The wave-particle duality of light, a cornerstone of quantum mechanics, has been extensively studied. However, questions persist about the path a single photon takes in double-slit experiments. Weak measurement, which minimizes measurement disturbance, offers a new perspective. This technique has been applied in various contexts, including observing the spin Hall effect of light and measuring quantum wavefunctions. The quantum Cheshire cat effect, where a particle's properties can be separated from its spatial location, provides an intriguing framework. This concept has been demonstrated experimentally for neutrons and optical systems. While initially seen as a possible measurement interference effect, weak measurement theory supports its paradoxical nature. Scaling challenges in weak measurement, involving multiple auxiliary pointers, motivated the use of imaginary-time evolution (ITE), a simpler method for extracting weak values. This paper experimentally addresses the fundamental challenge of separating the wave and particle attributes of a single photon, inspired by a recent thought experiment proposing this separation. The success of this separation could shed light on the photoelectric effect, considering only the wave or particle attributes separately.

Previous research has explored wave-particle duality extensively, deepening our understanding of its theoretical and experimental aspects. However, the question of a single photon's path remains debated. Weak measurement offers a less-disruptive approach to quantum state analysis, enabling the extraction of information without collapsing the state. Studies using weak measurements have demonstrated various applications. The quantum Cheshire cat effect, inspired by Alice in Wonderland, adds another layer of complexity, suggesting that a particle's properties can be decoupled from its location. Several experiments have demonstrated this effect for neutrons and photons. The authors address the scaling challenges in conventional weak measurements by utilizing ITE, a more efficient method for extracting weak values.

The experiment uses an improved MZI setup inspired by the quantum Cheshire cat concept. The authors prepare a superposition state of wave and particle attributes using a wave-particle toolbox. This toolbox involves a polarization beam splitter (PBS), a half-wave plate (HWP), and a beam displacer (BD) to create the initial state |ψ⟩ = cos α|Particle⟩ + sin α|Wave⟩. Polarizations are used to encode wave and particle attributes. The pre-selection stage involves the superposition state entering the MZI, creating a pre-selection state. Weak measurement is implemented using neutral density (ND) filters to simulate the disturbance in ITE. The transmission of the ND filter is related to interaction time (t), enabling weak value extraction via the slope of a linear fit. The post-selection stage involves exchanging particle and wave-like states using a series of wave plates and BDs, leading to the final state being projected onto detectors D1-D3. Quantum state tomography was performed on the output state of BS2 to verify the setup's performance. Different observables (Π_P^L, Π_P^R, Π_P^T, Π_W^L, Π_W^R) were selected to observe wave or particle attributes in specific paths, and their weak values were calculated using the formula: <A>w = (∂N*/∂t)/2, where N* is the normalized incidence rate.

The experimental setup achieved high fidelity (99.45 ± 0.26%) in quantum state tomography, demonstrating its effectiveness. By varying the transmission rates of ND filters and measuring the corresponding detection rates, the authors extracted weak values for different observables. The results confirmed that the particle attribute is primarily constrained to one path of the interferometer, while the wave attribute is constrained to the other, demonstrating spatial separation of wave and particle attributes. The proportion of wave and particle attributes in each path is determined by α. When α ≈ 45°, the weak values show an approximately even distribution of the wave and particle attributes across the two paths. Figure 3 illustrates the experimental data for α ≈ 45°, showing linear fits for different observables. The extracted weak values corroborate the theoretical predictions, confirming the spatial separation of wave and particle properties.

The successful experimental separation of wave and particle attributes of a single photon supports the quantum Cheshire cat effect and provides new insights into wave-particle duality. The results challenge our classical understanding of how particles behave and provide a new perspective on fundamental quantum mechanics. The use of weak measurement and ITE simplifies the experimental setup, making it more accessible for further studies. These findings could inspire further investigations into similar phenomena and open new avenues for exploring the foundations of quantum mechanics.

This study presents the first experimental demonstration of separating the wave and particle attributes of a single photon using the quantum Cheshire cat concept. The results, obtained using weak measurement and ITE, validate the theoretical predictions and offer a novel approach to studying wave-particle duality. Future research could explore the implications of this separation in other contexts, such as the photoelectric effect, and could investigate the interplay between wave and particle attributes in more complex quantum systems.

While the experiment demonstrates a high degree of fidelity, potential limitations might include imperfections in the optical components and the approximations made in the theoretical model. Further investigations could focus on minimizing these potential sources of error and improving the precision of weak value measurements. The current work focuses on demonstrating the separation; further research should explore applications of this technique.