Photonic logic devices in curved time: Electron teleportation and photon–electron entanglement on engineered static Gaussian acceleration fields

This work presents a theoretical framework for photonic quantum systems operating in curved-time environments, where engineered static Gaussian acceleration fields, analogous to strong gravitational gradients, couple local mass gradients to time dilation and generate discrete temporal eigenstates. In this picture, an observer may perturb the acceleration profile, making the clock rate position-dependent; time itself becomes an inhomogeneous coordinate that confines wavefunctions in the time domain. Solving the resulting curvature-modified Schrödinger equation for surface-acoustic-wave (SAW) and quartz-crystal-microbalance resonators reveals temporal qubits, localized clock modes that form the basis for quantum logic. A Hamiltonian incorporating curvature-driven, time-dependent potentials and dipole–field coupling enables coherent photon–qubit interactions, temporal tunneling, and logic-gate operations with no spatial wiring. SAW devices have been experimentally shown to facilitate quantum entanglement and single-electron transport. These phenomena are naturally compatible with the temporal curvature architecture introduced here, where static or modulated Gaussian acceleration profiles replace the need for propagating SAWs while preserving coherent control over temporal qubit dynamics. Such static Gaussian acceleration fields can induce electrostatic potential wells through mass–energy backreactions in a quantum system without applying an external electric field and energy. Numerical simulations highlight material-specific behavior: graphene supports delocalized temporal states, whereas carbon nanotubes (CNTs) and MoS2 exhibit strong time-mode confinement. In a 20 μm CNT wire, for example, a spatially varying clock-rate γ(x) creates a temporal potential landscape that guides an electron from one end to the other, an effect that manifests as curvature-driven “teleportation” along the nanotube. This work further proposes a bioinspired architecture in which polarization-sensitive quantum-dot arrays modulate excitonic potentials across temporal states, mimicking the multiplexed vision of insect compound eyes. By treating time as an active, programmable degree of freedom, Gaussian acceleration fields sculpt clock-dependent “electrostatic” wells, offering a gravitationally informed route to quantum information processing, and entanglement in time-curved logic architectures.