2) was estimated to be 1.1 1018 cm 3 using n ¼F/(eEexc) [1–exp(–αL)]/L because the excitation pulse duration is shorter than the cavity-photon lifetime, where e is the electron charge, Eexc ¼ 3.351 eV is the excitation energy, L ¼208 nm is the active layer thickness of CuBr, and α ¼8.2 104 cm 1 [27] is the absorption coefficient at Eexc. The Mott transition density was estimated to be 2.7 1019 cm 3 in the framework of random phase approximation [16]; therefore, the stability of the excitonic system completely holds in the cavitypolariton condensation regime. Hereafter, we describe the cavity-polariton condensation effect on the LP-PL dynamics. The temporal LP-PL profiles (open circles) at 10, 15, and 20 mW are shown in Fig. 4, where the system response is depicted by solid blue circles. The detection energy was fixed at the PL peak energy. Because the temporal PL profile
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obviously consists of rise, fast decay, and slow decay components, it is phenomenologically expressed as IPL(t)¼ –Ir exp(–t/τr)þ If exp (–t/τf) þIs exp(–t/τs), where τr, τf, and τs are the rise, fast decay, and slow decay times, respectively, and Ir ¼If þIs. The solid curves in Fig. 4 indicate the fitted results using a convolution method for the system response and IPL(t). The rise and decay times at 10 mW below the condensation threshold were estimated to be τr ¼16, τf ¼ 64, and τs ¼4.1 102 ps. The error in the fitting was 78%. The slow decay component can be assigned to donor-acceptor pair (DAP) recombination because the LP-PL band locates at the energy region of a broad DAP-PL band in CuBr [28]. As described above, the estimated LP lifetime is 0.73 ps. Thus, the fast decay component does not originate from the intrinsic LP decay process. Trapping processes of excitons at defects and impurities in the exciton reservoir may elongate the decay time [4]. It should be noted that the rise and decay times of the LP PL are markedly shortened by the cavity-polariton condensation. As shown in Fig. 4, the rise and fast decay components fully overlap with the system response at 15 and 20 mW. Therefore, the rise and decay times are estimated to be shorter than 2 ps that is the sampling time interval in the streak camera system. The very short rise time indicates that the LP relaxation process is dramatically accelerated by the cavity-polariton condensation. This can be explained by bosonic final state stimulation leading to non-equilibrium condensation [11,29]. The bosonic final state stimulation corresponds to stimulated scattering of the LP into the ground state under the condition that the occupancy at k// ¼0 is of the order of unity owing to the bosonic nature of the cavity polariton. We believe that the very short decay time reflects the intrinsic LP lifetime, 0.73 ps, because the bosonic final state stimulation eliminates the exciton trapping process elongating the decay time. The slow decay times estimated from fitting the temporal PL profiles, 60 and 61 ps, at 15 and 20 mW are almost equal to the fast decay time below the condensation threshold. This fact suggests that non-condensates of the cavity polariton remain in the condensation regime, which may be due to spatial inhomogeneity of the CuBr microcavity.
4. Conclusions We have investigated the PL dynamics of the LP at the ground state in the CuBr microcavity from the viewpoint of the cavitypolariton condensation examined by the excitation power dependence of the intensity, FWHM, and peak energy of the LP PL. The threshold-like changes of the PL characteristics as a function of excitation power are consistent with the previously reported experimental results for the cavity-polariton condensation. The decay time of the LP PL below the condensation threshold, 64 ps, is much longer than the estimated intrinsic cavity-polariton lifetime, 0.73 ps. In addition, the PL rise time is relatively long: 16 ps. The prominent finding is that the PL rise and decay times are markedly decreased by the cavity-polariton condensation, less than 2 ps. The possible origins of dramatically shortening the rise and decay times are the acceleration of the cavity-polariton relaxation process by the bosonic final state stimulation peculiar to nonequilibrium condensation and appearance of the intrinsic LP lifetime in the decay process.
Acknowledgement Fig. 4. Temporal LP-PL profiles (open circles) at 10, 15, and 20 mW, where the system response is depicted by solid blue circles. The solid curves indicate the fitted results using a convolution method for the system response and IPL(t).
This work was supported by a KAKENHI Grant Number 15H03678 from Japan Society for the Promotion of Science.
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