Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate

The fundamental mechanisms which control the phase coherence of the polariton Bose-Einstein condensate (BEC) are determined. It is shown that the combination of number fluctuations and interactions leads to decoherence with a characteristic Gaussian decay of the first-order correlation function. This line shape, and the long decay times ($\sim 150\mathrm{ps}$) of both first- and second-order correlation functions, are explained quantitatively by a quantum-optical model which takes into account interactions, fluctuations, and gain and loss in the system. Interaction limited coherence times of this type have been predicted for atomic BECs, but are yet to be observed experimentally.

Figure 1

Spectra corresponding to polariton emission from the bottom of the LP branch for detection angle $\Theta =\sim 0^{}°$ at excitation powers $P=1\mathrm{mW}$ and $30\mathrm{mW}$, respectively, below and above the threshold ($P_{\mathrm{th}}\sim 10–15\mathrm{mW}$) for condensation. Below threshold, the linewidth is broad ($\mathrm{FWHM}\sim 1.5\mathrm{meV}$), determined by the polariton lifetime ($\sim 1.5\mathrm{ps}$). By contrast, above threshold the emission consists of a number of very narrow lines with energy separations of $\sim 0.2\mathrm{meV}$ and linewidth of 0.06 meV (limited by the spectrometer resolution: the true linewidths (decay times) are obtained from the first-order correlation measurements). The inset shows the strongly nonlinear variation of the intensity of mode $E_1$ with power.

Figure 2

(a)–(d) Spectrally resolved, spatial images ($\sim 2\mu \mathrm{m}$ resolution) of the polariton emission for $P=3\mathrm{mW}$ (a) and $P=30\mathrm{mW}$ (b)–(d). The detection energies $E_1$ to $E_3$ for images (b) to (d) are given on the images and correspond to detection at the energies of the individual, resolved modes of Fig. 1.

Figure 3

(a) Variation of $g^{(1)}$ first-order correlation function versus delay time for a single condensate mode above threshold. (b) Phase coherence time ${\tau }_c^{(1)}$ of the condensate mode versus emission intensity showing a strong increase at threshold followed by saturation at powers approximately a factor of 2 above threshold. (c)–(d) Measured $g^{(2)}$ second-order correlation function versus delay time at powers $P=6$ and 30 mW, below (c) and a factor of 2 above (d) threshold, respectively. The full lines are fits with values for $g^{(2)}(0)$ and the coherence time, ${\tau }_c^{(2)}$ of 2 and 1.5 ps below threshold and 1.1 and 100 ps above.