Fig. 3: Experimental observations of multipath wave-particle transition in the delayed-choice experiment.

Measured transitions between particle and wave properties in several different scenarios: a–c classical mixture; f–h, quantum superposition; and k–m, intrinsic coherent quantum superposition. They are quantified by the probability distributions (normalized coincidences) for different {α, δ} of the control and {θ_d} of the target (θ_k = k(θ − π)) was chosen, in the 2-, 4-, and 8-path experiments. Density distributions (colored) represent experimental data, while contour lines (dashed) represent theoretical results. The F denotes the classical fidelity \({\sum }_{i}\sqrt{{p}_{i}{q}_{i}}\) summing over the whole space of (θ, α) or (θ, δ), where p_i and q_i are the measured and theoretical probabilities, respectively. High fidelities are obtained for all measurements. Results in a–c are consistent with classical optical multi-slit interference. The asymmetry of transition patterns in the quantum case f–h stem from quantum interference between wave and particle properties. Intrinsic coherent quantum superposition represents the intermediate particle-wave character, corresponding to the maximal wave-particle superposition, when α = 3π/2 or π/2. The δ-dependence of interference patterns in k–m, as an example measuring at α = 3π/2, confirms the existence of genuine wave-particle superposition. d, e Classical fringes, and i, j quantum fringes for the full-wave case at α = π, and full-particle case at α = 0, for d = 2, 4, and 8. The interference fringe becomes sharper for d-path interference; the multimode quantization results in a 1/d probability at the outport. Only when α = {0, π}, the classical and quantum fringes agree with each other. Examples of δ-dependence interference fringes for δ = {0, π/2} and α = 3π/2 in the n 2-path, and o 4-path experiments. The construction or destruction of interference appears by controlling the internal δ phase. Points represent experimental data, while lines represent theoretical values. All error bars (±3σ) are estimated from photon Poissonian statistics.