Bose-Einstein Condensation of Long-Lifetime Polaritons in Thermal Equilibrium

The experimental realization of Bose-Einstein condensation (BEC) with atoms and quasiparticles has triggered wide exploration of macroscopic quantum effects. Microcavity polaritons are of particular interest because quantum phenomena such as BEC and superfluidity can be observed at elevated temperatures. However, polariton lifetimes are typically too short to permit thermal equilibration. This has led to debate about whether polariton condensation is intrinsically a nonequilibrium effect. Here we report the first unambiguous observation of BEC of optically trapped polaritons in thermal equilibrium in a high-$Q$ microcavity, evidenced by equilibrium Bose-Einstein distributions over broad ranges of polariton densities and bath temperatures. With thermal equilibrium established, we verify that polariton condensation is a phase transition with a well-defined density-temperature phase diagram. The measured phase boundary agrees well with the predictions of basic quantum gas theory.

Figure 1

(a) Reflection of the excitation beam from the sample surface. The white circle indicates the region of the sample that is observed in photoluminescence (PL) imaging measurements after spatial filtering. (b) Normalized excitation light intensity along the $x=0$ line through the center of the excitation ring pattern shown in (a). (c) Spectrally resolved PL along $x=0$. The PL within the solid white lines is collected and imaged onto the spectrometer CCD in the far-field geometry for the polariton distribution measurements. The dashed white line indicates the photon energy gradient deduced from the low-density spectrum.

Figure 2

Energy distributions of polaritons in the center of the trap at (a) $\delta =-5\mathrm{meV}$ (weak interactions, nonequilibrium) and (b) $\delta =0\mathrm{meV}$ (strong interactions, nonequilibrium) at a bath temperature of $T_{\text{bath}}=12.5\mathrm{K}$ at different pump powers (see Supplemental Material for values [32]). The solid curves are best fits to the equilibrium Bose-Einstein distribution in Eq. (1). The fitted values of $T$ and $\mu$ are shown in Fig. 3. The power values from low to high are 0.12, 0.24, 0.45, 0.71, 0.93, 1.07, 1.10, 1.12, and 1.14 times of the threshold values $P_{\mathrm{BE}}$, which are 382 mW and 443 mW for detunings $\delta =5\mathrm{meV}$ and $\delta =0\mathrm{meV}$, respectively.

Figure 3

(a) Effective temperatures of polaritons for bath temperatures $T=12.5\mathrm{K}$ (blue points) and $T=22.5\mathrm{K}$ (red points) at different pump powers, extracted by fitting the energy distributions [shown in Fig. 2 for the 12.5-K case] to the equilibrium Bose-Einstein model. The dashed lines indicate the helium bath temperatures. (b) Reduced chemical potential $\alpha =\mu /k_{B}T$ for bath temperatures $T=12.5\mathrm{K}$ (blue points) and $T=22.5\mathrm{K}$ (red points) at different pump powers.

Figure 4

(a) The critical temperature as a function of lattice temperature for $\delta =0\mathrm{meV}$. The solid black line indicates $T_{\mathrm{BE}}=T_{\text{bath}}$. (b) Phase diagram of the transition to a degenerate Bose gas. The solid black line shows the best fit of a linear relation $N_{\mathrm{BE}}\propto T_{\mathrm{BE}}$.