Phase-Controlled Bistability of a Dark Soliton Train in a Polariton Fluid

We use a one-dimensional polariton fluid in a semiconductor microcavity to explore the nonlinear dynamics of counterpropagating interacting Bose fluids. The intrinsically driven-dissipative nature of the polariton fluid allows us to use resonant pumping to impose a phase twist across the fluid. When the polariton-polariton interaction energy becomes comparable to the kinetic energy, linear interference fringes transform into a train of solitons. A novel type of bistable behavior controlled by the phase twist across the fluid is experimentally evidenced.

Figure 1

(a) Far-field photoluminescence measured under nonresonant pumping. (Solid lines) Theoretical fits of the lower and upper polariton branches and (dashed lines) bare exciton and photon energy. The horizontal segment shows the energy and width for the resonant excitation conditions. (b) Sketch of the experimental configuration. (c) Spatially resolved emission measured along the wire in the linear regime, for $P=8\mathrm{mW}$, $\mathrm{\Delta }E=0.27\mathrm{meV}$, $d=50\mu \mathrm{m}$, and $\mathrm{\Delta }\phi \approx 0$. Dotted lines indicate the wire edges. The color scale is saturated in regions under the spots. (d) Measured intensity profile integrated in the transverse direction. (e) Intensity profile measured along the wire as a function of $\mathrm{\Delta }\phi$ for similar pumping parameters, well in the linear regime.

Figure 2

(a) Spatially resolved emission measured along the wire for $P=23\mathrm{mW}$ ($\mathrm{\Delta }E=0.27\mathrm{meV}$, $d=50\mu \mathrm{m}$, $\mathrm{\Delta }\phi \approx 0$). (b) Intensity profile integrated over the transverse direction. (c) Corresponding calculated emission profile. (d) Total measured emission intensity (integrated along both the transverse and longitudinal directions) as a function of pump power. The shaded gray region corresponds to the linear regime. (e) Measured and (f) calculated emission profile when scanning the power up (the low power data have been amplified by a factor of 10 for clarity). The horizontal red [blue] line corresponds to the profile shown in Fig. 1 [2].

Figure 3

(a),(c) Spatially resolved emission for $P=57\mathrm{mW}$, $\mathrm{\Delta }E=0.37\mathrm{meV}$, $d=50\mu \mathrm{m}$ and (a) $\mathrm{\Delta }\phi \approx 0$; (c) $\mathrm{\Delta }\phi \approx \pi$. (b),(d) Corresponding intensity profiles integrated over the transverse direction. (e),(f) Measured and (g),(h) calculated intensity profiles for increasing (e),(g) and decreasing (f),(h) phase difference $\mathrm{\Delta }\phi$ between the spots. White dotted lines indicate the value of $\mathrm{\Delta }\phi$ for which a soliton is expelled or generated. The measured number of solitons is indicated in white.

Figure 4

(a)–(d) Number of solitons measured when scanning $\mathrm{\Delta }\phi$ up (open symbols) and down (closed symbols). (a) Same parameters as in Figs. 3 and 3; (b) $\mathrm{\Delta }E=0.21\mathrm{meV}$, $P=42\mathrm{mW}$, $d=60\mu \mathrm{m}$; (c) $\mathrm{\Delta }E=0.35\mathrm{meV}$, $P=90\mathrm{mW}$, $d=40\mu \mathrm{m}$; (d) $\mathrm{\Delta }E=0.20\mathrm{meV}$, $P=103\mathrm{mW}$, $d=40\mu \mathrm{m}$. The fluctuations due to phase noise in the experimental setup are estimated on the order of $\pm 0.03\pi$.