Bose-Einstein Condensation of Plexcitons S.R.K
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Bose-Einstein condensation of plexcitons S.R.K. Rodriguez1*, M.A. Verschuuren2 & J. Gomez Rivas1,3 1Center for Nanophotonics, FOM Institute AMOLF, c/o Philips Research Laboratories, High Tech Campus 4, 5656 AE Eindhoven, The Netherlands. 2 Philips Research Laboratories, High Tech Campus 4, 5656 AE Eindhoven, The Netherlands. 3 COBRA Research Institute, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. *Correspondence to: [email protected] October 26, 2012 Bosons (particles with integer spin) above a critical density to temperature ratio may macroscopically populate the ground state of a system, in an effect known as Bose-Einstein Condensation (BEC) 1. The observation of BEC in dilute atomic gases was a great triumph of modern physics, a task requiring nK cooling of atoms2-3. Following these demonstrations, a quest for lighter bosons enabling BEC at higher temperatures came to light. Photons in a microcavity were destined to fulfil this quest. Their coupling to semiconductor excitons allowed the condensation of exciton-polaritons at a few K in solid- state4-6, and the condensation of photons was later observed in a liquid-state dye at room- temperature7. Distinctly, one of the most actively studied excitations in condensed matter, surface plasmon polaritons - collective oscillations of conduction electrons in metals -, has never been shown or predicted to exhibit BEC. The strong radiative and Ohmic losses in metals, together with the lack of a suitable (e.g. harmonic) potential for thermalisation, are likely the reasons for this. Here we demonstrate BEC in a plasmonic system for the first time. Surface plasmon polaritons in a periodic array of metallic nanorods couple strongly to excitons in a room-temperature solid-state dye acting as a heat bath, and bosonic quasiparticles known as plexcitons8are formed. By increasing the plexciton density through optical pumping, we observe the thermalisation and ground state accumulation of 1 plexcitons in the angular spectrum and in real-space. Jointly, polarization build-up of the emission takes place. A new state of light-matter emerges upon plexciton condensation, and a coherent radiation field emanates from this quantum phase transition. We find the plexciton condensate to be the warmest and least massive of any condensate yet reported, and thus envisage its suitability for solid-state studies of macroscopic quantum many-body physics. Surface plasmon polaritons - bosonic excitations at the interface of a metal and a dielectric - have attracted broad scientific interest due to their potential for manipulating light at a subwavelength scale9. For instance, the Localized Surface Plasmon Resonances (LSPRs) of metallic nanoparticles enables them as antennas for light, converting free-space radiation into localized energy and vice versa10, 11. If an exciton couples strongly to the LSPR field, plexcitons are formed8. LSPRs generally suffer from strong radiative damping and Ohmic losses, and their non-propagating character grants them a flat angular dispersion. Therefore, LSPRs do not provide the trapping potential necessary for plexciton thermalisation and ground-state accumulation, which is likely the reason for which plexciton BEC has never been discussed. However, in a periodic array of metallic nanoparticles, LSPRs may hybridize with diffraction orders radiating in the plane of the array, i.e., Rayleigh anomalies12. Extremely sharp resonances (~1 meV line width) were predicted to arise under such conditions13, and experiments have been approaching this prediction 14-16. The narrow and dispersive character of these resonances, known as surface lattice resonances (SLRs), allows tailoring the spectral-angular distribution of spontaneous emission17, 18. Here we exploit the unique features of SLRs strongly coupled to excitons in solid-state dye molecules to enter the regime of BEC in a plasmonic system for the first time. Plexcitons emerge 2 from the SLR-exciton strong coupling (see Supplementary Information), and their thermalisation is driven as in a photonic gas19: by re-absorption and re-emission in the dye layer, which acts as a heat bath. By increasing the pump irradiance, which in turns increases the plexciton density, we observe the ground state accumulation of plexcitons above a critical pump irradiance. The photonic component of plexcitons leaks out of the open system, thus enabling the study of BEC through the emitted light field. Figure 1a illustrates the sample. A periodic array of silver nanorods was fabricated onto a fused silica substrate by a substrate conformal nanoimprint technique20. The dimensions of the 3 rods are 230 x 70 x 20 nm , and the lattice constants are ax = 380 nm and ay=200 nm. A 20 nm layer of Si3N4 was deposited on top of the array to prevent the silver from oxidizing. A 700 nm layer of polyvinyl alcohol (PVA) with Rhodamine 6G (R6G) dye at 66 weight % was spin- coated on top. The high concentration of R6G favours BEC over photon lasing, since the emission is largely quenched (quantum efficiency <0.01) but the smaller molecule separation facilitates the emergence of a common wavefunction. The green beam in Fig. 1a depicts the incident laser (2.326 eV, ~200 fs pulses), which pumps the exciton reservoir in the R6G layer incoherently (see Methods). Figure 1b shows the R6G layer absorption coefficient α as green area, and the normalized emission as red area. The normal incidence extinction, for a polarization parallel to the nanorod short axis, is shown as a thick blue line. The high R6G concentration makes it difficult to observe the response of the array at energies where R6G absorbs strongly, since the absorption length reaches 140 nm. Therefore, in Fig. 1c we show the extinction of the same nanorod array covered by a similar PVA/R6G layer, but with a 3 weight % R6G concentration. The incident light is polarized parallel to the short axis of the nanorods, and the in-plane component of the wave vector k|| points along the long axis. The high and low 3 energy extinction bands in Fig. 1c are SLRs associated with the (+1, 0) and (-1, 0) diffraction orders, respectively. A symmetric electric field distribution makes the (+1, 0) SLR couple strongly to the incident plane wave with k||=0, forming a harmonic-like potential with a low effective polariton mass21. This is the trapping potential we use for thermalising plexcitons, as depicted by the black line in Fig. 1c. The power-dependent plexciton emission is shown in Fig. 2. We collect light with a polarization parallel to the short-axis of the nanorods, and k|| along the long-axis. Figure 2a shows the emission at k||=0, where a peak emerges near 2.12 eV above the critical pump 2 irradiance Pc= 90 W/cm required for BEC. The peak energy and power-dependent spectral behaviour is rather close to what was reported for a photon BEC in a microcavity7. The similarity is based in that we are using the same dye, although in solid rather than liquid state. The spectral characteristics are significantly different from those of plasmonic-feedback photon lasers, where an optical mode is selectively amplified until oscillation is established22, 23. This amplification normally occurs in the red-tail of the emission, where negligible re-absorption by the dye eases population inversion (a condition inherently far from thermal equilibrium). Polariton lasers, whose properties are also distinct from those of photon lasers24, have also been demonstrated in the emission red-tail25,26. Instead, optical BEC emerges near the emission/absorption spectral cross-over, since the interplay of these two processes drives the system into a thermodynamic phase transition. Figure 2b shows the emission at the BEC energy for increasing pump irradiance. Two distinct regimes are observed: the red (blue) line fits the data below (above) criticality. Figures 2c and 2d show the angle-resolved emission at 1.1 Pc and 2.6 Pc, respectively. The emission was normalized to the plexciton ground-state energy (peak at k||=0) for each pump irradiance to plot 4 the data in the same colour scale. A power-dependent condensation manifests as a lower population of the high energy states. A blue-shift of the ground state energy is also observed. Similar shifts were observed in exciton-polariton condensates5, 6, and have been attributed to exciton-exciton interactions at high densities27. Figure 2e shows the plexciton occupation n at energy E normalized to the ground state occupation n0 with energy E0. The black squares and blue circles are obtained by following the emission maxima along the plexciton branch in Fig. 2c and Fig. 2d, respectively. The red curves (E E0 )k BT are fits of the Bose-Einstein distribution function n / n0 1/(e 1) to the experiments, with kB the Boltzmann constant. The effective plexciton temperature T and chemical potential μ extracted from the fits are T= 2640 K and μ= -160 meV for Fig. 2c, and T= 1230 K, μ= -70 meV for Fig. 2d. Condensation is confirmed by the two-fold reduction in T and μ. Increased optical pumping induced R6G photo-degradation, thus preventing further condensation. Full equilibrium is not established because the effective plexciton temperature is still warmer than the lattice, thus suggesting quasi-equilibrium only, as reported for exciton-polaritons24. From the measurements 2 2 2 -38 -7 in Fig. 2d we deduced the effective plexciton mass meff = ħ /( E / k|| ) = 8·10 kg, i.e., 10 times the electron rest mass. This extremely small mass explains the large plexciton critical temperatures, which are ~2 and ~10 orders of magnitude higher than in exciton-polariton and atomic systems, respectively. The real-space emergence and polarization build-up of the condensate are studied through optical microscope measurements in Fig. 3. A bandpass filter peaking at 2.13 eV with a 0.04 eV full width at half maximum (FWHM) was placed before the CCD detector, to collect only the emission from the condensate.