Extending Wheeler's delayed-choice experiment to space

Abstract

Gedankenexperiments have consistently played a major role in the development of quantum theory. A paradigmatic example is Wheeler's delayed-choice experiment, a wave-particle duality test that cannot be fully understood using only classical concepts. We implement Wheeler's idea along a satellite-ground interferometer that extends for thousands of kilometers in space. We exploit temporal and polarization degrees of freedom of photons reflected by a fast-moving satellite equipped with retroreflecting mirrors. We observe the complementary wave- or particle-like behaviors at the ground station by choosing the measurement apparatus while the photons are propagating from the satellite to the ground. Our results confirm quantum mechanical predictions, demonstrating the need of the dual wave-particle interpretation at this unprecedented scale. Our work paves the way for novel applications of quantum mechanics in space links involving multiple photon degrees of freedom.

Fig. 1. Pictorial representation of Wheeler’s delayed-choice experiment in space.

A photon wave packet enters the first BS of an interferometer, which extends along thousands of kilometers in space. The interferometer can be randomly arranged according to two configurations that correspond to the presence or absence of the second BS (in/out BS) located on Earth. Following Wheeler’s idea, the configuration choice is performed when the photon has already entered the interferometer. In our actual implementation, the interferometer begins and terminates on the ground, extending up to the target satellite, and the measurement choice performed on ground is space-like separated from the photon reflection by the satellite.

Fig. 2. Scheme of the experimental setup and detection histograms.

A pulsed laser synchronized with the MLRO atomic clock exits the MZI in two temporal and polarization (pol) modes. The sHWP leaves the pulses unperturbed, and the telescope directs the beam to a target satellite. After the reflection, the photons are collected on the ground by the same telescope and injected into the optical table. The photons pass through the sHWP whose behavior is set according to the bit b extracted from an on-demand QRNG. The QRNG is inquired twice in each 100-ms cycle of the experiment, as detailed in the main text. In the inset, a 1-s sample of the extracted bits is shown. At the MZI output, two wave plates, a PBS, and two single-photon detectors (SPDs) perform a polarization measurement in the {|+⟩, |−⟩} basis. According to the value b of the random bit, interference or which-path measurement is performed, as shown by the detection histograms for a passage of the Starlette satellite. The counts in the central peak on the left histogram are comparable to the sum of the counts associated to the lateral peaks on the right one, as expected. HWP, half–wave plate; QWP, quarter–wave plate.

Fig. 3. Minkowski diagram of the experiment.

Along the temporal axis (not to scale) a 100-ms cycle between two SLR pulses is represented. The x axis represents the radial coordinate (not to scale) from the detectors, where x₀ is the position of both the sHWP and the QRNG. The dotted line is the satellite worldline. We only considered the detections in the temporal window τ, as detailed in the main text. A fast FPGA controller synchronized in real time with the MLRO tracking system drives the two shutters and the QRNG. For each cycle, we performed two independent measurements via the random bit extracted by the QRNG at times ${\mathit{t}}_{{\mathit{b}}_1}$and ${\mathit{t}}_{{\mathit{b}}_2}$, causally disconnected from the photon reflection at the satellite. The cycle is repeated for each 100-MHz train between two SLR pulses.

Fig. 4. Experimental results for the interference and which-path configurations.

Relative frequencies f_± of counts in the two detectors Det_± as a function of the kinematic phase ϕ introduced by the satellite for the passages of Beacon-C and Starlette satellites. The error bars are estimated using the Poissonian error associated to counts. We show the relative residuals as a function of ϕ below each plot. We note that, at the point ϕ ≈ 0 and ϕ ≈ 2π, the same subset of data was selected. In the interference configuration, we estimated a visibility ${\mathcal{V}}^{\mathit{B}}=40\pm 5\%$ for Beacon-C and ${\mathcal{V}}^{\mathit{S}}=39\pm 4\%$ for Starlette from the fitted data.