Spatial Coherence of a Polariton Condensate

We perform Young’s double-slit experiment to study the spatial coherence properties of a two-dimensional dynamic condensate of semiconductor microcavity polaritons. The coherence length of the system is measured as a function of the pump rate, which confirms a spontaneous buildup of macroscopic coherence in the condensed phase. An independent measurement reveals that the position and momentum uncertainty product of the condensate is close to the Heisenberg limit. An experimental realization of such a minimum uncertainty wave packet of the polariton condensate opens a door to coherent matter-wave phenomena such as Josephson oscillation, superfluidity, and solitons in solid state condensate systems.

Figure 1

A sketch of the double-slit experiment setup. Upper: the LP spatial distribution is imaged to a CCD at plane C. Lower: a double-slit is inserted at plane A and imaged by lens II to a virtual plane B. The CCD at plane C, a distance $D$ from plane B, captures the double-slit interference pattern.

Figure 2

(a) Raw image of the interference pattern, slit separation $r=2.7\mu \mathrm{m}$, $P/P_{\mathrm{th}}=7$. (b) Measured (symbols) intensity $I(x)$ for $r=2.7\mu \mathrm{m}$, $P/P_{\mathrm{th}}=6.7$ and fitting by Eq. (1). Fitted $g^{(1)}(r)=0.560\pm 0.006$. (c) Same as (b), for $r=2.7\mu \mathrm{m}$, $P/P_{\mathrm{th}}=0.5$, and $g^{(1)}(r)=0.09\pm 0.02$.

Figure 3

(a) $g^{(1)}(r)$ vs $P/P_{\mathrm{th}}$ for different slit separations $r$ as labeled in the figure. (b) $g^{(1)}(r)$ vs $r$ for different pump rates $P/P_{\mathrm{th}}$ as given in the legend. The symbols are measured $g^{(1)}(r)$. The solid lines are fittings by Eq. (3). The dashed line at $P/P_{\mathrm{th}}=7$ is a fitting by Eq. (2). The dash-dotted line marks where $g^{(1)}(r)=1/e$. (c) $r_c$, the $1/e$ decay length of $g^{(1)}(r)$, vs $P/P_{\mathrm{th}}$ (circles) and $\Delta k$ vs $P/P_{\mathrm{th}}$ (triangles).

Figure 4

(a) System size $2\omega$ vs pump rates $P/P_{\mathrm{th}}$. Symbols are the data. The solid line is a fitting by Eq. (5), with ${\omega }_p=13.3\pm 0.1\mu \mathrm{m}$, ${\omega }_c=6.1\pm 0.1\mu \mathrm{m}$. The dotted line is a fitting by Eq. (4) for comparison, with ${\omega }_p=11.9\pm 0.2\mu \mathrm{m}$. (b) The position and momentum uncertainty product ${\sigma }_k{\sigma }_r$ vs $P/P_{\mathrm{th}}$. The dash-dotted line indicates the minimum uncertainty of ${\sigma }_k{\sigma }_r=1/2$.