Polariton laser using single micropillar GaAs-GaAlAs semiconductor cavities
Polariton lasing is demonstrated on the zero dimensional states of single GaAs/GaAlAs micropillar cavities. Under non resonant excitation, the measured polariton ground state occupancy is found to be as large as . Changing the spatial excitation conditions, competition between several polariton lasing modes is observed, ruling out Bose-Einstein condensation. When the polariton state occupancy increases, the emission blueshift is the signature of self-interaction within the half-light half-matter polariton lasing mode.
pacs:78.55.Et, 71.36.+c, 78.45.+h
Boson statistics can lead to massive occupation of a single quantum state and trigger final state stimulation. This stimulation is responsible for the bright coherent emission of light in a laser. Another fascinating property of massive bosons in thermal equilibrium is their ability to accumulate in the lowest energy state under a given critical temperature. First predicted in 1925,(1) the experimental observation of Bose Einstein condensation was achieved in the mid 1990s for ultra-cold atoms.(2); (3) Demonstrating such bosonic effects with matter waves in a solid state system is very interesting both from fundamental point of view but also for applications since it could provide a new source of coherent light. Cavity polaritons are an example of quasi-particles behaving as bosons at low density.(4); (5) They are the exciton-photon mixed quasi-particles arising from the strong coupling regime between quantum well (QW) excitons and a resonant optical cavity mode. Because of their very small effective mass ( times that of the hydrogen atom) cavity polaritons are expected to condensate at unusually high temperatures (up to room temperature in wide band gap microcavities).(6) These last years, massive occupation of a polariton state has been observed in semiconductor two-dimensional (2D) cavities and attributed to Bose Einstein condensation(7); (8) or to polariton lasing.(9) More recently, polariton condensation has been claimed in a localized energy trap (10) where the trap dimensions are sufficiently large for the system to present a 2D continuum of polariton states. In these experiments, the clear distinction of a thermodynamic phase transition (Bose Einstein condensation) from a kinetic stimulated scattering (polariton lasing) is still debated.
In this letter, we demonstrate polariton lasing in micrometric sized GaAs/GaAlAs micropillar cavities. In such zero-dimensional (0D) cavities, polariton states are confined in all directions and present a well defined discretized energy spectrum.(11); (12) The absence of translation invariance lifts the wave-vector conservation selection-rules in polariton scatterings. In GaAs 2D microcavities, these selection rules are responsible for inefficient polariton-phonon or polariton-polariton scattering, preventing the build-up of a large occupancy in the lower energy states.(13); (14); (15); (16) In this work, we show that polariton scattering is very efficient in micropillar cavities. Under non resonant excitation, a threshold corresponding to a measured occupation factor equal to unity is observed, followed by a massive occupation of the lowest energy polariton state. At higher excitation power, the progressive transition from the strong to the weak coupling regime is evidenced with the onset of conventional photon lasing.
Moving the excitation spot toward the micropillar edge, non-linear emission can be triggered on higher energy polariton states. Such behavior is characteristic of a polariton laser with competing stimulated scattering toward several polariton modes. It rules out Bose-Einstein condensation where only massive occupation of the ground state is expected. Finally the spectral blueshift of the polariton laser line is shown to be induced by the polariton self-interaction within the lasing mode. This experiment is the first demonstration of a solid state matter-wave laser on 0D states.
Our sample, grown by molecular beam epitaxy, consists in a GaAlAs cavity surrounded by two GaAlAs/GaAlAs Bragg mirrors with 26 and 30 pairs in the top and bottom mirrors respectively. Three sets of four 7 nm GaAs QWs are inserted at the antinodes of the cavity mode electromagnetic field: one set is located at the center of the cavity layer and the two others at the first antinode in each mirror.(17) A wedge in the layer thickness allows continuous tuning of the cavity mode energy with respect to the QW exciton energy (). The exciton-photon detuning is defined as . 20 to 2 m size square and circular micropillars were fabricated along the wafer using electron beam lithography and reactive ion etching (see inset of Fig. 1(a)). Photoluminescence (PL) experiments are performed on single micropillars using a cw Ti:Saph laser focused onto a 3 m diameter spot with a microscope objective. For excitation powers exceeding 1 mW, the laser beam is chopped using an acousto-optic modulator with 1% duty cycle at 10 kHz. The emission is collected through the same objective, spectrally dispersed and detected with a nitrogen cooled CCD camera. The sample is maintained at 10 K in a cold finger cryostat. The laser is tuned to the first reflectivity minimum on the high energy side of the mirror stop-band (around 740 nm), typically 80 meV above the exciton resonance.
In micrometer sized pillar cavities, photons are confined along all directions: vertically by the Bragg mirrors and laterally by the index of refraction contrast between air and semiconductor. As a result, micropillars exhibit discrete 0D photon modes.(11) In the strong coupling regime, polaritons come from the mixing between each of these 0D photon modes and the QW excitons.(12) Fig. 1(a) presents a PL spectrum measured on a single 4 diameter circular micropillar. The emission energies measured on micropillars of identical diameter along the cavity wedge are summarized in fig.1(b). The emission spectrum in fig. 1(a) presents several discrete emission lines on the low energy side of the exciton line centered around 1607 meV. The energy of these discrete lines strongly varies with the layer thickness: they are attributed to 0D photon modes. For large negative detuning, the 130 eV linewidth of these optical modes corresponds to a quality factor of 12000. Each of these photon modes presents the anticrossing(18); (19) with the exciton line, characteristic of the strong coupling regime. The 0D polariton energies can be fitted using a 15 meV Rabi splitting (as in the planar cavity). Note that contrary to 2D cavities, the uncoupled exciton line is observed because in-plane exciton emission is extracted through the pillar side. Since the exciton line is broadened by strain relaxation in the etching process, the upper polariton state could not be resolved. Further evidence of the strong coupling regime is obtained by observing the exciton-photon anticrossing on a single micropillar using temperature tuning.(20)
PL spectra taken for increasing pump powers on a 6 m circular pillar are shown in fig. 2. A spectrum taken at very low power is shown in the inset: several discrete polariton modes emit on the low energy side of the exciton line. The polariton ground state corresponds to a exciton photon mixed state (measured detuning meV). Two excitation regimes can be distinguished. For (fig.2(b)), the emission undergoes a pronounced blueshift and broadening. The density of electron-hole pairs per QW injected for is estimated to be around cm per QW, reaching the exciton screening density. In this excitation range, the strong coupling regime is progressively screened(21); (22); (23) and eventually the system enters the weak coupling regime, with emission of uncorrelated electron-hole pairs through the cavity modes. The strong coupling regime saturation is observed for excitation densities consistent with previous reports in 2D samples(21) or in aluminium-oxide-aperture nanocavities(24). Above 40 mW, a threshold is observed due to the onset of conventional photon lasing on the 0D photon modes(25).
Let us now concentrate on the strong coupling regime ( mW, fig.2(a)). The emission behavior is marked by a sharp nonlinear increase of the ground state PL intensity. As summarized in Fig. 3(a), when P varies from 0.3 mW up to 3 mW, the integrated intensity increases by four orders of magnitude. The occupancy N of the lowest energy polariton state can be experimentally estimated using: , where is the cavity photon lifetime, is the power emitted by the considered polariton mode, E its emission energy and its exciton part(13). Directly relating the emission intensity to an actual polariton population may not always be possible since emission at the polariton energy could also come from correlated electron-hole pairs, as reported for bare excitons(26). Nevertheless this analysis is valid at low density and low temperature, the regime where polariton non-linearities are observed in the present work. As shown in Fig. 3(a), the onset of the polaritonic non-linearity occurs when the measured polariton occupancy exceeds unity. Above threshold, the scattering of excitons toward the lowest energy polariton state is stimulated, leading to the formation of a macroscopically occupied polariton state. The polariton population of the lower energy state increases up to 10.
The polariton linewidth amounts to meV at low excitation power, and slightly broadens with the onset of polariton-polariton interaction. At threshold, associated to the build-up of the large polariton occupancy, a spectral narrowing, down to 0.15 meV, shows that the coherence time becomes longer than the radiative lifetime of single polaritons.
Polariton stimulated scattering is obtained on micropillars with diameter down to 2 m and for detunings down to 20 meV. Working at higher temperatures, polariton lasing occurs up to 45 K. Above 50 K or for very large negative detunings, only the second non-linearity associated to photon lasing is observed. Let us underline that in the unpatterned 2D sample, only conventional lasing was achieved(16). Reducing the cavity dimensionality is the key step to achieve polariton quantum degeneracy under non-resonant excitation.
Fig. 4 presents PL measurements on a 6 m micropillar (with 0.3 meV for the lowest polariton mode) using two different excitation geometries. On the left part of Fig.4, the laser spot is centered on the micropillar surface. As described above, stimulated scattering occurs toward the lowest energy mode (named M1). The data of the right part are recorded with the excitation spot shifted toward the micropillar edge, as schematically indicated in the figure. Under this excitation geometry, stimulated scattering is observed toward the first excited polariton states (named M2). Further increasing the excitation power, competition between polariton modes also triggers stimulated scattering toward M1 and M3. This experiment demonstrates that the polaritonic non-linearity can not be interpreted in terms of a thermodynamic phase transition (analogous to Bose-Einstein condensation) because in this framework, the largest occupancy is always expected on the system ground-state. In the present experiment, the non-linearities are not governed by thermodynamics but by the kinetics of the scattering process toward the low energy polariton states. Such bosonic stimulation of polariton scattering has been named ”polariton laser”(27); (28) in analogy to the atom laser(29). Using this now well accepted name, one must keep in mind that the stimulation mechanism is very different from that in a conventional photon laser: it is not the emission of radiation that is amplified but a scattering mechanism, following the non-resonant excitation. As in a conventional photon laser, multi-mode polariton lasing can be triggered depending on the excitation condition. The electromagnetic field of the lowest energy mode (named HE, see ref.(12)) presents an antinode at the micropillar center and decays at the edge. It is therefore favored when the center of the pillar is excited. On the contrary, the second polariton line gathering three degenerate modes within the mode linewidth (EH, HE and HE), is favored under edge excitation since these modes present an antinode at the periphery. Thus the pump excitation geometry triggers stimulated scattering toward polariton modes with matching field spatial distribution.
Contrary to conventional photon lasers, the lasing mode of a polariton laser is macroscopically occupied with half-matter half-light bosons i.e. with interacting bosons. Exciton-exciton interaction and the resulting exciton blueshift has been extensively studied in the 80’s(30); (31) and recently revisited within the framework of excitonic polaritons(32). Polariton-polariton interaction originates from coulomb interaction between the fermionic constituents (electron and hole) of their exciton part. As the occupancy of the polariton states increases, self-interaction within the lasing mode induces a spectral blueshift of the emission(33). Fig. 4(e) summarizes the spectral blueshift of M1 and M2 both under central and edge excitation conditions. The blueshifts are plotted as a function of the polariton occupancy, obtained by normalizing the emission intensity by the intensity at threshold. M3 is not reported because the contribution from HE, at higher energy than EH and HE(12) could not be correctly deconvoluted. The curves in fig.4(e) are strikingly identical regardless of the mode number or the excitation conditions. This indicates that the blueshift only depends on the number of polaritons within the considered state. For instance, when multimode lasing is achieved, each lasing mode presents its own blueshift, corresponding to its own occupancy. Thus the blueshift does not come from interaction with high energy excitons or electron-hole pairs, but mainly from the self-interaction energy within the considered mode. Notice that the present results evidence a blueshift logarithmically varying with the occupancy whereas theoretical calculations predicts a linear behavior(33). Further theoretical investigation is probably needed to quantitatively describe the observed self-interaction energy.
To conclude, polariton lasing is demonstrated on the discrete modes of a GaAs/GaAlAs micropillar cavity. A sharp threshold associated with a spectral narrowing shows the onset of stimulated scattering toward the lowest energy polariton state. The polariton state occupancy is measured to reach . Changing the excitation spatial symmetry, multimode polariton lasing is triggered, demonstrating that the observed feature can not be described in terms of Bose Einstein condensation. Contrary to photon lasing obtained at higher excitation power, the polariton self-interaction within the macroscopically occupied state induces a continuous blueshift of the emission as the state occupancy builds up. These results, obtained in the well controlled GaAs semiconductor system, open the way toward an electrically pumped polariton laser(34) and will stimulate future experiments to investigate the emission quantum statistics of such a solid-state matter-wave laser.
We are grateful to D. Le Si Dang for fruitful discussions. This work was funded by the european project “Clermont 2” (MRTN-CT-2003-503677), by ”C’nano Ile de France” and ”Conseil Général de l’Essonne”.
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