Superradiant Droplet Emission from Parametrically Excited Cavities

Superradiance occurs when a collection of atoms exhibits a cooperative, spontaneous emission of photons at a rate that exceeds that of its component parts. Here, we reveal a similar phenomenon in a hydrodynamic system consisting of a pair of vibrationally excited cavities, coupled through their common wave field, that spontaneously emit droplets via interfacial fracture. We show that the droplet emission rate of two coupled cavities is higher than the emission rate of two isolated cavities. Moreover, the amplified emission rate varies sinusoidally with distance between the cavities, as is characteristic of superradiance. We thus present a hydrodynamic phenomenon that captures several essential features of superradiance in optical systems.

Figure 1

The experimental setup (see also Supplemental Material, Fig. 1 [31]). (a) A schematic illustration of a circular bath with two cavities spanned by a thin layer of fluorinated oil. The bath is vertically oscillated by an electromagnetic shaker, resulting in the emission of droplets from the two cavities. (b) A rare generation event in which two droplets are about to be created simultaneously. Scale bar, 3 mm.

Figure 2

Images of the instantaneous wave field generated by the cavities (red circles). (a) A single cavity. Two cavities with center-to-center distances of (b) $d=8\mathrm{mm}$, (c) $d=10.5\mathrm{mm}$, (d) $d=12\mathrm{mm}$, and (e) $d=87\mathrm{mm}$.

Figure 3

Experimental measurements of the droplet emission rate. (a) Dependence of the anomalous emission rate, ${\mathrm{\Gamma }}_N(d)=[\mathrm{\Gamma }(d)-2{\mathrm{\Gamma }}_0]/2{\mathrm{\Gamma }}_0$ (black dots) on center-to-center intercavity distance $d$. Each data point represents an average over a time interval of 300 seconds, corresponding to roughly 950–1300 droplet emission events. The dashed curve represents $A{\cos }^2(2kd)$, with $A=1.36$ and $k=0.85{\mathrm{mm}}^{-1}$ being the experimentally measured Faraday wave number in the vicinity of the cavities. (b) Time series of the emission events from a single cavity over a 300-second interval indicates the unpredictability of a single emission event. (c) Histogram of the interemission time intervals and its comparison to the first passage time model [36]. The red curve represents an inverse Gaussian distribution as given by Eq. (2). (d) Measured correlation $C$ of the drop emission event in the two cavities as a function of their separation distance $d$. The upper dashed line represents two uncorrelated cavities.