Breakdown of Temporal Coherence in Photon Condensates

The temporal coherence of an ideal Bose gas increases as the system approaches the Bose-Einstein condensation threshold from below, with coherence time diverging at the critical point. However, counterexamples have been observed for condensates of photons formed in an externally pumped, dye-filled microcavity, wherein the coherence time decreases rapidly for increasing particle number above threshold. This Letter establishes intermode correlations as the central explanation for the experimentally observed dramatic decrease in the coherence time beyond critical pump power.

Figure 1

The breakdown of temporal coherence in photon condensates. The figure shows the ground state coherence time ${\tau }_0$ as a function of the pump rate ${\mathrm{\Gamma }}_{\uparrow }$, obtained from Eq. (2) (solid-black line) and via Eq. (5) (black crosses). In the background, the steady state population of the lowest six photon modes ([0,5]) inside the cavity for different pump rates is shown. The coherence of the condensed ground state decreases at the condensation threshold of mode ([2]) (dotted-gray line). For the numerical study, the cavity cutoff (the ground state) frequency is ${\omega }_0=535\mathrm{THz}$, with mode spacing of $\mathrm{\Delta }\omega =1.7\mathrm{THz}$. The photon loss and the molecule decay rate are equal to $\kappa \approx 0.2\mathrm{THz}$ and ${\mathrm{\Gamma }}_{\downarrow }\approx 3\times {10}^{-5}\mathrm{THz}$, respectively. The absorption and emission rates are calculated from experimental data [33].

Figure 2

Variation of the term $({\mathcal{A}}_0+{\mathcal{E}}_0){\mathbf{f}}_{00}$ in Eq. (5) as a function of the pump rate ${\mathrm{\Gamma }}_{\uparrow }$ (solid-red line), as it converges to $(\kappa +{\mathbf{A}}_0){\mathbf{h}}_0$ (dashed-blue line). The term starts decreasing at the condensation threshold of mode ([2]) (dotted-gray line). Importantly, this decrease is not accompanied by drop in ground state population $n_0$, as evident from Fig. 1. The inset closes in on the drop of the term around the threshold. The system parameters are the same as Fig. 1.

Figure 3

The contributing terms in the ground state population, the second excited mode and the intermode correlation as a function of rate of pumping. (a) Ground state population, $n_0=n_e+n_c$ (red, solid), along with the terms arising due to stimulated emission $n_e\propto {\mathcal{E}}_0{\mathbf{f}}_{00}$ (blue, dashed) and intermode correlation $n_c\propto {\sum }_{j\ne 0}({\mathcal{E}}_j+{\mathcal{A}}_j){\mathbf{f}}_{0j}{n}_{j0}$ (black, dotted). (b) Population of the ground state $n_0$ (red, solid) and the second-excited mode $n_2$ (blue, dashed dotted), along with the absolute value of the mode correlation $|n_{02}|$ (black, dashed) and $\sqrt{n_0{n}_2}$ (black, dotted). The system parameters are the same as in Fig. 1.