Decondensation in Nonequilibrium Photonic Condensates: When Less Is More

We investigate the steady state of a system of photons in a pumped dye-filled microcavity. By varying pump and thermalization the system can be tuned between Bose-Einstein condensation, multimode condensation, and lasing. We present a rich nonequilibrium phase diagram which exhibits transitions between these phases, including decondensation of individual modes under conditions that would typically favor condensation.

Figure 1

The upper panel depicts the mode populations $n_m$ as functions of pump rate for a constant thermalization rate $\gamma =1.8$. One can clearly see how mode [0, 1] condenses and then decondenses with increasing pump rate. The lower panel depicts the fraction of excited molecules $f_m$ accessible to any mode, and substantiates that the decondensation of mode [0, 1] is congruent with a decrease of $f_{[0,1]}$. This is highlighted in the central panel, which is a magnification of the lower panel.

Figure 2

Phase diagram of the photon gas as function of pump rate ${\mathrm{\Gamma }}_{\uparrow }$ and thermalization coefficient $\gamma$. Different colors indicate the number of condensed modes with the sole exceptions of “laser,” which indicates condensed phases of the system without condensation in the ground mode, and “truncated,” indicating potential truncation errors as the highest considered mode has condensed. Capital letters indicate which modes are condensed in a given region. Narrow areas in which only one of modes $[m_x,m_y]$ and $[m_y,m_x]$ are condensed are treated as if both modes are condensed in order to avoid structures that are too detailed; the fine structures between regions $I$ and $J$ and adjacent to region $M$ are a result of this. Rough phase boundaries in the top left region are due to limited numerical accuracy. The analytic estimates for various phase transitions indicated by white lines coincide very accurately with the numerically obtained thresholds. The cut for $\gamma =1.8$ through the phase diagram depicted in Fig. 1 is indicated by bold arrows.