1.2.2. Experimental Realization of Wheeler's Delayed-Choice Gedanken Experiment[1]

We report the realization of such a delayed-choice experiment in a scheme close to the ideal original proposal.

The delayed-choice scheme is implemented as follows. Linearly polarized single photons are sent by a polarization beamsplitter BS input through an interferometer (length 48 m) with two spatially separated paths associated with orthogonal S and P polarizations (Fig. 2). The movable output beamsplitter BS output consists of the combination of a half-wave plate, a polarization beamsplitter BS′, an electro-optical modulaor (EOM) with its optical axis oriented at 22.5° from input polarizations, and a Wollaston prism. The two beams of the interferometer, which are spatially separated and orthogonally polarized, are first overlapped by BS′ but can still be unambiguously identified by their polarization. Then, the choice between the two interferometer configurations, closed or open, is realized with the EOM, which can be switched between two different configurations within 40 ns by means of a homebuilt fast driver: Either no voltage is applied to the EOM, or its half-wave voltage V p is applied to it. In the first case, the situation corresponds to the removal of BS output and the two paths remain uncombined (open configuration). Because the original S and P polarizations of the two paths are oriented along prism polarization eigenstates, each “click” of one detector D1 or D2 placed on the output ports is associated with a specific path (path 1 or path 2, respectively). When the V p voltage is applied, the EOM is equivalent to a half-wave plate that rotates the input polarizations by an angle of 45°. The prism then recombines the two rotated polarizations that have traveled along different optical paths, and interference appears on the two output ports. We then have the closed interferometer configuration.

Any description in which light is treated as a classical wave, such as the semiclassical theory with quantized photo-detectors , predicts that these numbers of counts should obey the inequality $$\alpha=\frac{N_C\times N_T}{N_1\times N_2}\ge 1$$ Violation of this inequality thus gives a quantitative criterion that characterizes nonclassical behavior. For a single-photon wavepacket, quantum optics predicts perfect anticorrelation (i.e., a = 0) in agreement with the intuitive image that a single particle cannot be detected simultaneously in the two paths of the interferometer (2). We measured a = 0.12 ± 0.01, hence we are indeed close to the pure single-photon regime.

Our realization of Wheeler’s delayed-choice gedanken experiment demonstrates that the behavior of the photon in the interferometer depends on the choice of the observable that is measured, even when that choice is made at a position and a time such that it is separated from the entrance of the photon into the interferometer by a space-like interval.