Organic Polariton Lasing and the Weak to Strong Coupling Crossover

Following experimental realizations of room temperature polariton lasing with organic molecules, we present a microscopic model that allows us to explore the crossover from weak to strong matter-light coupling. We consider a nonequilibrium Dicke-Holstein model, including both strong coupling to vibrational modes and strong matter-light coupling, providing the phase diagram of this model in the thermodynamic limit. We discuss the mechanism of polariton lasing, uncovering a process of self-tuning, and identify the relation and distinction between regular dye lasers and organic polariton lasers.

Figure 1

(a) Cartoon illustrating our model: many molecules ($N$-level systems) are coupled to a cavity mode. (b)–(d) Weak coupling behavior. (b) Emission and absorption spectra of the molecules. (c) Weak coupling phase diagram. The cyan dashed line marks the phase boundary without vibrational dressing ($S=0$). (d) Dominant molecular transitions coupled into the lasing mode at threshold. All energies are measured in units of $ϵ\equiv 1$, other parameters are $S=0.1$, ${\omega }_v=0.2$, ${\mathrm{\Gamma }}_{\downarrow }=\kappa ={10}^{-4}$, ${\mathrm{\Gamma }}_z=0.03$, ${\gamma }_v=0.02$, $k_B{T}_v=0.025$, $N_v=4$.

Figure 2

Evolution of phase diagrams with increasing coupling, $g\sqrt{{\mathcal{N}}_m}$ (values as shown). Dash-dotted (yellow) lines indicate the cuts shown in Fig. 3. Parameters as in Fig. 1.

Figure 3

Nature of the lasing instability. Top [(a)–(c),(g)–(i)]: Real (right, solid cyan) and imaginary (left, gray scale) parts of linearized eigenvalues $\xi$. The gray scale indicates the photon component of that mode. The yellow dashed line highlights which imaginary part corresponds to the mode that is unstable (i.e., has a positive real part). The pink dotted line shows the effective photon frequency, ${\omega }_c^{\mathrm{eff}}$. Bottom [(d)–(f), (j)–(l)]: Vibrational composition of the unstable mode. Parameters as in Fig. 1.

Figure 4

(a)–(c) Phase diagrams at various cavity frequencies. The red, dashed line shows the weak-coupling theory phase boundary; see Ref. [45]. (d) Minimal critical pump strength (optimized over cavity frequency) as a function of matter-light coupling. The red shading indicates the weak to strong coupling crossover.