<p>Photonic quantum emulator utilizes photons to emulate the quantum physical behavior of a complex quantum system. Recent study in spatiotemporal optics has enriched the toolbox for designing and manipulating complex spatiotemporal optical wavepackets, bringing new opportunities in building such quantum emulators. In this work, we demonstrate a new type of photonic quantum emulator enabled by spatiotemporal localized wavepackets with spherical harmonic symmetry. The spatiotemporal field distribution of these wavepackets has the same distributions of the wavefunction solutions to the potential-free Schrödinger equation with two controllable quantum numbers. A series of such localized wavepackets are experimentally generated with their localized feature verified. These localized wavepackets can propagate invariantly in space–time like particles, forming a new type of photonic quantum emulator that may provide new insight in studying quantum physics and open up new applications in studying light-matter interactions and quantum optics.</p>