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Large coupling strengths in exciton-photon interactions are important forquantum photonic network, while strong cavity-quantum-dot interactions havebeen focused on s-shell excitons with small coupling strengths. Here wedemonstrate strong interactions between cavities and p-shell excitons with agreat enhancement by the \textit{in situ} wave-function control. The p-shellexcitons are demonstrated with much larger wave-function extents and nonlocalinteractions beyond the dipole approximation. Then the interaction is tunedfrom the nonlocal to local regime by the wave-function shrinking, during whichthe enhancement is obtained. A large coupling strength of $210\ \mu\mathrm{eV}$has been achieved, indicating the great potential of p-shell excitons forcoherent information exchange. Furthermore, we propose a distributed delaymodel to quantitatively explain the coupling strength variation, revealing theintertwining of excitons and photons beyond the dipole approximation.

Enhanced Strong Interaction between Nanocavities and p-shell Excitons Beyond the Dipole Approximation