Polariton Bose–Einstein Condensate at Room Temperature in an Al(Ga)N Nanowire–Dielectric Microcavity with a Spatial Potential Trap

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Polariton Bose–Einstein condensate at room temperature in an Al(Ga)N nanowire–dielectric microcavity with a spatial potential trap

Ayan Dasa,1, Pallab Bhattacharyaa,1, Junseok Heoa, Animesh Banerjeea, and Wei Guob

aCenter for Photonic and Multiscale Nanomaterials, Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109; and bDepartment of Electrical and Computer Engineering, University of Michigan, Dearborn, MI 48128

Edited by Paul L. McEuen, Cornell University, Ithaca, NY, and approved December 21, 2012 (received for review June 28, 2012) A spatial potential trap is formed in a 6.0-μm Al(Ga)N nanowire dynamic condensation only if the polariton relaxation time is by varying the Al composition along its length during epitaxial much shorter than the polariton (photon) lifetime. A large growth. The polariton emission characteristics of a dielectric micro- number of pioneering experiments have been performed to re- cavity with the single nanowire embedded in-plane have been stud- alize a BEC with cavity polaritons (19–21). These observations ied at room temperature. Excitation is provided at the Al(Ga)N end have been mostly limited to cryogenic temperatures. However, of the nanowire, and polariton emission is observed from the low- by engineering the polariton scattering rates and lifetimes and by est bandgap GaN region within the potential trap. Comparison of using evaporative cooling techniques (21), it may be possible to the results with those measured in an identical microcavity with achieve a degenerate and coherent Bose gas in a solid-state a uniform GaN nanowire and having an identical exciton–photon system at room temperature. Because of the loss through the detuning suggests evaporative cooling of the polaritons as they photonic component, which also provides the opportunity to are transported into the trap in the Al(Ga)N nanowire. Measure- probe the system, the exciton–polariton system will exhibit this ment of the spectral characteristics of the polariton emission, their condensed state only for a short period. momentum distribution, ﬁrst-order spatial coherence, and time- GaN with a bandgap of 3.4 eV has a large exciton binding

resolved measurements of polariton cooling provides strong evi- energy of 26 meV. Hence, a large Rabi splitting of 56 meV (18) ENGINEERING dence of the formation of a near-equilibrium Bose–Einstein conden- and a trap depth larger than kBT have been measured at room sate in the GaN region of the nanowire at room temperature. In temperature for GaN-based quantum well (17) and nanowire – contrast, the condensate formed in the uniform GaN nanowire microcavities (18). Room-temperature operation provides en- dielectric microcavity without the spatial potential trap is only hanced polariton–phonon scattering rates and efficient polariton in self-equilibrium. thermalization. Additionally, the exciton screening density in GaN is larger than that in GaAs due to a smaller Bohr radius in Bose–Einstein condensation | exciton–polariton 2 the former (∼1/aB ). Baumberg et al. (22) have reported spontaneous symmetry breaking of the polarization of polaritons at osons are fundamental particles in nature having integral room temperature in a GaN device. We have recently reported Bspin, with occupation in equilibrium characterized by Bose– the observation of ultralow threshold polariton lasing at room Einstein statistics, and exhibiting a phenomenon known as temperature (19) and dynamic condensation at ∼90 K (23) in a bosonic final-state stimulation, or Bose stimulation. The latter single GaN nanowire–microcavity device. GaN nanowires grown produces stimulated emission and gain in a conventional laser. It on Si are relatively free of extended defects and mismatch strain can also produce an equiphase degenerate condensate in equi- (24–30). Additionally, a modified cavity field concentrated within librium, termed a Bose–Einstein condensate (BEC) (1). A BEC the nanowire ensures a strong interaction between the photons characteristically demonstrates long-term temporal coherence and excitons (18). The design of the nanowire embedded in the and long-range spatial coherence. In solid-state systems excitons dielectric microcavity used in the present study is illustrated in behave as bosons when the mean distance between excitons is Fig. 1. The nanowire is grown on silicon and consists of graded much larger than the exciton Bohr radius. Owing to their light Al(Ga)N along the length, which creates a spatial potential trap. mass, it is possible to observe Bose condensation at standard In this paper we report the results of strong coupling experi- cryogenic temperatures; the possibility of observing an excitonic ments performed with such a nitride-based compositionally – BEC has been explored with Cu2O(2 4), CuCl (5, 6), and with graded nanowire microcavity. We demonstrate the formation of – – GaAs AlGaAs coupled quantum wells (7 9). It is also possible a near-equilibrium polariton BEC at room temperature. to observe a BEC in a solid-state system with exciton–polaritons (10–12), which are formed in a microcavity by strong coupling Results and Discussion between cavity photons and excitons. Polaritons have the ex- The Al(Ga)N nanowire consists of a 2.5-μmAl Ga N re- ∼ −8 0.05 0.95 tremely small mass of the cavity photon (mpol 10 matom), gion, followed by 2-μm graded Al(Ga)N, 1-μm GaN, and 0.5-μm giving rise to the possibility of forming a BEC at much higher graded Al(Ga)N terminating in Al0.05Ga0.95N(Fig.1A). The spatial temperatures, even at 300 K. To form a degenerate condensate, polaritons with higher energy relax by a combination of polar- – – iton phonon and polariton polariton scattering and eventually Author contributions: A.D. and P.B. designed research; A.D. and J.H. performed research; condense by phase-coherent bosonic final-state stimulation. At J.H., A.B., and W.G. contributed new reagents/analytic tools; A.D. analyzed data; and P.B. the same time, polaritons are lost from the system as photons wrote the paper. which have a small lifetime. The polariton gas can be in self- The authors declare no conflict of interest. equilibrium, or quasi-equilibrium, when the polariton relaxation This article is a PNAS Direct Submission. time and lifetime are comparable and the polariton temperature Freely available online through the PNAS open access option. TLP remains larger than the ambient (lattice) temperature 1To whom correspondence may be addressed. E-mail: [email protected] or pkb@umich. Tlattice. Coherent light output, generally described as polariton edu. – lasing (13 18), can be observed under these conditions. A co- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. herent BEC in equilibrium with the lattice would be formed by 1073/pnas.1210842110/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1210842110 PNAS Early Edition | 1of6 Downloaded by guest on October 5, 2021 Fig. 1. (A) Schematic of the Al(Ga)N nanowire showing the variation of the exciton energy as a function of position. The exciton energies at the AlGaN end and the GaN region are estimated from the measured photoluminescence peaks as shown. Photon and exciton fraction of the LPB at kjj ∼ 0 are also shown as a function of position in the trap. (B) Schematic representation of the dielectric microcavity with a single Al(Ga)N nanowire of diameter 50 nm and length 6 μm buried in the center of a λ- sized cavity. The microcavity is etched into square

mesas ∼10 μm in size with 1 μm of the Al0.05Ga0.95N end of the nanowire exposed. (C) High-resolution transmission electron microscope image of a GaN nanowire reveals that the nanowires are relatively free of extended defects and stacking faults. (Inset) Selected area diffraction pattern conﬁrming that the nanowires have a wurtzite structure and grow along the c axis.

potential profile is also shown in the figure. The Al composition is the distance from the center of the trap and k = 2.6 × 106 eV/ at the ends of the nanowire is estimated to be 5% from the cm2) is created during nanowire growth by the Al(Ga)N alloying measured exciton luminescence peak (31) of 356 nm (3.483 eV) process. The corresponding quantum level spacing of 8.75 meV (Fig. 1A) and from independent X-ray diffraction measurements. is much smaller than kBT = 26 meV at 300 K, so that the con- The average polariton diffusion length for this range of alloy tinuum approximation for the polariton states in the trap region composition is estimated to be 61 μm(Supporting Information). is valid. In similar experiments with GaAs-based microwires (34), it The energy difference between Al0.05Ga0.95N and GaN, or the was observed that the polaritons diffuse in opposite directions height of the spatial potential trap, is 85.7 meV over a distance from the excitation spot but do not form a condensate at the en- of ∼3.5 μm. The single nanowire is positioned in the microcavity ergy minimum, except at the excitation spot. In both GaAs-based such that ∼1 μm of the Al0.05Ga0.95N region is exposed from the microwires and our GaN nanowires, polaritons are confined in mesa and optical excitation is provided at this end (Fig. 1B). We a 1D system and the polariton density of states changes. However, will henceforth refer to this sample with the spatial trap as the there is no evidence of any change in the polariton–polariton Al(Ga)N nanowire microcavity (sample 1). Another sample scattering rate (34, 35). The phonon distribution, on the other consisting of a single GaN nanowire (700-nm-long) microcavity hand, remains the same as in bulk. Compared with polaritons (sample 2) and having the same cavity photon–exciton detuning confined in a 2D system, there is polariton confinement in an δ was also fabricated for comparison of experimental results. additional direction in the nanowires. Due to the breaking of Microphotoluminescence spectra from the GaN nanowire ex- translational symmetry, the momentum conservation is relaxed and hibit the three free excitons XA, XB,andXC and the corre- the polariton–phonon scattering rate is expected to increase (36). sponding donor bound (DB) transitions. Of these, the XA and When the nanowire of sample 1 is selectively excited at the DBXA transitions are the most dominant in the spectra and Al0.05Ga0.95N end, the exciton–polaritons which are more pho- hence coupling of the XA exciton to the cavity mode is only ton-like will relax to lower energies by scattering as they drift and considered for analyzing measured polariton dispersion charac- diffuse to the central GaN region where they are less photon- teristics with the coupled oscillator model (18). like. The polariton–phonon scattering rate will gradually in- To understand the following results more completely, we will crease due to the increasing exciton–photon detuning in the elaborate on the nature of our samples and describe the relevant microcavity. At the same time the higher energy polaritons (at physical processes. The nanowires in both samples, by virtue of higher kjj values) will be lost as photons, thereby providing their dimensions, are quasi-1D in the context of polariton con- evaporative cooling. The coldest polaritons near kjj ∼ 0 will reach finement. In an ideal uniform infinitely long 1D system, a BEC the bottom of the potential trap in the GaN region. cannot be observed because long-wavelength thermal fluctua- The polariton dispersion characteristics of the Al(Ga)N tions destroy long-range correlation (32, 33). Additionally, the nanowire microcavity were determined from measured angle- energy density of states ρ(E) does not vanish in the limit of E → 0. resolved photoluminescence (0°–30°) data recorded for low ex- In the presence of a potential trap or a disorder, or for a finite citation densities, which show strong polariton luminescence size as in sample 2, a Bose–Einstein-like phase transition is pos- corresponding to the GaN (center) region of the nanowire. The sible. The trap present in sample 1 is characterized by a length of results were analyzed with a coupled oscillator model taking into 2 3.5 μm and a parabolic potential variation U = (1/2) kx (where x account the coupling of the XA exciton and the cavity mode;

2of6 | www.pnas.org/cgi/doi/10.1073/pnas.1210842110 Das et al. Downloaded by guest on October 5, 2021 values of Rabi splitting Ω = 48 meV and cavity-to-exciton threshold 2,700 times larger in value (18). Although these detuning δ =+2 meV are derived. The same value of δ is derived characteristics indicate coherent polariton emission, or polar- for sample 2 with the single GaN nanowire. iton lasing, they do not reveal the properties of the degenerate The integrated intensity of polariton luminescence, recorded Bose gas. It is evident, however, that the incorporation of the at room temperature in the normal direction (kjj ∼ 0), as a spatial potential trap produces noticeable differences in the function of pump power exhibits a nonlinear behavior accom- characteristics of polariton emission. panied by a sharp decrease of the emission linewidth. Fig. 2 A–C To gain a better understanding of the polariton dynamics and illustrates these characteristics for the Al(Ga)N nanowire micro- the occupation of the LPs in kjj space, we have performed angle- cavity (sample 1). Similar data recorded for the GaN nanowire resolved photoluminescence measurements as a function of ex- sample (sample 2) are illustrated in Fig. 2D. As observed in Fig. citation density for samples 1 and 2. Pulsed excitation has been 2A, the emission spectra exhibit a second peak with smaller used and hence the polariton density and temperature may intensity. We believe this peak corresponds to a transverse change with delay after the excitation pulse. However, for exci- mode due to localization by dielectric-cavity–induced photonic tation powers for which the polariton relaxation time remains disorders (15, 17, 37). The incident excitation energies at the larger than or comparable to the polariton emission time con- 2 threshold of the nonlinearity are 102 and 125 nJ/cm for samples stant, the distribution of LP density in kjj space can be considered 1 and 2, respectively, and the minimum emission linewidths are invariant (14, 23). Under these conditions a time-integrated 0.43 and 1.1 meV, respectively. The reductions in threshold emission intensity obtained from the pulsed excitation mea- power and emission linewidth agree with the observation made surement is a good approximation for the LP density. This ap- by Balili (38), where similar trends were recorded for an increase proximation is not valid at higher excitation powers due to faster in locally applied stress (trap depth) to the GaAs/AlGaAs QW relaxation dynamics of the polaritons. Below the threshold for microcavity. Fig. 2C shows the variation of the lower polariton nonlinear emission the photoluminescence spectra remain broad (LP) and upper polariton (UP) peak energies. The extremely and of comparable intensity for all angles (Fig. 3). Above small shift in energy of the LP mode (∼1.5 meV compared with threshold the emission is characterized by a spectrally narrow Ω = 48 meV) indicates that the system remains in the strong and strong peak at kjj ∼ 0. The relative occupancy, or the coupling regime over the entire range of excitation energy. In LP number density per kjj state, at 300 K, is plotted against addition, the linewidth of 0.43 meV for sample 1 (Fig. 2B)isat E−E(kjj ∼ 0) for different excitation powers in Fig. 4 A and B the resolution limit of the spectrometer and the true emission for the Al(Ga)N nanowire (sample 1) and GaN nanowire (sample linewidth could be smaller than this value. The coherence times 2) microcavities, respectively. We have arbitrarily set the ground- ENGINEERING corresponding to the minimum measured emission linewidths state occupancy to be unity at threshold (20). Far below the are 9.6 ps (sample 1) and 3.75 ps (sample 2). The upper bounds nonlinear threshold the polariton scattering rate is inadequate to − of the LP density at threshold are 2.2 × 1016 cm 3 (sample 1) and relax the polaritons and the LP distribution remains nonthermal. 16 −3 2.7 × 10 cm (sample 2), using the relation NLP < Eth/(Epump D). Near and above threshold the relaxation dynamics is fast enough These polariton densities are 3 orders of magnitude smaller than and dynamic condensation leads to a higher occupancy at or near 19 −3 the exciton Mott density (39) of 3 × 10 cm . In a single GaN ground state (kjj ∼ 0). At the higher excitation powers a bimodal nanowire microcavity device, identical to sample 2, we have distribution of the occupancy characterized by a sharp increase in 2 measured a value of Eth = 92 nJ/cm at 300 K. We also measured LP occupancy near kjj ∼ 0 is observed for sample 1 having the conventional photon lasing in the same device with an energy spatial potential trap. In the range (0.9–1.0)Pth, the occupation

Fig. 2. (A) Emission spectra measured in the normal direction as a function of incident energy density for the Al(Ga)N nanowire device for sample 1. (B) Vari- ation of integrated emission intensity and emission linewidth as a function of injection energy density measured for sample 1. (C) Variation of UP and LP energies in sample 1 with injection energy density, as deduced from excitation-dependent photoluminescence. (D) Variation of integrated emission intensity and emission linewidth vs. injection energy density measured for the single GaN nanowire device (sample 2).

Das et al. PNAS Early Edition | 3of6 Downloaded by guest on October 5, 2021 Fig. 3. Momentum distribution of polaritons at different excitation levels obtained from angle-resolved measurements and displayed as false-color plots. Horizontal axis displays the in-plane momentum and vertical axis displays the emission energy in a false-color scale. False-color scale is linear with red and blue representing high and low values, respectively. Exciton and cavity photon energies are also indicated.

in kjj space can be described by the Maxwell–Boltzmann (MB) the filling of the exciton reservoir in the Al0.05Ga0.95N region of distribution. Above threshold, a Bose–Einstein (BE) distribution, the nanowire with excitation, is limited by system resolution. The = + -1 – NBE(k) 1/[exp(E/kBTLP)(1 N0 ) 1], can be used to analyze decay time decreases with increasing excitation, reflecting en- = the polariton occupation data. For P Pth and 1.1Pth in sample 1, hanced polariton relaxation into the kjj ∼ 0 states in the GaN = values of TLP 296.3 and 300.7 K, respectively, are obtained by (trap) region of the nanowire. The transport and scattering of the analyzing the data. The significant bimodal polariton distribution polaritons from the exciton reservoir in the Al0.05Ga0.95N region of the occupancy N(E(kjj)) at high excitation levels in sample 1, of the nanowire into the bottom of the lower polariton branch predicted from steady-state quasi-equilibrium theory (40, 41) and (LPB) (kjj ∼0) in the GaN region was described earlier. This verified by experiments (42), is a strong indication of the formation of a Bose condensate. In contrast, a distinct bimodal distri- complex dynamic process can be analyzed by detailed Monte bution is not observed for sample 2 without the spatial potential Carlo simulation to determine the polariton scattering times at trap, although the detuning is the same (δ =+2 meV). A value of each point in the nanowire, which is beyond the scope of the TLP = 357 K is derived for P = 0.9Pth for sample 2. For an ideal present work. Instead, we describe the evaporative cooling due -1 BEC, the chemical potential μ given by −μ/kBT = ln(1+N0 ) tends to emission of hot polaritons escaping as photons as the to zero. A fit to the occupation data of sample 1 for P = 1.1Pth with polaritons are transported along the trap and the population a BE distribution yields a time-averaged μ = −12 meV, which redistribution in momentum space due to polariton-phonon indicates the formation of a quantum degenerate Bose gas at and polariton–polariton scattering at each point in the trap by room temperature. Furthermore, as the false color plots of Fig. 3 asingletimeconstantτtherm in the coupled rate equations indicate, at this excitation the condensate at kjj ∼ 0 is described by − extremely small values of Δk ∼1 × 104 cm 1 and ΔE ∼ 0.5 meV. Time-resolved photoluminescence (TRPL) measurements have dnR = ð Þ − nR − nR [1] P t τ τ been made with 267-nm pulsed excitation and a streak camera dt R therm with an overall temporal resolution of 5 ps. The transient data

recorded at room temperature for sample 1 are shown in Fig. 5A. dn0 n0 nR The rising part of the transient, which principally corresponds to = − + : [2] dt τ0 τtherm

Fig. 4. Polariton occupancy plotted as a function of energy in a semilogarithmic scale for various normalized excitation powers for (A) the Al(Ga)N nanowire device (sample 1) and (B) the uniform GaN nanowire device (sample 2). For each excitation power, the zero of the energy scale corresponds to the energy of the kjj ∼ 0 state. The solid lines represent calculated polariton occupation according to either a Maxwell–Boltzmann distribution (around threshold) or a Bose–

Einstein distribution (above threshold) with a suitable temperature of the LP cloud TLP.

4of6 | www.pnas.org/cgi/doi/10.1073/pnas.1210842110 Das et al. Downloaded by guest on October 5, 2021 Fig. 5. (A) Transient polariton emission measured as a function of the incident energy density in the Al(Ga)N nanowire device (sample 1). (B) normalized plots of the thermalization time as a function of the incident power obtained from a solution of a two-level rate model for both samples 1 and 2.

Here, P(t) represents the excitation as a Gaussian pulse centered therefore provides direct evidence of coherence in the ﬁrst-order at t = 0, nR and n0 represent the populations in the Al0.05Ga0.95N correlation of the polariton emission and an estimate of the reservoir and the condensate at kjj ∼ 0 in the GaN region, re- spatial coherence length of the condensate along the length spectively, and τ0 is the polariton lifetime in the condensate. The (or c axis) of the nanowire. Below threshold, the contrast exciton lifetime in the reservoir τR is usually much larger (∼1 ns) remains within the noise margin for any overlap between the

than τ0 and therefore the corresponding term in the rate equa- images, indicating that there is negligible coherence across the ENGINEERING 2 tion is neglected. The value of τ0 = τph/jC(kjj = 0)j = 0.55 ps, condensate. Above threshold, a maximum contrast of 21% is where τph = 0.26 ps is obtained from the cavity Q ∼ 600 and jC observed at P = 1.1 mW for complete overlap between the two 2 (kjj = 0)j is the photon fraction in the LPB at kjj ∼0 (Fig. 1A). images and the contrast decreases as the images are moved apart. The ratio τtherm/τ0 is plotted against the relative excitation power The linewidth (FWHM) of the contrast profile is ∼1.2 μm, which in Fig. 5B. It is evident that the value of τtherm decreases rapidly is a measure of the size of the condensate formed in the trap at P/Pth ∼ 1 and reaches 0.09τ0 at the highest excitation power. above threshold and it is approximately equal to the length of the Similar TRPL measurements were also made on the GaN nano- GaN region in the nanowire. wire microcavity (sample 2) and the transient data were again The polarization of the polariton emission was also measured as 1 2 τ analyzed by the coupled rate equations and . In this case therm a function of incident power and the output was found to be linearly represents the overall scattering (relaxation) time from the res- polarized below and above threshold. In contrast, in bulk/quantum ervoir to the condensate at kjj ∼ 0, neglecting the nonlinear time well planar microcavities, spontaneous symmetry breaking is re- constants and polariton densities characterizing the intermediate sponsible for a linearly polarized emission above threshold (22). The τ τ polariton scattering processes. The variation of therm/ 0 with ex- measured polarization is shown in the Supporting Information and citation power for sample 2 is also shown in Fig. 5B and it is the results can be understood in the context of the geometry of our evident that in this case τtherm tends to saturate at a value comparable to that of τ0 (0.6τ0). This steep decrease of τtherm/τ0 observed for sample 1 is reported for a microcavity polariton emitter. From the measured linewidths of polariton emission from sample 1, the coherence time τcoherence increases from 0.34 ps below threshold to a value of ∼10 ps just above threshold. The latter is significantly larger than the polariton lifetime (τ0) of 0.55 ps at kjj ∼ 0. In turn, τ0 is larger than τtherm by an order of magnitude above threshold. We therefore believe that the incorporation of graded Al(Ga)N in the nanowire, which forms a potential trap and enables evaporative cooling, assists the dynamic condensation process and singularly creates a degenerate Bose condensate close to equilibrium at 300 K. In contrast, in the GaN nanowire sample, polariton–phonon scattering is not sufficient to cool the polaritons and the condensate is in self-equilibrium. Additional characteristics of a BEC include long-range coherence and spontaneous symmetry breaking of the polarization of the polaritons. We have measured the first-order correlation of the polariton luminescence with a Michelson interferometer. The continuous wave excitation source is a 325-nm HeCd laser and the incident power is varied from 0.3 to 1.5 mW. The experimental arrangement, schematically shown in the Supporting Fig. 6. Interference fringe contrast measured as a function of the dis- Information, creates a double image of the condensate with μ placement between a double image of the polariton emission for two in- a spatial resolution of 0.3 m. Fig. 6 shows the measured contrast cident cw pump powers in the Al(Ga)N nanowire device (sample 1). (Inset) (Imax − Imin)/(Imax + Imin) of the fringes as a function of dis- Measured intensity variation at zero displacement as a function of relative

placement between the images in the two arms. The measurement phase between double images for Pinc = 1.2 mW.

Das et al. PNAS Early Edition | 5of6 Downloaded by guest on October 5, 2021 sample shown in Fig. 1B andintheSupporting Information.The The nanowires are dispersed on half of the Si3N4 cavity and single nanowires are selected by e-beam lithography. Square-shaped mesa microcavities of nanowire is embedded in-plane in the microcavity. The XA exciton– polariton emission is collected in the direction vertical to the c axis 10-μm side are formed by photolithography and etching on a Si substrate. of the nanowire. The emission must therefore be linearly polarized Sample 2 consists of a single GaN nanowire of length and diameter equal to in a direction perpendicular to the c axis and the direction of 700 and 50 nm, respectively, fully embedded in an identical dielectric microcavity. Time-integrated photoluminescence (PL) measurements were emission, independent of the excitation intensity. Polariton super- performed on the microcavity samples by nonresonant excitation with the ﬂuidity and associated quantized vortices observed in exciton– linearly polarized output of a frequency-tripled (λ = 267 nm, frep = 80 MHz, polariton condensates (43, 44) and dilute atomic gas BECs (45, 46) and pulse width of 150 fs) Ti:sapphire laser. A doublet lens was used to focus

could not be investigated because of the intrinsically weak emission the pump beam at an incident angle of 20° on to the exposed Al0.05Ga0.95N from the 1-μm GaN region in the nanowire microcavity, which limits end of the nanowire. The excitons created by optical absorption enter the any imaging of the interference pattern and subsequent extraction microcavity and spontaneously form exciton–polaritons which then drift and of phase information. diffuse to the center GaN region of the nanowire. However, this arrange- In conclusion, a spatial polariton trap was created along the ment does not completely prevent light backscattered by the lower DBR length of an Al(Ga)N nanowire and strong coupling effects were from exciting the entire nanowire. A finite-difference time-domain calcu- – lation, taking into account the excitation and sample geometry, indicates investigated in the polariton emission of a planar nanowire ∼ dielectric microcavity sample. It is evident that the trap assists in that the intensity of excitation by the scattered light in the GaN region is 1% – of the incident excitation intensity (Supporting Information). Hence, the evaporative cooling of the optically excited exciton polaritons as number of exciton–polaritons directly generated in the GaN region of the they are transported along the nanowire to form a near-equi- nanowire is negligible. The luminescence was collected from the center GaN librium BEC in the lowest bandgap GaN region of the nanowire. region of the nanowire by a 1.5-μmcorefiber patch cord and transmitted to ∼ Materials and Methods a spectrometer (with a spectral resolution of 0.05 nm). The collection optics is located on extended rails of a goniometer centered at the sample and has an The experimental sample 1 consists of a single graded bandgap Al(Ga)N angular resolution of 1°. For experiments with sample 2, the entire mesa- μ ∼ λ nanowire of length equal to 6 m and diameter 50 nm embedded in a Si3N4 shaped microcavity is uniformly illuminated by the same laser. cavity surrounded by SiO2/Si3N4 distributed Bragg reflectors (DBRs) on top and bottom. The nanowire sample is grown by molecular beam epitaxy on ACKNOWLEDGMENTS. The authors acknowledge the help provided by (001) silicon substrate and has the wurtzite crystalline form with the c axis H. Deng and L. Zhang. This work has been supported by the National Science parallel to the growth direction. The typical nanowire density is ∼1011 cm−2. Foundation MRSEC Program under Grant DMR-1120923.

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