Exceptional Point Dynamics in Photonic Time Crystals for Enhanced Optical Sensing

Abstract: Exceptional points (EPs) in non-Hermitian photonics offer singular sensitivity enhancements but have thus far been realized almost exclusively in spatially engineered platforms with fixed geometries and limited tunability. Here we extend EP physics into the temporal domain by introducing balanced gain--loss modulation in a photonic time crystal (PTC). A time-periodic refractive-index modulation $n(t)=n_{0}+δn\cos(Ωt)$ generates an effective non-Hermitian Floquet Hamiltonian that supports coalescence of quasi-eigenmodes in frequency space, constituting a genuine \textit{temporal exceptional point}. Using a reduced two-mode model for the dominant frequency sidebands, we derive a non-Hermitian dimer Hamiltonian $H_{\mathrm{PT}}(Δ,γ,κ)$ that is strictly $\mathcal{PT}$-symmetric for $Δ=0$ and identify the exact EP condition. Numerical analysis reveals the associated Riemann-sheet topology, mode exchange and Berry-phase accumulation upon encirclement of the EP, and the characteristic $\sqrt{\varepsilon}$ perturbation response indicative of enhanced sensing. We further construct a non-Hermitian transmission model that is exact within the reduced two-mode description, compute the Cramér--Rao bound (CRB) for temperature estimation under an explicit noise model, and show that EP-enhanced sensitivity persists when compared to a linewidth-matched Hermitian reference under identical resource constraints. Monte Carlo simulations confirm that the CRB is saturable using spectral measurements. These results establish temporal non-Hermiticity as a new paradigm for dynamically reconfigurable, broadband, and geometry-independent exceptional-point photonics.