Coherent Oscillations in an Exciton-Polariton Josephson Junction

We report on the observation of spontaneous coherent oscillations in a microcavity polariton bosonic Josephson junction. Condensation of exciton polaritons here takes place under incoherent excitation in a double potential well naturally formed in the disorder. Coherent oscillations set on at an excitation power well above the condensation threshold. The time resolved population and phase dynamics reveal the analogy with the ac Josephson effect. A theoretical two-mode model describes the observed effects, explaining how the different realizations of the pulsed experiment can be in phase.

Figure 1

(a) Time integrated real space image of the luminescence. The dash-dotted line is the line selected by the streak camera, and the solid lines with dashed edges enclose the linear disorder valley in which the double well potentials are frequent. (b) Time resolved photoluminescence along the dash-dotted line in (a) for $P<P_{\mathrm{OT}}$. (c) Same as in (b) but for $P>P_{\mathrm{OT}}$. The incident pulse defines the zero time.

Figure 2

Time resolved interferograms along the dash-dotted line of Fig. 1a formed by the superposition of the luminescence of the right and left wells. (a) $P<P_{\mathrm{OT}}$. The lack of currents is clearly seen with the constant phase relation between the two wells (straight fringes in time). (b) Same as in (a) but for $P>P_{\mathrm{OT}}$. The oscillatory current of particles is due to the linearly increasing relative phase in time which provokes the tilting of the fringes.

Figure 3

Temporal evolution of relative well population and relative well phase. The relative population (squares) oscillates symmetrically around zero, and the phase (circles) is following the population oscillations. A striking feature is that the phase shows small amplitude sawtoothlike oscillations. The region between 5 and 35 psec had a very low overall intensity and thus the relative phase could not be calculated.

Figure 4

Theoretical simulations. (a) Phase evolution for individual realizations for low excitation powers. (b) Populations in left [gray (red) line] and right (black line) well for the three realizations of (a). (c) Averaged relative phase modulo $2\pi$ and normalized populations from (a),(b). Panels (d)–(f) are the same as panels (a)–(c), only this time for excitation intensity above the oscillation threshold. Both the phase and the populations have very similar behaviors for different realizations demonstrating the effect of the phase-locking mechanism. The non-negligible fluctuations of the phase are the reason for the smoothed sawtooth phase profile [19].