Dissipative Phase Transition with Driving-Controlled Spatial Dimension and Diffusive Boundary Conditions

We investigate theoretically and experimentally a first-order dissipative phase transition, with diffusive boundary conditions and the ability to tune the spatial dimension of the system. The considered physical system is a planar semiconductor microcavity in the strong light-matter coupling regime, where polariton excitations are injected by a quasiresonant optical driving field. The spatial dimension of the system from 1D to 2D is tuned by designing the intensity profile of the driving field. We investigate the emergence of criticality by increasing the spatial size of the driven region. The system is nonlinear due to polariton-polariton interactions and the boundary conditions are diffusive because the polaritons can freely diffuse out of the driven region. We show that no phase transition occurs using a 1D driving geometry, while for a 2D geometry we do observe both in theory and experiments the emergence of a first-order phase transition. The demonstrated technique allows all-optical and in situ control of the system geometry, providing a versatile platform for exploring the many-body physics of photons.

Figure 1

Sketch of the experimental setup. The laser is slaved using a proportional-integral-derivative (PID) controller, an arbitrary function generator (AFG) and an acousto-optic modulator loop to produce a power ramp; its intensity profile is reshaped using a spatial light modulator. Two photodiodes (PD) measure the power inside disks of diameter $l_D=5\mu \mathrm{m}$ at the center of the beams at the sample input and output. (a) Pump intensity profile shaping method: the light (dark) beam represents the zero (first) order of the diffracted beam from the SLM. (b) Output intensity from the sample as a function of the input intensity, plotted for a pump detuning of $\mathrm{\Delta }=\gamma$ and a 2D top-hat drive of diameter $l=30\mu \mathrm{m}$. (c) SLM phase pattern (upper) for obtaining 2D (left) and 1D (right) flat-top beam profiles (middle) of different sizes and intensities (bottom).

Figure 2

(a) [(b)] Theoretical (experimental) results for the steady-state polariton density $n_D^{\mathrm{SS}}$ averaged over the probing disk as a function of the drive intensity $I$ for different top-hat spot sizes $l$ (see color bar) in the 1D configuration with detuning $\mathrm{\Delta }=\gamma$. (c) The maximum derivative $\mathcal{S}(l)$ for each top-hat size $l$ normalized by the maximum derivative at $l_0=15\mu \mathrm{m}$, for both theoretical and experimental results (see legend). (d)–(f) The same quantities as in (a)–(c) for the 2D configuration. The dashed line in (d) is the prediction of the mean-field theory in Eq. (5). Note that as the top hat increases in size, the slope in the 1D configuration quickly saturates for increasing size $l$, while in the 2D configuration the slope sharply increases in both theory and experiment, as expected for a first order phase transition.