Fig. 2: Collective particle motion.
From: Non-Hermitian dynamics and non-reciprocity of optically coupled nanoparticles
The time traces and statistics of the particles’ position z1 (blue) and z2 (orange) differ in the weakly coupled (ga/γ ≈ 0.01 and ΔΩ/γ ≈ 1.18, top row), linear (ga/γ ≈ 0.32 and ΔΩ/γ ≈ 1.19, middle row) and nonlinear regime (ga/γ ≈ 1.04 and ΔΩ/γ ≈ 1.37, bottom row). In the middle and bottom rows, the system is in the \({{{\mathcal{PT}}}}\) symmetry-broken phase. a, The histograms of the particles’ motion show an increasing variance (top to middle) and eventually the transition from linear into nonlinear motion (bottom). b, Uncoupled particles move independently, which is confirmed by the uniform distribution of the phase delay \(\bar{\psi }\) between the oscillators. On the other hand, in the \({{{\mathcal{PT}}}}\) symmetry-broken phase the histograms show a preferred phase \({\bar{\psi }}_{\max }\) as z1 and z2 are strongly correlated. The black lines mark the most probable phase delay \({\bar{\psi }}_{\max }\). c, The joint z1–z2 distributions show the transition from a thermal motion (top) to a correlated motion (middle) to a limit cycle (bottom).
