Extended Data Fig. 4: Inferred experimental dynamical matrices.
From: Optomechanical realization of the bosonic Kitaev chain
The dynamical matrix \({{\mathcal{M}}}_{a}\) describing the evolution of mode operators \({a}_{j},{a}_{j}^{\dagger }\) is inferred from the measured susceptibility matrix χ through \({{\mathcal{M}}}_{a}={{\mathcal{T}}}^{-1}{({\rm{i}}\chi )}^{-1}{\mathcal{T}}\), where \({\mathcal{T}}\) is the matrix that transforms from mode basis \(\{{a}_{j},{a}_{j}^{\dagger }\}\) to the quadrature basis {xj, pj}. A perfect bosonic Kitaev chain has purely imaginary \({{\mathcal{M}}}_{a}\), that is, no on-site detunings and purely imaginary coupling rates. In our experiments, the real part of the diagonal elements of \({{\mathcal{M}}}_{a}\) indicates a small residual detuning (averaged across the four participating modes) of 3%, 5% and 7% of the mechanical linewidth γ for G = 0.75, 1, 1.25, respectively. The first two modes have higher optomechanical couplings g0 and are therefore more susceptible to fluctuations and nonlinearities in the optical spring effect.
