Bose-Einstein Condensation of Plexcitons S.R.K

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

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

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

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. An analyzer before the detector discriminates polarizations. Light within the angular cone |k||| < 1.4 rad/µm was collected by the objective

5 with NA=0.25. Figures 3a and 3b show the emission from the R6G layer out of and in the presence of the nanorod array, Iout and Iin, respectively. In Fig. 3c we plot Iin/Iout, and in Fig. 3d we do the same for the horizontal polarization. The vertical polarization (parallel to the nanorod short axis) is enhanced by the nanorod array, while the horizontal polarization is quenched. This polarization build-up of the emission is a signature of BEC, albeit also a signature of lasing.

Notice also the elliptical shape of the emission enhancement in Fig. 3C, which we attribute to the form of the potential. The narrow angular bandwidth of the SLR with k|| along the horizontal direction expands the emission spot along this direction. Conversely, the broad angular bandwidth of a LSPR (see Supplementary Information) contracts the spot along the vertical direction.

The spatial extent of the condensate is assessed by deconvoluting Iin with the point spread function of the optical system, which we approximate as Iout. Deconvolutions for 0.7 Pc, 1.3 Pc, and 2.6 Pc, are shown in Figs. 3e, 3f, and 3g, respectively. Below Pc there is no peak. As the pump irradiance increases above Pc, a sharp peak emerges in the centre: the condensate. From the measurements at 2.6 Pc we estimate the full width at half maximum of condensate to be ~ 10 ±

3μm. It is noteworthy that a similar length is obtained by inserting the effective plexciton mass and temperature at 2.6 Pc into the expression for the thermal de Broglie wavelength Λ, which

2 yields   h / 2mkBT  7m .

In conclusion, strongly coupled surface plasmon polariton-exciton modes (plexcitons) were shown to exhibit Bose-Einstein Condensation. An extremely small plexciton mass makes this the warmest condensate yet reported. We envisage these results to stimulate further studies of quantum phase transitions with metallic nanoparticles, thus bringing plasmonic systems into the domain of macroscopic quantum critical phenomena.

Methods Experimental techniques. The extinction was measured with the light from a halogen lamp, which was collimated and linearly polarized. The transmission through the sample with the nanorod array was normalized to the transmission through the sample without the array (just the substrate, Si3N4, and R6G layers), to obtain the zeroth-order transmittance T0. We define 1-T0 as the extinction. This is shown in colour as a function of the in-plane component of the wave vector k|| and the incident photon energy. Figure S2 shows the extinction of the same sample illuminated with the three other possible combinations of incident wave and polarization vectors.

For the emission measurements the sample was optically pumped by the output of an optical parametric oscillator with 533 nm, ~200 fs pulses, and 80 MHz repetition rate. The pump beam impinged at 15° with respect to the sample’s normal. The much larger in-plane wave vector of the pump (k|| = 3 rad/μm) with respect to the plexciton thermalisation spectral range ensures that excitons are injected incoherently. We verified the emission above and below BEC criticality to be practically the same under different excitation angles. Resonant pump enhancements by the nanorod array are also excluded by this observation, and the fact that the absorption length at 533 nm is 140 nm. The pump beam is largely absorbed before it reaches the nanorod array, since the

R6G layer is 700 nm. The emission was collected by a fibre-coupled spectrophotometer. A notch filter at 533 ±1 nm was used to filter the excitation, and an analyzer discriminated the polarization of the emission. Both extinction and emission measurements were done with computer controlled rotation stages with an angular resolution of 0.2°, i.e., ∆k|| <0.04 rad/μm at

2.12 eV (the BEC energy).

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Acknowledgments

This work was supported by the Netherlands Foundation for Fundamental Research on Matter

(FOM) and the Netherlands Organization for Scientific Research (NWO), and is part of an industrial partnership program between Philips and FOM.

Author Contributions

S.R.K.R. and J.G.R. contributed to the experimental idea. M.A.V. fabricated the nanorod array and S.R.K.R. fabricated the luminescent layer. S.R.K.R. performed the experiments and analyzed the data, and together with J.G.R. wrote the paper. All authors discussed the results.

Figure captions

Figure 1: Spatial and spectral properties of the sample. a, A silver nanorod array stands on a

SiO2 substrate. The red curves on the nanorods represent the electromagnetic field decaying out of the plane (surface plasmon polaritons). The thin gray layer represents the passivating Si3N4.

The orange layer is the R6G/polymer layer. The green beam represents the incident laser, pumping the R6G exciton reservoir. Plexcitons are formed by the exciton-plasmon coupling. b,

Normalized PL (red) and absorption coefficient α (green) of the R6G layer without the nanorod array. The blue line is the normal incidence extinction of the nanorod array covered by the same

R6G layer, normalized to the extinction of the same layer without the array. The green line indicates the pump energy. c, Variable angle extinction of the same nanorod array with a similar

R6G/polymer layer, but with a lower R6G concentration. The black line indicates the trapping potential for plexciton thermalisation, which is schematically represented by the black circle.

Figure 2: Plexciton thermalisation and BEC as a function of the pump irradiance. a, Emission

2 spectra at different fractions of the critical pump irradiance Pc = 90 W/cm for BEC. The output/input power relation is shown in b, where the blue (red) line fits the data above (below)

BEC criticality. Variable angle emission (normalized to the ground state), with a polarization parallel to the short axis of the nanorods, at 1.1 Pc in c, and at 2.3Pc in d, both in the same colour scale. The red lines are the calculated Rayleigh anomalies -diffracted orders in the plane of the array- assuming a refractive index of n=1.54. e, Plexciton occupation n at energy E normalized to the ground state occupation n0 with energy E0. Dark squares are data from c and blue circles from d. The red lines in e are Bose-Einstein distribution fits to the data, from which we extract

11 the effective plexciton temperature T and chemical potential μ to be T= 2640 K and μ= -160 meV in c and T= 1230 K and μ= -70 meV in d.

Figure 3: False-colour optical microscope measurements and analysis of the emission from the

R6G layer outside, Iout, and inside, Iin, the nanorod array. The scale bar in a holds for a-d. The yellow arrows indicate the polarization axis set on the analyzer. a, Iin and b, Iout at a pump power

2.6 Pc in the same colour scale, representing counts/s. c, and d, are Iin/Iout for the two orthogonal polarizations, at the same input power (2.6 Pc) and in the same colour scale. Deconvolution of Iin with Iout is shown at 0.7 Pc in e, 1.3 Pc in f, and 2.6 Pc in g.

Supplementary Information

Sample Fabrication

The nanorod array was fabricated by substrate conformal imprint lithography, a nano-imprint technique enabling accurate reproduction of nanoscale features over large (>cm2) distances20.

The use of a flexible silicone rubber allows for nanofabrication to be done even in the presence of moderate substrate defects and contamination. The master from which the stamp was moulded was created by electron-beam lithography of ZEPP520 positive tone resist. Figure S1 shows a scanning electron microscope image of the imprinted resist layer used in this fabrication.

Subsequent processing involved perpendicular evaporation of 20 nm silver, lift-off, and plasma- enhanced chemical vapour deposition of a 20 nm Si3N4 layer.

On top of the array we spin-coated a solution of water, ethanol, Rhodamine 6G dye (R6G), and polyvinyl alcohol (PVA). Water and ethanol were first mixed at a weight ratio of 11:9. Two weight % PVA was added to the water-ethanol solution, and heated to 60° C while stirring to enhance solubility. R6G dye was added at 66 weight % with respect to PVA for the BEC experiments. We spin-coated at 500 RPM for 60 s, and consequently baked the sample at 90° C for 5 minutes. The layer thickness was measured by profilometry, and confirmed by ellipsometry measurements, from which we also extracted the optical constants and the absorption coefficient of the layer.

Supporting Measurements

Figure S2 shows the extinction of the same sample used for the BEC experiments. Here, the sample is probed for the three other combinations of in-plane wave vector k|| and polarization

14 vector E, of the incident plane wave with respect to the nanorod array. The peak in extinction spanning the entire angular spectrum at 2.15 eV in Fig.S2a is a Localized Surface Plasmon

Resonance (LSPR) along the short axis of the nanorods. The flat angular dispersion of LSPRs makes them unsuitable for BEC, since they do not provide the trapping potential necessary for thermalisation and condensation. We verified this by pumping the sample in the same way as done for the experiments in Fig. 2, but collecting light with the orthogonal wave vector. As expected, no condensation was observed in the emission with this wave vector. The large angular bandwidth of the LSPR in Fig. S2a is responsible for the spatial expansion of the photoluminescence enhancement observed in Fig. 3c along the horizontal direction (the same direction of k|| in the measurements in Fig. S2a). Figures S2b and S2c show the extinction spectra for E parallel to the long axis of the nanorods. No resonances are observed in these two cases, and the extinction practically vanishes. Again, we verified the emission with this polarization for both orientations of k||. Instead of an emission enhancement with respect to the

R6G layer without the nanorod array, we observed emission quenching. This quenching is shown in the measurements of Fig. 3d as evidence of polarization build-up.

To verify the strong coupling of R6G molecules to surface plasmon polaritons, we present in Fig.

S3 a dispersion diagram in light extinction for the same orientations of k|| and E used in the BEC experiments, i.e. Ey, kx. These are the same measurements included in Fig. 1c, but in a wider spectral range. The splitting (>110 meV) of the (+1,0) SLR as it anti-crosses the R6G molecular resonance (shown in Fig. 1) indicates that the system enters into the strong coupling regime for this lower concentration already. By further increasing the concentration to 66 weight % (as used for the BEC measurements), it was not possible to observe any feature in extinction at the R6G

15 absorption band because the incident field is entirely absorbed (within our measurement capabilities) by the R6G layer.

Suppplementray Figure captions

Figure S1. Scanning electron microscope image of the resist used for the fabrication of the nanorod array. The scale bar denotes 500 nm.

Figure S2 Variable angle extinction of the same sample used in the BEC experiments, for the other three possible combinations of incident in-plane wave vector k|| and polarization vector E. a, Ey, ky, b, Ex, kx, and c, Ex, ky, where x points along the long-axis of the nanorods, and y along the short-axis, as indicated in Fig. S1. The blue lines indicate the calculated Rayleigh anomalies

–diffracted orders in the plane of the array – with refractive index n=1.54.

Figure S3 Variable angle extinction of the same nanorod array used for the BEC experiments, covered by a similar layer of PVA but with lower R6G concentration: 3wt%. The blue lines indicate the calculated Rayleigh anomalies –diffracted orders in the plane of the array – with refractive index n=1.54. The polarization and in-plane component of the incident wave vector are the same as for the BEC experiments, i.e. Ey, kx. These are the same measurements shown in

Fig. 1C, but in a wider spectral range to display the band splitting near 2.25 eV arising from the

R6G-SLR strong coupling.