Temperature dependence of pulsed polariton lasing in a GaAs microcavity

Exemplary dispersions at various temperatures are shown in figure 1. The curves were measured at excitation powers just above the first nonlinearity observed, as will be discussed below. As can be seen from figure 1(f), the LP branch can be observed at temperatures up to T = 110 K. Thus, the regime of NMC persists over the whole temperature range over which zero detuning can be achieved on our sample. This behaviour is in agreement with other investigations [11, 12, 18]. In order to identify the polariton and photon lasing thresholds at different temperatures, we apply the two-threshold criteria presented in [15]. We first discuss the results obtained in the spectral domain, and compare these with the emission's temporal behaviour.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

From the dispersion curves shown in figure 1, the integrated intensity as well as the energetic position of the emission with zero in-plane momentum ($\left |k_{\parallel}\right |\leqslant 0.16\,\mu \mathrm {m}^{-1}$) were extracted. The evolution of both quantities in relation to the excitation power is shown in figures 3 and 4 for different temperatures up to 110 K. Let us focus first on the temperature range up to 50 K. Here, mainly three different regimes can be identified: first, starting at low excitation powers, the emission intensity increases linearly. At these polariton densities, only the thermally populated LP branch is seen, and the emission energy remains almost constant. Further, when the power is increased, a strongly nonlinear behaviour is observed in the integrated intensity, followed by a regime of sub-linear increase. In the emission energy, a distinct blue shift is observed at this first threshold P_th1, followed by a further continuous blue shift and a regime of almost constant spectral position. Note that this intermediate continuous blue shift is not that pronounced at 50 K. Further, the shape of the dispersion is observed to change at this excitation power P_th1: the dispersion curve is mainly flat in this regime [15, 19]. This first nonlinear change in intensity, energy and dispersion shape is attributed to the onset of pulsed polariton lasing.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

At higher density, denoted by P_th2 in figure 3(a), the intensity starts to increase again at least linearly, while the energy undergoes another considerable blue shift. The emission then comes predominantly from a slightly blue-shifted cavity photon mode (C_BS). This is shown exemplarily for T = 50 K in figure 2(a). Here, the system has changed to the weak coupling regime and operates as a conventional photon lasing device. Interestingly, the microcavity shows a tendency for another shift of the emission energy into the red at very high excitation powers. The emission occurs then mainly from the bare cavity mode, as can be seen in figure 2(b). However, this red shift is of the order of the emission linewidth at these densities, which is roughly 2 meV. Note also that the true linewidth of the microcavity emission is only accessible in low-noise continuous-wave measurements. Nevertheless, a non-negligible part of the emission still occurs at a blue-shifted spectral position. Moreover, for larger k_∥ values, the dispersion follows mainly that of a blue-shifted cavity mode (C_BSn), which was calculated considering a different refractive index. This change in the refractive index is known to be related to high charge carrier densities [20].

At an increased temperature of 70 K the situation is somewhat unclear: the blue shift of roughly 5.5 meV that occurs at the first threshold is comparable with half the Rabi splitting, which would suggest that the system has changed to the weak coupling regime. This can be seen in figure 1(d): the emission mode is rather close to the bare cavity mode. Also, the shape of the dispersion at larger k_∥ values is not unambiguous, as it lies between a blue-shifted LP (labelled LP_BS) and a red-shifted cavity photon mode (labelled C_RS). While a blue-shifted LP would be a hint of the persistence of NMC, a red-shifted cavity mode would point to photon lasing [21]. This would, however, be inconsistent with the blue shift of the cavity mode that we observe at excitation powers above the second threshold for T⩽50 K. Also, at higher excitation powers a second jump in the emission energy of ⩾1 meV is observed. It is only at this stage that the system is definitively in the weak coupling regime, and the emission then agrees perfectly with the cavity photon dispersion.

When going to even higher temperatures, in our experiments 90 and 110 K, only a single threshold can be seen in the accessible excitation power range. It is accompanied by a nonlinear increase in the intensity as well as by a large blue shift of 7 meV, which is half the Rabi splitting of our sample. As depicted in figures 1(e) and (f), the emission comes from the bare cavity photon mode. Contrary to the behaviour at lower temperatures, the emission energy seems to remain constant at very high emission powers at these high temperatures; the dispersion follows strictly the cavity parabola. Further, the jump in intensity at the photon lasing threshold is more prominent than the jumps at both thresholds for T ⩽ 70 K. This is expected and can be explained as follows. As shown in figure 3, the intensity of the LP below threshold decreases with temperature as non-radiative recombination processes become more relevant. However, in the regime of photon lasing, we assume that non-radiative recombination becomes negligible as radiative recombination dynamics should become faster, which results in a more pronounced jump. Note also that the reduction in photon lasing threshold excitation power at 90 K compared to the value at 70 K is in good qualitative agreement with [14].

Thus, two thresholds at excitation powers P_th1 and P_th2 have been observed in angular resolved measurements at temperatures up to 70 K. They are manifested in the clear changes in the integrated intensity as well as in the emission energy.

Let us briefly discuss the different energy shifts. At the transition to polariton lasing, the emission shifts into the blue. This blue shift is generally attributed to repulsive polariton–polariton interactions. However, another effect may also play a role. Recently, it has been shown that the ac Stark shift may induce a shift of the polariton modes into the blue [22]. Considering the magnitude of that blue shift and the necessary pump powers, the effect should certainly play only a minor role in our experiment. Further, as mentioned above, the emission just above P_th2 stems from a slightly blue-shifted cavity mode. A shift of a similar magnitude was observed in a multiple quantum-well structure and is attributed to a Stark-shifted exciton resonance [23]. However, the role of the exact spectral position of the exciton resonance in the high-particle-density regime above P_th2 should be negligible. Finally, we note that a red shift similar to the one we observe at very high excitation densities has been attributed to the electronic Kerr effect [24]. It is, however, difficult to compare these results with the present work, as the experimental conditions were quite different.

Another interesting quantity is found in the relative positions of the two thresholds, ρ_P = P_th1/P_th2, as depicted in figure 5, where all IO curves are plotted on a comparable scale. To realize comparability we express the excitation densities in fractions of the lasing threshold P_th2. Therefore, as mentioned above, we assume that in the photon lasing regime the dynamics become so fast that non-radiative recombination becomes negligible and the emitted intensity therefore becomes directly proportional to the inserted carrier density independent of temperature. While at 10 K the relative excitation density ratio of the first to the second threshold takes on a value of 0.16, it slightly decreases to 0.13 at 30 K (figure 5, inset). This finding agrees with previous studies showing that a slightly increased lattice temperature tends to lower the polariton condensate threshold for not too positive detunings. However, the exact range of detunings where this decrease of the threshold occurs was shown to vary from sample to sample and probably also depends on the excitation conditions [13, 25]. Generally, previous studies have shown the polariton bottleneck to become more efficiently suppressed at around 30 K due to beneficial phonon scattering [26].

Zoom In Zoom Out Reset image size

At even higher temperatures, ρ_P increases up to a value of 0.31 at 70 K. To some degree this increase for T > 30 K is expected and can be explained as follows: on the one hand, the Mott transition basically occurs either due to wave function overlap of the inserted carriers or due to an ionization catastrophe [27], causing screening and thus further ionization when a certain number of carriers are inserted into the system. In both cases the transition carrier density—which is assumed to coincide with P_th2—is not expected to show a significant temperature dependence unless very low temperatures way below 10 K are investigated for E_b ∼ 10 meV considered here [28]. On the other hand, it is known that the scattering rate from the exciton reservoir towards the bottom of the LP branch is inversely proportional to the exciton temperature, thus increasing also the excitation power necessary for polariton condensation [29]. Both effects lead to an increase of ρ_P.

Following [15], we now compare the spectroscopic data discussed so far with the results obtained in the temporal domain. Therefore, we monitored the equal-time second-order correlation function

$$\begin{equation} g^{(2)}(\tau=0)=\frac{\langle \hat{a}^\dagger \hat{a}^\dagger \hat{a} \hat{a} \rangle}{\langle \hat{a}^\dagger \hat{a} \rangle^2}, \end{equation} \tag{ 1 }$$

where $\hat {a}^\dagger$ and $\hat {a}$ denote photon creation and annihilation operators of the mode of interest, as well as the emission pulse duration in relation to the excitation density. The signatures of spontaneous emission in the thermal regime and photon lasing are values of g⁽²⁾(0) equal to 2 and 1, respectively, corresponding to the emission of thermal light below threshold and coherent light in the photon lasing regime. The temporal evolution of the emission pulse and thus the emission pulse duration can be derived from the same data set as used to quantify photon correlations [15]. To quantify the pulse duration, the Gaussian standard deviation has been chosen in order to facilitate correction of jitter-influenced errors at short pulse lengths [17].

Photon correlations and emission pulse durations at various temperatures are shown in figures 6 and 7, respectively. At temperatures up to 70 K two thresholds corresponding to the onset of polariton and photon lasing can be identified. At T = 10 K, the pulse duration shortens to 5 ps when approaching the first threshold and then increases again in the polariton lasing regime to approximately 17 ps. Beyond the second threshold the emission pulse duration decreases to the bare cavity lifetime of approximately 2 ps. The corresponding g⁽²⁾(0) shows a decrease from the thermal regime value of 2 towards a value close to 1 at the first threshold, reflecting thus a high degree of second-order coherence. This is followed by an increase towards values around 1.3. This increase in g⁽²⁾(0) can be explained considering scattering processes between polaritons with wave vector k_∥ = 0 and polaritons with k_∥ ≠ 0 [30, 31]. These processes increase above the threshold to polariton lasing, acting thereby as a noise source for the mode around k_∥ = 0. Consequently, this results in a loss of second-order coherence, thus increasing the g⁽²⁾(0) values at excitation powers between the two thresholds.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Above the second threshold, g⁽²⁾(0) reduces to unity, indicating the Mott transition and the onset of standard photon lasing. So far the data agree with the results presented in [15].

The positions of the two thresholds are also in good accordance with the positions of the nonlinearities in the IO curve shown in figure 3. At elevated temperatures up to 50 K, the situation is similar. Also for these temperatures, the evolution of the pulse duration and the equal-time correlations g⁽²⁾(0) show a two-threshold behaviour. However, in the polariton lasing regime the increase in pulse durations tends to decrease with increasing temperature. We interpret this behaviour in terms of an acceleration of the relaxation dynamics of the non-resonantly excited carriers towards the polariton dispersion, as discussed above. Again, the results obtained at 70 K do not allow for a clear distinction between two thresholds: while the pulse duration exhibits a small increase at intermediate powers, g⁽²⁾(0) basically decreases monotonically from a thermal to a coherent value.

At even higher temperatures the situation changes significantly. At 90 and 110 K only a single threshold is visible in both the pulse duration and the g⁽²⁾(0). It occurs at a threshold excitation density 3–10 times higher than the first threshold evidenced at lower temperatures, and roughly coincides with the excitation densities at the second threshold seen there. Therefore, we consider it a reasonable assumption to link this single threshold to the onset of standard photon lasing.