Collective Pairing of Resonantly Coupled Microcavity Polaritons

We consider the possible phases of microcavity polaritons tuned near a bipolariton Feshbach resonance. We show that, as well as the regular polariton superfluid phase, a “molecular” superfluid exists, with (quasi-)long-range order only for pairs of polaritons. We describe the experimental signatures of this state. Using variational approaches we find the phase diagram (critical temperature, density, and exciton-photon detuning). Unlike for ultracold atoms, the molecular superfluid is not inherently unstable, and our phase diagram suggests it is attainable in current experiments.

Figure 1

(a) Illustration of one- and two-particle energy scales, showing how the cavity-exciton detuning $\delta$ determines the interchannel detuning $\nu$. (b) Lower (LP) and upper (UP) polariton dispersions [solid (magenta) lines], along with the cavity $C$ (exciton $X$) dispersion [dashed [red (blue)] lines] for $\delta =2\mathrm{meV}$. (c) Dependence of the rescaled polariton mass at zero momentum $m_{\text{LP}}(\mathbf{k}=0)/m_X$ [left (black) line] and of the interchannel detuning $\nu$ [right (red) line] on $\delta$. Plots are for GaAs parameters (${\mathrm{\Omega }}_R=4.4\mathrm{meV}$, $|E_b|=2\mathrm{meV}$ [27], photon mass $m_C={10}^{-4}{m}_X$, exciton mass $m_X=0.4m_e$).

Figure 2

$T=0$ phase diagram for a GaAs microcavity, plotting cavity-exciton detuning $\delta$ versus chemical potential $\mu$ (left) or total density $n$ (right). The normal phase $\mathrm{N}$ is white, MSF shaded light gray, and AMSF is dark gray. First [thick (red)] and second [thinner (blue)] order lines are separated by tricritical points (blue circles), while critical end points are (red) diamonds. Horizontal dot-dashed lines connect the same chemical potential first order boundaries in the phase separated (PS) region. Dashed lines are the mean-field boundaries neglecting quantum fluctuations.

Figure 3

Finite temperature phase diagrams with the same notation, color scheme, and GaAs parameters as in Fig. 2. The critical end point of Fig. 2 is now replaced by a triple point (purple square). Temperature is fixed to $T=4\mathrm{K}$ ($k_{B}T=0.34\mathrm{meV}$) in the top panels, while detuning is $\delta =10\mathrm{meV}$ in the bottom ones.