1. Introduction

Recently light sources incorporating pronounced quantum mechanics based properties like single photon sources or coherent sources of entangled photons have become of high interest for applications in quantum information processing and quantum cryptography [1, 2]. In order to realize these structures individual emitters have to be placed in high quality resonators where they are used to populate the cavity modes with individual photons. During the last few years, a variety of studies on semiconductor based cavities with embedded quantum dots (QDs) has been carried out in the framework of cavity quantum electrodynamics studies. This has allowed one to observe the regimes of weak and strong coupling in solid state micro- and nanocavities [3, 4, 5, 6]. In addition, lasing based on a low number of QDs has been observed in high quality cavities [7, 8, 9]. Semiconductor cavities with QDs are particularly appealing for studies of single quantum dot lasing effects as they permit to observe pronounced cavity quantum electrodynamics effects. First indications of single dot influence on the lasing characteristics have been reported recently for microdisk based microcavities [10]. Here, we present detailed studies of single quantum dot lasing effects in high Q micropillar cavities.

Semiconductor quantum dots have been widely investigated due to their potential to realize lasers with attractive properties including temperature independent low laser thresholds and high efficiencies [11, 12]. These semiconductor lasers are typically based on thousands of quantum dots, as the gain of an individual dot is by far too small to overcome the losses of these devices. Due to variations of the quantum dots in size and composition the properties of these lasers are largely determined by inhomogeneous broadening effects, which suppress the importance of ideal dot properties. As many dots are required to sustain lasing, conventional laser structures are not suitable for the realization of a source of coherent photons from a single emitter. An ultimate solid state laser would be reached if the gain provided by a single dot would be strong enough to overcome the losses of the cavity. In general, the average number of photons n_SQD emitted spontaneously by a single resonant QD into the cavity mode can be expressed by [13]

Here β denotes the spontaneous emission (SE) coupling factor, which describes the fraction of the spontaneous emission coupled into the cavity mode and f_QD is the occupation probability of the quantum dot by a single exciton. τ_sp and τ_ph represent the spontaneous emission lifetime of the exciton and the photon lifetime of the resonantly coupled quantum dot microcavity system, respectively.

In order to observe lasing, i.e., the emission of a coherent stream of photons, the average number of photons in the cavity has to be larger than unity [14]. As β and f_QD cannot exceed 1, Eq. 1 essentially requires the photon lifetime to be of the order or larger than the spontaneous emission lifetime of the emitter in order to realize a single QD laser. It is well known, that both time scales can be tailored widely by using high quality resonator structures. In these resonators high reflectivity of the mirrors is reflected in a long photon lifetime, which is related to the cavity quality factor Q and the photon frequency ω by τ_ph=Q/ω. Simultaneously, the spontaneous lifetime of an emitter on resonance with the cavity is shortened significantly in high-Q microcavities [3, 4, 15] and becomes comparable to τ_ph which should result in a considerable single quantum dot gain contribution.

2. Growth, fabrication, and test set-up

We have investigated the contribution of individual quantum dot excitons to lasing in optically pumped high-Q micropillar laser structures. The cavities are based on epitaxially grown Bragg reflectors formed by 30 (bottom) and 26 (top) quarter wavelength layer pairs of AlAs and GaAs, between which a GaAs cavity with a thickness of one wavelength of the laser light is inserted. Photons are generated by a low density (n≈1×10¹⁰ cm^-2) layer of InGaAs quantum dots with an In content of approximately 45 % placed in the center of the cavity. In order to obtain lateral mode confinement, high quality micropillars were etched with diameters of d_c=1.6 µm and a height of about 6 µm. Details on the fabrication technology are given in Ref. 16. In order to investigate single quantum dot gain effects, the number of non resonant QD excitons contributing to lasing should be as small as possible. Based on the QD density of the wafer, we estimate that there are in total about 200 dots within the active layer of the 1.6 µm diameter micropillar. The average spectral density of single dot transitions close to the cavity mode depends on the wafer position and amounts to 1-5 QD exciton lines per meV for the pillars used in this study. The low spectral density of non resonant QD transitions is crucial for the investigation of the role of individual QDs on lasing. On the other hand, non resonant dots provide a background population of the optical mode, e.g., by a self-tuning mechanism described in Ref. 8.

The transition from spontaneous emission to laser operation was investigated by optical pumping at 514 nm with an Argon-ion laser in continuous wave (CW) mode or by pumping at 790 nm with a mode-locked Ti:Sapphire laser providing 150 fs pulses. The micropillar cavities were mounted in a variable temperature cryostat in order to tune individual QDs through the resonance with the cavity mode. The tuning makes use of the different temperature dependences of the band gap and of the refractive index, resulting in a pronounced shift of the quantum dot exciton energies with temperature and a comparatively small temperature dependence of the optical mode, respectively [5]. The emitted light was dispersed by a 1 m double monochromator and detected by a LN₂ cooled CCD. The spectral resolution of the CW set-up is about 30 µeV. Photon correlation experiments were performed in pulsed mode using a Hanbury Brown & Twiss setup consisting of a 50/50 fiber-coupled beam splitter and two single photon counting modules with a time resolution of 700 ps in combination with a 0.55 m monochromator providing a spectral resolution of about 70 µeV.

3. Experimental results

3.1 Experiments under continuous wave excitation

The inset in Fig. 1 shows photoluminescence (PL) spectra from a micropillar (pillar A) used for the CW lasing studies recorded at low excitation power (10 µW). The off-resonance spectrum at 25 K includes the cavity mode (C) with a spectral width of γ_c=85 µeV (FWHM) at an energy E_c=1.33744 eV, as well as a single QD exciton emission line (X). We determine a quality factor Q of 16.000 for the laser cavity. By decreasing the temperature, the QD exciton X is shifted in resonance with the cavity mode C at 18 K which is associated with a strongly enhanced emission intensity of the exciton line due to the Purcell effect. The average spectral density of single dot transitions close to the cavity mode is of the order of 2-4 dots per meV for this pillar. This ensures that only a small number of non-resonant QDs contributes to lasing and enables the investigation of the role of individual resonant QDs on lasing.

 

Fig. 1. Dependence of the output intensity on the excitation power for an optically pumped (CW at 514 nm) quantum dot micropillar laser structure (pillar A) with a diameter d_c of 1.6 µm. X: Quantum dot exciton, C: Cavity mode. For T=T_res=18 K (X on resonance with C, full dots) we observe a steeper slope of the output versus the pump power than in the off-resonance case at T=25 K (detuning by 0.2 meV, open circles). The high slope section of the output starts at lower pump for the on-resonance case indicating a lower laser threshold due to the single dot on resonance. Inset: Photoluminescence spectrum at low excitation intensity (CW, 10 µW) at a temperature of 18 K (single dot emission line X on-resonance with C) and 25 K (off-resonance case). The empty cavity mode has a Q-factor of about 16000 (γ_c=85 µeV).

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Figure 1 shows the output intensity of the micropillar laser versus the pumping power with the QD exciton on-resonance (18 K, solid points) and off-resonance (25 K, open circles). In both cases we observe lasing associated with a superlinear increase of the output intensity above the threshold power. Due to the high quality factor of our structure a significant part of the spontaneous emission is coupled into the lasing mode, in particular when the QD is on resonance. This results in a rather smooth transition from spontaneous to stimulated emission at threshold. The single dot contribution results in a steeper increase of the light output versus pumping power and in a shift of the onset of the steep slope section of the light output trace, i.e. the lasing threshold, to lower pumping powers.

 

Fig. 2. (a) Output intensities and average photon number emitted by the laser structure (pillar A) as determined by fits with Eq. 2 versus the pump power for on-resonance (T=18 K, full dots) and off-resonance (T=25 K, open circles) conditions of the cavity mode and a single quantum dot exciton. Fitting the experimental data according to Eq. 2 yields a β-value of 0.96 (0.59) for the on- (off-) resonance case and threshold pump powers of 18 µW and 37 µW for on- and off-resonance condition, respectively. Dash–dotted line: linear output-input dependence extrapolated from the below threshold data in the non-resonant case. Inset: Off-resonance cavity mode linewidth as a function of excitation power. (b) Output intensity of pillar B as a function of the excitation power. Laser action is absent for this structure which is attributed to an insufficient background gain contribution as a result of a very low spectral density (<1 QD transition lines/meV) of non resonant QDs in the vicinity of the cavity mode. Inset: Low excitation µPL spectrum of pillar B with a diameter of 1.6 µm (Q=17.000) for T=18 K (QD exciton X on-resonance with cavity mode C) and T=24 K (off-resonance).

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The dependence of the laser output for the QD exciton on-resonance (18 K, solid dots) and off-resonance (25 K, open circles) conditions is depicted in Fig. 2(a) for a wider range of pumping powers in a double logarithmic representation. At low excitation the output depends linearly on the pumping power. For T=25 K we observe a clear deviation of the output intensity from the linear excitation dependence (indicated by the dash-dotted line) to a superlinear variation at about 35 µW, indicating the laser threshold. In the data measured on-resonance the kink of the output characteristic is much less pronounced, reflecting a particularly high β–factor. For still higher excitation powers the output intensity changes to a linear dependence again, when stimulated emission is dominating and the carrier number and the gain are clamped. The lasing action is also reflected in linewidth narrowing above threshold. This characteristic is depicted in Fig. 2(a) (inset) where the emission mode linewidth is plotted as a function of pump power. Near threshold a slight kink is observed which is associated with the phase transition into lasing [8]. A significantly different power dependence is observed for another micropillar (pillar B) for which the fundamental cavity mode with a Q-factor of 17.000 is located at a wafer position with a rather low spectral density of less than one QD transition per meV as can be seen in the inset of Fig. 2(b). Here, resonance behavior is also observed and the output intensity increases in a linear way with increasing excitation power up to about 100 µW when saturation of the intensity sets in. This behavior clearly reflects the role of background gain contribution of non-resonant QDs. While population of the cavity mode by non-resonant QDs is strong enough to reach the laser threshold for pillar A even under off-resonant conditions, a characteristic kink in the input-output curve associated with the onset of lasing is absent for pillar B even under resonance condition. The absence of lasing for pillar B is attributed to strongly reduced background gain contribution due to the low density of non-resonant QD transitions in the vicinity of the cavity mode.

Using a rate-equation approach the experimental data shown in Fig. 2(a) can be used to determine the lasing threshold defined by the average photon number in the cavity exceeding 1 and to extract the value of β. The model assumes that nonradiative recombination is negligible and relates the excitation intensity I to the photon number p in the lasing mode by [8, 14, 17]

with the scale factor A=ħω/τ_phδβ and the dimensionless parameter ζ=N ₀ βVτ_ph/τ_sp including the mode frequency ω, the photon conversion efficiency δ, the transparency carrier concentration N₀ and the volume of the active material V. Fitting the experimental data, we determine spontaneous emission coupling factors β of 0.96 and 0.59 for on- and off-resonance conditions, respectively. In particular for the on-resonance case the present value is close to the theoretical limit ß=1, as expected for the present high quality cavities. For A and ζ we obtain A=14, ζ=51 on-resonance and A=9, ζ=16 off-resonance. The relation A_on-res/A_off-ress≅β_offres/β_onres≅0.6 indicates a consistent fitting of both output dependencies. It is necessary to point out that this modeling is not free from ambiguities since the rate equations were derived for an atomic multiparticle model. It would be required to include a real semiconductor description for a more precise modeling [18]. The fits to the experimental data indicate that the threshold occurs at an external excitation power of 18 µW when the dot is on-resonance with the cavity mode, about half the value of 37 µW obtained in the off-resonance case. We would like to point out that for an excitation wavelength of 514 nm as used in the CW studies the external excitation power is about three orders of magnitude higher than the effective internal excitation power, mainly due to the strong absorption in the GaAs mirror layers of the upper DBR.

It is interesting to estimate the single dot contribution at threshold according to Eq. 1. For this estimation it is crucial to know the modified emission rates 1/τ_C and 1/τ_X when the QD is resonant with the cavity. These rates depend in turn on the coupling constant g and are given via 1/τ_X=2Im{E ₊}/ħ and 1/τ_C=2Im{E _-}/ħ by the imaginary parts of the complex Eigenenergies E _± of the Hamiltonian describing strong and weak coupling in a single quantum dot microcavity system [19]

The coupling constant g can be determined by temperature dependent measurements which allow one to vary the detuning between the QD exciton and the cavity mode. Temperature tuning for pillar A is depicted in Fig. 3(a). The QD exciton X is shifted in and out of resonance with the cavity mode C by increasing the temperature from 14 K to 25 K, where resonance associated with a strong enhancement of intensity of the exciton line is observed at 18 K. In order to describe the experimental data we applied a two oscillator model which considers interaction between the exciton mode and the cavity mode in terms of the coupling constant g [20, 21]. Best agreement with the experimental data was found for g=18 µeV for which a series of spectra was calculated under variation of the detuning and plotted in Fig. 3(b). A comparison of the extracted coupling strength of g=18 µeV with a threshold value of g_{th, strong coupling}=γ_c/4=21 µeV for the present pillar shows that our system is near the onset of strong coupling [5]. This regime is very attractive for the study of single quantum dot lasing effects since it is characterized by a strong reduction of the emitter’s spontaneous emission lifetime. On the other hand, normal mode splitting characteristic for the strong coupling regime is not observed yet which would disrupt a non-resonant pumping of the system [22]. Near the onset of strong coupling the mixing of exciton and photon mode leads not only to an increase of the exciton recombination rate but also to a decrease of the cavity decay rate. Taking further into account that the spontaneous lifetime τ_free amounts to about 600 ps as determined by ensemble measurements on a sample with a removed upper DBR, we obtain modified lifetimes of τ_X=26 ps and τ_ph=11 ps on resonance according to Eq. 3. This numbers imply a Purcell factor of τ_free/τ_X=23 and a single dot contribution of n_SQD≈0.42 (for β=1 and f_QD=1) on the mean cavity photon number, i.e., at threshold about one out of two photons is emitted by the resonant QD into the cavity mode. We would like to point out that n_SQD≈0.42 corresponds to an upper limit estimation since the spontaneous lifetime τ_X=26 ps is on the order of the carrier capture time determined to be between 15 ps and 60 ps [23, 24] which might limit the quantum dot occupation probability to f_QD<1 even for high excitation levels.

 

Fig. 3. (a) Temperature tuning of a single QD exciton (X) into resonance with the cavity mode (C) (pillar A). Strong enhancement of the exciton emission intensity is observed near resonance at 18 K. (b) Calculated spectra for a coupling strength of g=18 µeV as a function of the detuning between X and C. (c) Demonstration of the single QD gain contribution at several excitation powers below and above laser threshold of P_th≈40 µW. The dispersion of X and C depicted in the lowest panel exhibits line crossing at resonance (18 K at P=1 µW) as a sign of the weak coupling regime. The upper four panels show the output intensity, i.e. the sum of the integrated intensities of X and C, normalized to the respective off resonance value as a function of temperature. The gain contribution of a single quantum dot is reflected in the strong increase of the output intensity, i.e. the sum of the integrated intensities of X and C, at resonance. A small shift of the resonance to lower temperatures is attributed to a local heating of the pillar with increasing excitation power.

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The single dot gain contribution was further studied by temperature dependent measurements performed on pillar A at several excitation levels below, near and above laser threshold. By lineshape-fitting we obtained the integrated intensities of the exciton line and the cavity mode as a function of temperature or detuning, respectively. The sum of both intensities normalized to the respective off-resonance value is plotted in Fig. 3(c) vs. temperature for excitation powers of 1 µW, 30 µW, 70 µW and 100 µW. For the lowest excitation power of 1 µW the dispersion of the exciton line and the cavity mode is also shown. We observe crossing behavior of X and C which reflects that the coupling strength is not high enough to reach the onset of strong coupling. In fact, the sum of the emission intensities of X and C increases by a factor of 2.5 at resonance. This enhancement factor which reflects the contribution of photons emitted by the exciton X on the average photon number in the cavity is reduced to 60 % at 30 µW excitation power, i.e. slightly below off-resonance threshold power (cf. Fig. 2(a)). Even above threshold a pronounced resonance behavior is observed with a single dot gain contribution of, e.g., 30 % at 70 µW. Here, we would like to point out that the enhancement factors of 60 % and 30 % observed slightly below and above the threshold, respectively, are consistent with the above estimated single dot contribution of about 40 % at threshold. The decrease of the single dot gain contribution with increasing excitation power is mainly attributed to an enhanced population of the cavity mode by non resonant QDs at high excitation powers [8] in conjunction with a saturation of the single dot gain contribution.

3.2 Photon correlation experiments

The contribution of photons emitted by a single QD to the lasing characteristics can be investigated alternatively by photon correlation measurements. This type of measurement allows one to determine the degree of second-order coherence of a light field with intensity I, which provides information about the non-classical nature of the emitted light. Of special interest is the value g⁽²⁾(0), which is usually determined by a HBT type experiment. For QD based microcavity structures strong photon antibunching with g⁽²⁾(0)=0 is expected in the limit of a single emitter at low pumping [25], whereas g⁽²⁾(0)=1 is expected well above the laser threshold [8, 26].

In order to assess the contribution of a single QD to the lasing we performed investigations of the laser output intensity - pump power characteristics in parallel with g⁽²⁾(t) measurements under pulsed excitation. These experiments were carried out on pillar C (Q=16000, 2–4 QD transitions/meV) for which resonance of a single QD exciton with the lasing mode occurs at 25 K. The intensities in Fig. 4(a) show a clear resonance behaviour similar to the CW data shown in Fig. 2(a). In order to extract the β-factors and the threshold values for the measurement after pulsed excitation we have applied rate-equations given in Ref. 14 in conjunction with a calibration by the stationary model to determine the photon number. The rate-equations were solved numerically assuming that the photo-generated carrier density decreases exponentially after the initial laser pulse. Modeling the experimental data yields an averaged threshold power of 0.4 µW and β=0.95 on-resonance and an averaged threshold power of 0.65 µW and β=0.40 off-resonance, respectively.

 

Fig. 4. Output intensity and average photon number (a, top panel) and second order correlation function g⁽²⁾_meas(0) (b, bottom panel) of the micropillar laser (pillar C) versus time averaged pumping power (pulsed excitation at 790 nm) for a single dot exciton X on-resonance and off - resonance. Experimental data: on - resonance (T=23 K): full dots; off-resonance: open circles (T=39 K). (a) Output intensity respectively photon numbers versus pump power characteristics. Solid line: Calculation for the on-resonant case. The horizontal and vertical lines mark the laser threshold in the case of the dot being on-resonance. Dashed line: Calculation for the off-resonance case. (b) Second order correlation experiments: on-resonance: strong antibunching with g⁽²⁾_meas(0) down to 0.36 is observed at low excitation power indicating a nonclassical single dot emitter. Even at the lasing threshold for the on-resonance case (indicated by the vertical line) clear antibunching occurs, reflecting a significant single dot contribution to the lasing.

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g⁽²⁾(0) was determined at the spectral position of the cavity mode for on- and off-resonance conditions at different powers below and above the lasing threshold. As indicated by the solid dots in Fig. 4(a), we observe clear photon antibunching for low excitation powers for the on-resonance case. At the lowest excitation power (230 nW) g⁽²⁾_min(0)=0.36 is measured. Here, the nonzero value of g⁽²⁾_min(0) is attributed to the contribution from background light generated e.g. by other QD emitters in the vicinity of the cavity mode. When the QD is on-resonance we observe photon antibuching with g⁽²⁾_thres(0)~0.7 even at the lasing threshold marked by the vertical dashed line in Fig. 4.

We have used both values to estimate the single dot contribution to the spontaneous emission below threshold and to the stimulated emission at threshold. In the presence of background illumination of the cavity mode the measured g_meas⁽²⁾(0) values are related to the background free value of a single photon emitter g⁽²⁾(0)=0 via the intensity ratio ρ=S/(S+B) of the single photon signal S normalized by the total (signal and background (B)) according to [27]

For the lowest excitation power the measured g_meas⁽²⁾(0)=0.36 results in S~4 B, i.e., about 80% of the photons in the mode are due to the single dot on resonance. At the lasing threshold this rough estimate yields that about 50 % of the photons in the cavity mode are due to the single dot, which is in good agreement with the estimation given above according to Eq. 1 for a similar pillar. g_meas ⁽²⁾(0) approaches 1 above threshold pump power, which indicates that there is a transition region between the single dot emission regime and the region where more and more non-resonant QDs contribute to lasing.

In the non-resonant case (open circles in Fig. 4(b) the situation is qualitatively different with g⁽²⁾(0)≅1 at all pump powers while the onset of lasing was associated by a photon bunching behavior, i.e. g⁽²⁾(0)>1, near threshold in recent publications. However, it is clear that the tendency of observing bunching reduces a) with increasing β and b) with lowering the number of emitters contributing to lasing [18]. This prediction is in line with recent experiments where a maximum of g⁽²⁾(0) from up to 1.7 in [26] via 1.2 in [8] to 1.12 in [10] has been reported. In the off-resonance case we attribute the emission to gain contributions of about 10 QD excitons located at energies near the cavity mode. Thus the absence of photon bunching in the off-resonance data can be explained in terms of the high β of the present device in combination with the low number of about 10 non-resonant QDs contributing to lasing. Besides, a stronger influence of spontaneous emission in the high β regime might also hinder the observation of bunching near threshold due to a reduced coherence time [26]. In fact, we usually observe photon bunching near laser threshold for similar micropillar lasers showing lower Q (and lower β values) and a strong overlap of the lasing mode with the QD emission band, i.e., a larger number of QDs contributing to lasing.

4. Conclusions

In summary we have observed single dot controlled lasing effects in micropillar cavities. The contribution of a single dot exciton on resonance with the cavity mode results in an increase of the laser efficiency and a lower laser threshold compared to situations without a dot in resonance. Through intensity and correlation studies we estimate that the contribution of the resonant dot to the population of the lasing mode at threshold is about 40 - 50 percent in the present structures. Our results indicate the feasibility of semiconductor lasers based entirely on a single dot which would open up a wide variety of applications in quantum optics based communication technologies.