Experimental evidence for the physical delocalization of individual photons in an interferometer

Abstract

It is generally assumed that the detection of a single photon as part of an interference pattern erases all possible which-path information. However, recent insights suggest that weak interactions can provide non-trivial experimental evidence for the physical delocalization of a single particle passing through an interferometer. Here, we present an experimental setup that can quantify the delocalization of individual photons using the rate of polarization flips induced by small rotations of polarization. The results show that photons detected in equal superpositions of the two paths are delocalized when detected in a high probability output port, and "super-localized" when detected in a low probability output port. We can thus confirm that delocalization depends on the detection of photons in the output of the interferometer, providing direct experimental evidence for the dependence of physical reality on the context established by a future measurement.

Figures (7)

• Figure 1: Illustration of the measurement dependence of photon delocalization. (a) shows localized photons detected in path 1 or path 2. At the initial beam splitter, the path of each photon is selected randomly. (b) shows a delocalized photon detected after interference at a second beam splitter. In this case, it is conceivable that the photon is physically delocalized, with a larger part of the photon in one path and a smaller part in the other. The photon physically separates into two quantities that propagate along the two different paths.
• Figure 2: Method for observing photon delocalization. Vertically polarized photons are injected into a two-path interferometer. We apply local operations to the polarization using two Half-Wave-Plates(HWPs), HWP1 and HWP2, placed into the two paths of the interferometer. HWP1 rotates the polarization by a small angle $\theta_0(\ll 1)$, and HWP2 rotates the polarization in the opposite direction by the same angle $-\theta_0 (\ll 1)$. Since the probability of a polarization flip from V-polarization to H-polarization is proportional to the square of the rotation angle, localized photons all flip with the same probability, $P(H|1)=P(H|2)$. When interference is observed, the polarization flip probabilities $P(H|\pm)$ observed in the output ports change, where lower flip probabilities indicate that the local rotations can cancel each other. The flip probabilities $P(H|\pm)$ thus provide direct evidence for the delocalization of photons inside the interferometer.
• Figure 3: Illustration of the experimental setup with a Sagnag-like interferometer. The vertically polarized input photons were emitted by a laser, which is weakened using an ND filter to obtain a photon rate of 110000/s on average. A beam splitter(BS) with a 50:50 split was used for preparation of the superposition state. The relative phase $\phi$ was controlled by tilting either of two glass plates placed on two paths in the interferometer. The output photons were counted by two Avalanche photo detectors(APD) for 100s at each phase, where Glan-Thompson Polarizers (GT) were used to distinguish horizontal and vertical polarization.
• Figure 4: Probabilities $P(+)$ and $P(-)$ of detecting the photons in the respective output ports of the interferometer at different phases $\phi$. The phase was changed $-22.5\degree$ to $202.5\degree$ in steps of $5.625\degree$. The visibilities obtained from the data are 0.9575 for the $+$ output and 0.9629 for the $-$ output. These visibilities include the decoherence effects induced by the local polarization rotations in the paths.
• Figure 5: Delocalization of photons observed in output ports preferred by constructive interference. Graph (a) shows the phase dependence of $P(H|-)$, where constructive interference is observed for $\phi>90\degree$. Graph (b) shows the phase dependence of $P(H|+)$, where constructive interference is observed for $\phi<90\degree$. The solid circles represent the measurement results when the two paths interfered at the output. Solid squares and solid diamonds represent the data obtained when one of the paths was blocked. This data represents a value of $A^2(\pm)=1$, characteristic of localized photons. The axes on the right side of the graphs give the corresponding values of $A^2(\pm)$ based on this comparison. Delocalization is directly observed whenever constructive interference favors the output port in which the photon was detected.