Optomechanically induced transparency in the presence of a strong Duffing nonlinearity

Optically probing the quantum nonlinearities of a single-mode optomechanical system has historically been hindered by extremely weak bare optomechanical couplings. This paper investigates whether introducing a strong mechanical Duffing nonlinearity—an intrinsic anharmonic term in the mechanical oscillator—can enhance quantum signatures in optomechanically induced transparency (OMIT) experiments. The authors analyze a driven optomechanical cavity featuring a strong Duffing term by transforming the system into a rotating frame, applying displacement transformations, and using a squeezing transformation to properly isolate the quantum linear and nonlinear interactions. By diagonalizing the linear Hamiltonian into polariton modes, the study derives the specific resonant conditions—particularly where the upper polariton energy equals twice the lower polariton energy—that dramatically amplify nonlinear scattering between photon-like and phonon-like polaritons.

The central finding is that a strong Duffing nonlinearity generates an effective three-wave mixing interaction between polaritons that bypasses the limitations of standard optomechanical coupling. When the rescaled Duffing parameter is much greater than unity, the effective cooperativity governing the characteristic OMIT spectral dip is controlled by the Duffing coefficient and mechanical frequency rather than the weak single-photon optomechanical coupling. This scaling vastly increases the effective cooperativity, raising it by orders of magnitude compared to traditional setups. Furthermore, the analysis reveals two distinct detuning regimes. When the cavity detuning exceeds twice the mechanical frequency, the resonance occurs at relatively modest driving strengths, keeping squeezing parameters low and producing a sharp, highly visible transparency dip on top of the broad cavity lineshape.

These results provide a viable pathway to observe genuine quantum effects of mechanical nonlinearities using standard OMIT configurations without requiring ultra-strong single-photon coupling regimes. Because the underlying enhancement mechanism relies on a resonant three-wave mixing process, the same parameter regimes and driving strategies can be directly translated to other quantum state engineering protocols, such as the generation of non-classical mechanical cat states or advanced photon-phonon entanglement schemes in optomechanical circuits.