Collective state transitions of exciton-polaritons loaded into a periodic potential

We study the loading of a nonequilibrium, dissipative system of composite bosons—exciton polaritons—into a one-dimensional periodic lattice potential. Utilizing momentum resolved photoluminescence spectroscopy, we observe a transition between an incoherent Bose gas and a polariton condensate, which undergoes further transitions between different energy states in the band-gap spectrum of the periodic potential with increasing pumping power. We demonstrate controlled loading into distinct energy bands by modifying the size and shape of the excitation beam. The observed effects are comprehensively described in the framework of a nonequilibrium model of polariton condensation. In particular, we implement a stochastic treatment of quantum and thermal fluctuations in the system and conclude that polariton-phonon scattering is a plausible energy relaxation mechanism enabling transitions from the highly nonequilibrium polariton condensate in the gap to the ground band condensation for large pump powers.

Figure 1

Schematics of the semiconductor microcavity: (a,b) Details of the textured cavity region (see text); (c) Angle-resolved photoluminescence spectra below condensation threshold shows formation of a band-gap polariton spectrum resulting from evanescent coupling between mesa traps. Red lines show calculated single-particle energy bands [6] in the effective periodic potential of the depth $4.5$ meV. The measurements are recorded at a detuning between the cavity photon and exciton energies of $\mathrm{\Delta }=E_C-E_X=-14$ meV (at $k=0$ of the ground Bloch band), which is comparable to the Rabi splitting, $E_R=11.5$ meV. Continuous background contribution to the polariton emission is indicated by the red dashed line.

Figure 2

Experimental (a)–(d) and theoretical (e)–(h) study of the condensation in the one-dimensional array of mesas for an excitation with a narrow pump beam focused on a mesa (“on-site” excitation regime). (a)–(d) Far-field photoluminescence spectra recorded at various pump powers. (e)–(h) The dependence of polariton occupation at different energies as a function of in-plane momenta, $k_{\parallel }$, calculated using Eqs. (1) and (2). Large/small occupation numbers correspond to strong/weak intensity of the cavity emission in (a)–(d). The calculated occupation is integrated over the transverse-to-array coordinate, $y$. Shown are: (e) and (f) emission below the condensation threshold at the pump rates $P_0=1 \mu {\mathrm{m}}^{-2}{\mathrm{ps}}^{-1}$ and $P_0=10 \mu {\mathrm{m}}^{-2}{\mathrm{ps}}^{-1}$, respectively; (g) formation of the polariton condensate at the boundaries of the BZ in the vicinity of the threshold at $P_0=16 \mu {\mathrm{m}}^{-2}{\mathrm{ps}}^{-1}$; (h) condensation above the threshold at $P_0=20 \mu {\mathrm{m}}^{-2}{\mathrm{ps}}^{-1}$. The pump has a Gaussian profile with the FWHM of (a)–(d) $3.8 \mu \mathrm{m}$ and (e)–(h) 5 $\mu \mathrm{m}$ accounting for exciton diffusion. The multiple parabolic branches in (e)–(g) are artifacts of Fourier transformations and accumulation of many realizations of the profiles during the Monte Carlo calculations. As such, they do not have any physical meaning and do not affect the polariton dynamics.

Figure 3

Experimental images of the off-site versus on-site pumping with a tightly focused pump spot of 2 $\mu \mathrm{m}$ FWHM and formation of corresponding gap state condensates: (a) Sketch of the position of the pump laser spot aligned with respect to the polariton potential. (b) Far-field spectra of the gap state, corresponding with the pump-potential alignment. (c) Corresponding real space images of polariton emission. White dashed line indicates position of the pump spot.

Figure 4

Experimental and numerical spectra of polariton condensate in the high-power limit. (a,b) measured exciton-polariton dispersions for pump powers of 11 and 32 mW, respectively; (c,d) dependence of particle occupation at different energies as a function of in-plane momentum, $k_{\parallel }$, calculated using (1) and (2) at the pump rates (c) $P_0=30$ and (d) $P_0=40 \mu {\mathrm{m}}^{-2}{\mathrm{ps}}^{-1}$.