GENERAL SCIENTIFIC SUMMARY
Introduction and background. In quantum mechanics, we often fall into difficulties when deciding the value of a physical quantity in the middle of a time evolution. Hardy's paradox, a photonic version of which is shown in the figure, is one of the most striking examples. We constructed this interferometer and observed the trajectories of photons via weak measurement, which causes little disturbance on the interferometer in a single run but still reveals information on the trajectories after many repetitions of the same experiment.

Main results. In our experiment, we implemented weak measurement by imprinting the path information onto polarizations of the photons with adjustable strength. We separately confirmed that the readouts of the measurement faithfully revealed path information, and that disturbances on the interferometers were small. Then we recorded the readouts when simultaneous detection occurred. The recorded results showed the paradoxical nature, namely, they indicated that for each photon, the probability of taking the overlapping arm was almost unity, while the joint probability was around zero.

Wider implications. Quantum paradoxes have often been discussed through logical inferences on physical quantities that are beyond the reach of experimental observation. Through weak measurement, we have revealed a paradoxical nature of quantum mechanics in a more direct way, namely, via experimental observation. We hope our results offer a renewed insight into the foundations of quantum mechanics.

Figure. Photonic version of Hardy's paradox. MZ1 is adjusted such that photon 1 arrives at C₁ only if MZ1 has been disturbed by photon 2. The same goes for MZ2. When both detectors detect photons simultaneously, we may thus infer that photon 1 has taken the path O₁, and that photon 2 has taken O₂. However, if two photons encounter each other at BS3, a two-photon interference effect would force them to exit from the same side of BS3, and hence there should be no simultaneous detection.

42.50.Dv Quantum state engineering and measurements

03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)

42.50.Xa Optical tests of quantum theory

Optics, quantum optics and lasers

Quantum information and quantum mechanics

Issue 3 (March 2009)

Received 10 December 2008

Published 4 March 2009