Real-space collapse of a polariton condensate

Abstract

Microcavity polaritons are two-dimensional bosonic fluids with strong nonlinearities, composed of coupled photonic and electronic excitations. In their condensed form, they display quantum hydrodynamic features similar to atomic Bose-Einstein condensates, such as long-range coherence, superfluidity and quantized vorticity. Here we report the unique phenomenology that is observed when a pulse of light impacts the polariton vacuum: the fluid which is suddenly created does not splash but instead coheres into a very bright spot. The real-space collapse into a sharp peak is at odd with the repulsive interactions of polaritons and their positive mass, suggesting that an unconventional mechanism is at play. Our modelling devises a possible explanation in the self-trapping due to a local heating of the crystal lattice, that can be described as a collective polaron formed by a polariton condensate. These observations hint at the polariton fluid dynamics in conditions of extreme intensities and ultrafast times.

Figure 1. Snapshots of the polariton fluid density and phase at significant instants in the fs experiment.

(a,e,i) (first row) Density maps of the planar polariton fluid on a 80 × 80 μm area as three-dimensional view and (b,f,j) (second row) amplitude maps as two-dimensional view (the dashed circles depict the initial pump spot FWHM). The three columns represent time frames at t=0 ps (a–d), 2.8 ps (e–h) and 10.4 ps (i–l). These time frames correspond, respectively, to the pulse arrival, the ignition of the dynamical peak and its long-lived state sitting at the centre of a ring structure (see also Supplementary Movies 1–3). (c,g,k) (third row) phase maps and (d,h,l) (fourth row) unwrapped phase profiles along the radius. The phase gradient subtends the superflow and here exhibits a reversal of the phase curvature, leading to the development of an opposite flow, toward the centre. The total number of particles intially excited in the whole area is 250 × 10³ polaritons (see Methods). The behaviour in time of the total population and of the centre density are shown in the Supplementary Fig. 2.

Figure 2. Dynamical charts of the complex wavefunction after fs excitation.

(a) Time-space chart of the polariton amplitude (the square root is used to enhance the contrast) sampled with a timestep δt=50 fs. The polariton fluid oscillates with a Rabi period of about 800 fs (vertical stripes in the map), while the central density rapidly decays to zero before starting to rise as a bright peak. An echo pulse due to a reflection from the substrate edge is visible at t=11 ps. (b) Time-space chart of the phase ϕ(t, y). In a,b two solid lines mark the phase disturbance delimiting the expanding region with large ∇Φ. (c) The time evolution of amplitude in momentum space, . The initial polariton population, featuring a very narrow Δk width (imparted by the photon packet), ejects an expanding disk developing into a ring. (d) map at t=26 ps, showing the dark/bright ring structures. (e) A y−E cut showing the energy of the fluid along the diameter. The central brightest spot is less blueshifted than its sides. (f) Time-integrated E−k_y dispersion under the femtosecond coherent excitation. The dashed arrows depict the opening up in the k space and are associated to the dashed lines in c. The periodic oscillations in the energy domain of f are due to interferences of time-delayed reflections from the substrate edge as explained in the Methods section.

Figure 3. Phase crosscuts during the fluid evolution and signature of dark ring solitons.

(a) Unwrapped radial phase profile at early time, showing the reversal of the phase curvature. (b) The sudden phase switch at t=1.5 ps is shown together with the associated amplitude profile. The dip in the intensity with the π-jump in phase is a signature of radial interference and of a possible dark ring soliton, surrounding the bright peak. (c) Radial phase profile at later time, taken each 5 ps over a 0–40 ps timespan. The phase slope increases with time up to ∇Φ∼2π/(5 μm)≃1.25 μm⁻¹. (d) Amplitude and phase profiles at 16 ps showing that a nonlinear interference is reshaping the fluid in a series of concentric rings.

Figure 4. Time-space charts and space maps for different femtosecond pulse power.

(a,d,g) Time evolution of the radial modulus for three different powers (left column), (b,e,h) relative amplitude and (c,f,i) phase ϕ(x, y) maps at t=12 ps (mid and right columns, respectively). Increasing the initial density leads to a faster central depletion and stronger rise-back reaction. In the third row the dominating feature is the bright peak, with an enhancement factor of almost 5 in intensity, while outradiated waves are faster but almost cancelled out on a relative scale. This demonstrates the strong nonlinearities acting in the central gathering of polaritons and in setting the radial momentum and speed of the ring waves. The three rows refer to initial total populations (initial top density) of 25 × 10³ (55 μm⁻²), 125 × 10³ (275 μm⁻²) and 450 × 10³ polaritons (1,000 μm⁻²), respectively, excited by femtosecond pulses.

Figure 5. Theoretical time-space charts and xy maps of the polaron model.

(a,b) The calculated magnitude of the polariton fluid as a function of y-coordinate and time (a) together with its phase (b). (c,d) The corresponding calculated energy profiles for the upper and lower polariton branches are shown in c,d, respectively. (e–g) Spatial maps of the wavefunction amplitude for the time t=0, 4 and 13 ps and associated (h–j) phase maps. The presented case correponds to the power P₆ in the series of the Supplementary Figs 15–16.