Stimulated cooling in non-equilibrium Bose-Einstein condensate

Abstract

We report on the experimental observation of stimulated cooling in the non-equilibrium Bose-Einstein condensate (BEC) of weakly interacting exciton-polaritons from approximately room temperature down to 20K. By resolving the condensate in energy-momentum space and performing interferometric measurements, we distinguish the condensate from thermalized particles yet occupying excited states macroscopically. In contrast to the analytical quantum theories of non-equilibrium BEC [Shishkov et al., Phys. Rev. Lett. 128, 065301 (2022)], we observe segmentation of the particle density along the excited states into two fractions both following Bose-Einstein distribution, albeit with different effective temperatures and chemical potentials. Our results indicate that the temperature of the weakly interacting Bose gas is universally set by the density-dependent chemical potential, revealing a defining property of non-equilibrium BECs. Finally, we demonstrate that the stimulated nature of the cooling process directly governs the emergence of quantum coherence of the condensate and shapes the dissipative properties of the excited states.

Figures (4)

• Figure 1: Nonequilibrium BEC. (a) Schematic of the polariton thermalization in the energy-momentum space. (b) Particle density distributions as a function of energy and momentum at $P/P_{\mathrm{th}}= 1.6$.
• Figure 2: Condensation area. (a) Particle density distribution in momentum space as a function of pump power $P$, normalized to the density at the BEC threshold $P_{\rm th}$. (b) Ground-state density (${\bf k}={\bf 0}$) as a function of pump power. (c) Momentum-resolved linewidth as a function of pump power. (d) Ground-state linewidth as a function of pump power. The gray line in (a) and (c) indicates the BEC size in momentum space, defined as the momenta ${\bf k}$ such that $\gamma_{\bf k} \leq \gamma_{{\bf k} = {\bf 0}} + (\bar{\gamma} - \gamma_{{\bf k} = {\bf 0}})/3$, where $\bar{\gamma}$ is average linewidth below BEC threshold
• Figure 3: Spontaneous-to-stimulated thermalization. (a) Distribution of particles over energies for different pump powers from below $0.6P_{th}$ to above $3.5P_{th}$ condensation threshold. Gray solid line is fit with the sum of two Bose--Einstein distributions $N_{\rm Pol} = n^{\rm BE}_{\bf k}(T_{\rm L}, \mu_{\rm L}) + n^{\rm BE}_{\bf k}(T_{\rm H}, \mu_{\rm H})$ at $P/P_{\rm th}=2.8$. Gray dashed lines are $n^{\rm BE}_{\bf k}(T_{\rm L}, \mu_{\rm L})$ and $n^{\rm BE}_{\bf k}(T_{\rm H}, \mu_{\rm H})$ at $P/P_{\rm th}=2.8$. Open dots corresponds the data points which obey condensation area defined in Fig. \ref{['fig:2']}. (b) Temperature, $T$, and (c) chemical potential, $\mu$, extracted from the fit of the distributions with $n^{\rm BE}_{\bf k}(T_{\rm L}, \mu_{\rm L})$ and $n^{\rm BE}_{\bf k}(T_{\rm H}, \mu_{\rm H})$ for the low-energy range $(2.55~{\rm eV},2.57~{\rm eV})$ (black bars, L) and high-energy range $(2.585~{\rm eV},2.61~{\rm eV})$ (red bars, H) respectively, as functions of pump power normalized to the BEC threshold $P/P_{\rm th}$. Error bars indicate the standard error of the fitted temperatures and chemical potentials.
• Figure 4: Universal scaling of thermalization $\bf{T(\mu)}$. The temperature of particles ($T$) versus their chemical potential ($\mu$) both obtained from Bose--Einstein fit for the frequency range $(2.55~{\rm eV},~2.57~{\rm eV})$ (black dots) and $(2.585~{\rm eV},~2.61~{\rm eV})$ (red dots). Horizontal and vertical error bars indicate the standard errors of the fitted temperature and chemical potential, respectively. Gray lines show the $T(\mu)$ dependence predicted for an ideal Bose gas in the canonical ensemble. Inset: Temperature versus chemical potential above the BEC threshold. The red shaded region highlights the part of the $T(\mu)$ dependence not captured by the equilibrium ideal-gas theory, beyond non-interacting particles picture. Note, the chemical potential of the lower energy fraction at the threshold is $\mu_{th}= -80~{\rm meV}$, according to the date in Fig. \ref{['fig:3']}c.