Ground-State Selection by Pure Energy Relaxation in Polariton Condensates

Abstract

We study nonequilibrium mode selection in dissipative exciton-polariton condensates incoherently pumped through an excitonic reservoir in the presence of pure energy relaxation. For a confined system in which a vortex mode is selected at threshold, we show that energy relaxation qualitatively changes the condensation scenario: as the pump increases, the asymptotic state evolves from a vortex condensate to a rotating mixed state and then to a ground-state condensate. Pure energy relaxation thus destabilizes condensation into excited states and promotes ground-state selection.

Figures (3)

• Figure 1: Bifurcation scenario for mode competition without ($\lambda=0$, upper row) and with ($\lambda>0$, lower row) pure energy relaxation. The central stripe summarizes the asymptotic condensate state as a function of the pump $\mathcal{P}$: gray, no condensation (trivial state); blue, vortex state; green, mixed state; red, ground state. The pump thresholds $\mathcal{P}_{BV}$, $\mathcal{P}_{BM}$, $\mathcal{P}_{BG}$, and $\mathcal{P}_{AM}$, obtained within the perturbative approach, are indicated on the stripe. Panels (a)--(c) show the phase portraits in the absence of energy relaxation for $\mathcal{P}<\mathcal{P}_{BV}$, $\mathcal{P}_{BV}<\mathcal{P}<\mathcal{P}_{BG}$, and $\mathcal{P}>\mathcal{P}_{BG}$, respectively. Panels (d)--(h) show the corresponding phase portraits in the presence of energy relaxation for $\mathcal{P}<\mathcal{P}_{BV}$, $\mathcal{P}_{BV}<\mathcal{P}<\mathcal{P}_{BM}$, $\mathcal{P}_{BM}<\mathcal{P}<\mathcal{P}_{BG}$, $\mathcal{P}_{BG}<\mathcal{P}<\mathcal{P}_{AM}$, and $\mathcal{P}>\mathcal{P}_{AM}$, respectively. Filled circles denote stable fixed points, while open circles denote unstable ones.
• Figure 2: Evolution of the modal projections onto the eigenmodes of the linear problem for different pump strengths. Panels (a)--(c) correspond to the case with energy relaxation, while panel (d) shows the same parameters as in panel (b), but without energy relaxation. The blue curves represent the ground state, the red curves the vortex mode with azimuthal index $m=1$, and the magenta curves the vortex mode with azimuthal index $m=-1$. Panels (a)--(c) correspond to pump values ${\cal P}=1.106$, ${\cal P}=1.172$, and ${\cal P}=1.238$, respectively. See the text for details.
• Figure 3: Asymptotic condensate states in the presence of energy relaxation. Panels (a)--(c) show the condensate density distributions for three representative pump values. Panel (a) corresponds to the vortex state formed at ${\cal P}=1.106$. Panel (b) shows a snapshot of the rotating mixed state at ${\cal P}=1.172$; the white curve indicates the trajectory of the phase singularity. Panel (c) shows the ground-state condensate formed at ${\cal P}=1.238$. Panel (d) shows the normalized angular momentum ${\cal M}$ versus pump ${\cal P}$ (left axis) and the total condensate population $N$ (right axis), both with and without energy relaxation. Solid curves correspond to numerical simulations of Eq. \ref{['GPE']}, while dashed curves show the predictions of the perturbative theory. The thresholds $\mathcal{P}_{BM}$, $\mathcal{P}_{BG}$, and $\mathcal{P}_{AM}$ are indicated by vertical dashed lines.