Asking Photons Where They Have Been

We present surprising experimental evidence regarding the past of photons passing through an interferometer. The information about the positions through which the photons pass in the interferometer is retrieved from modulations of the detected signal at the vibration frequencies of mirrors the photons bounce off. From the analysis we conclude that the past of the photons is not represented by continuous trajectories, although a “common sense” analysis adopted in various welcher weg measurements, delayed-choice which-path experiments, and counterfactual communication demonstrations yields a single trajectory. The experimental results have a simple explanation in the framework of the two-state vector formalism of quantum theory.

Figure 1

(a) Measured power spectrum of the signal from the quad-cell photo-detector shows frequencies of oscillation of internal mirrors $A$ and $B$ of the Mach-Zehnder interferometer. (b) Only the frequency of mirror $B$ remains in the power spectrum of the signal when the second beam splitter of the interferometer is taken out.

Figure 2

(a) Measured power spectrum of the signal from the quad-cell photodetector shows frequencies of oscillation of all internal mirrors of the interferometer. (b) When the inner interferometer is tuned in such a way that the beam of light passing through it does not reach the photodetector, the power spectrum of the signal in the photodetector still shows frequencies of the mirrors of this interferometer. (c) These frequencies (and all other signals) disappear when we block the lower arm of the large interferometer without changing anything in the upper arm.

Figure 3

The two-state vector description of the photon inside the interferometer includes the standard forward evolving quantum state (red line) and the backward evolving quantum state (green dashed line) of the photon detected by the quad-cell photodetector. It provides an explanation of the observed power spectrum: frequencies $f_C$, $f_A$, and $f_B$ are present while $f_E$ and $f_F$ are not. The photon was present only where both forward and backward quantum wave functions do not vanish.

Figure 4

Detailed experimental setup.