Single-photon measurements confirm Richard Feynman’s vision of quantum mechanics

Every which way Photons can take so many possible paths. (Courtesy: S Zhu) Physicists have confirmed the two foundational postulates of Richard Feynman’s path-integral approach to quantum mechanics in a real-world experiment for the first time. This comes nearly 80 years after Feynman first published his path-integral formulation, which describes the time evolution of quantum systems. Fundamental thought experiments, such as Schrödinger’s cat, the Einstein–Podolsky–Rosen paradox and the quantum double-slit experiment have always been important for developing the theories of quantum mechanics. As technology improves, some thought experiments have been realized in the lab, confirming many aspects of quantum theory. However, thought and real experiments thus far have not addressed the fundamental question: how do quantum systems evolve between initial and final states? This question, explains Shi-Liang Zhu of South China Normal University in Guangzhou, lies at the heart of Feynman’s path integral postulates for his famous propagator equation. The postulates, first proposed in 1948, have never been directly tested – despite their foundational role in modern physics. Indeed, the path-integral formulation has been critical for the development of fields ranging from quantum field theory to cosmology and has provided a unified framework that connects quantum mechanics with classical physics through the principle of least action. The path integral’s predictions also underpin modern quantum science, from condensed matter physics to quantum statistical physics. As quantum theory was developed, several “pictures” emerged of how a quantum system evolves with time – including the Schrödinger and Heisenberg pictures. The Schrödinger equation, the Heisenberg equation and the Feynman propagator equation are formally equivalent formulations of quantum mechanics, explains Zhu. “However, while the first two are typically treated as fundamental postulates, the Feynman propagator equation is derived from two underlying postulates. This derivational asymmetry makes experimental tests of Feynman’s postulates particularly compelling.” Not a simple sum The first postulate is that a quantum particle does not travel along a single trajectory when moving from point A to point B; and instead every probable path contributes to its trajectory. The second postulate is that all possible paths have the same probability (or equal-magnitude amplitudes) and differ only by a path-dependent phase factor. This is very different from simply summing all the probabilities as in classical physics. At time ti, explains Zhu, a particle is localized at xi with its wave function denoted as ψ(xi, ti). The probability of the particle reaching xf at time tf is therefore determined through all possible paths connecting points A at (xi, ti) and B at (xf,tf). The j-th path contributes a probability amplitude ϕj. Feynman postulated that the probability P of the particle reaching xf at time tf equals the absolute square of the sum of probability amplitudes ϕj for all paths. As mentioned, all these contribute equally in magnitude, with each contribution’s phase being given by the classical action (in units of the Planck constant, ħ). “We have now directly measured the probability amplitudes ϕj of more than 1.4 million possible paths taken by single photons in an optical system,” says Zhu. “We did this by dividing the region between the starting point A and the end point B into a grid of points. We connected adjacent points by line segments and then measured the propagator for each segment. In total, there are 175 possible paths.” The results from this experiment, which is detailed in Science Advances, validate the first postulate with a mean absolute percentage error of 4.45% and a fidelity of 94.9%. They also confirm the second postulate with 94.7% fidelity. Reconstructing millions of path amplitudes The paper’s first author Yong-Li Wen notes: “because there were so many possible paths that the photons could take, the primary challenge in our experiments was to achieve sufficient accuracy to reconstruct millions of path amplitudes, since even marginal errors in individual propagator measurements accumulate multiplicatively, destroying phase coherence and rendering the reconstructed path distribution nearly random. “We overcame this problem through four key technical advancements: amplifying the signals; designing a customized high-precision imaging system; implementing real-time normalization via a reference beam to correct for photon fluctuation errors; and making sure the set-up was mechanically stable on the nanoscale.” These innovations improved single-photon propagator fidelity from 87.6% to 98.5%, something that allowed the team to resolve the global structure of path amplitudes with unprecedented precision. Feynman diagrams provide insight into quasiparticles in solids Read more The work establishes a powerful experimental framework for investigating path integrals in quantum systems, Zhu tells Physics World. “By confirming that quantum probabilities arise from path interference and that phases are governed by classical action, we provide experimental evidence supporting the view that quantum paths reflect physical reality rather than being mere mathematical artefacts.” The high-precision propagator methodology could also be used to study quantum-to-classical transitions and decoherence mechanisms, where understanding the role of interfering paths is essential, he adds. And it could be extended to probe fundamental phenomena such, as entangled histories and indefinite causal order across multiple space–time points. Beyond fundamental physics, the technique may make quantum simulations of complex condensed matter and quantum field theory phenomena, including instantons and magnetic monopoles, easier. “Perhaps most excitingly, by enabling precise propagator measurements in diverse environments, this framework could eventually be extended to interacting systems and curved space–times, allowing for valuable experiments with artificial quantum systems,” says Zhu. Want to read more? Registration is free, quick and easy Note: The verification e-mail to complete your account registration should arrive immediately. However, in some cases it takes longer. Don't forget to check your spam folder. If you haven't received the e-mail in 24 hours, please contact customerservices@ioppublishing.org. E-mail Address Register