Observation of the quantum paradox of separation of a single photon from one of its properties

We report an experimental realization of the quantum paradox of the separation of a single photon from one of its properties (the so-called “quantum Cheshire cat”). We use a modified Sagnac interferometer with displaced paths to produce appropriately pre- and postselected states of heralded single photons. Weak measurements of photon presence and circular polarization are performed in each arm of the interferometer by introducing weak absorbers and small polarization rotations and analyzing changes in the postselected signal. The absorber is found to have an appreciable effect only in one arm of the interferometer, while the polarization rotation significantly affects the signal only when performed in the other arm. We carry out both sequential and simultaneous weak measurements and find good agreement between measured and predicted weak values. In the language of Aharonov et al. and in the sense of the ensemble averages described by weak values, the experiment establishes the separation of a particle from one its properties during the passage through the interferometer.

Figure 1

Experimental apparatus. Pairs of correlated, horizontally polarized 810-nm photons are generated by spontaneous parametric down-conversion in a beta-barium borate crystal (DC) pumped by a 405-nm diode laser (PL). Detection of one photon (the idler) heralds the production of the other photon (the signal). The signal photon travels through a modified Sagnac interferometer with displaced paths implemented with a nonpolarizing beam splitter (BS). Microscope glass slides (GS) are used to adjust the relative path length in the interferometer, where the tilt of one slide is controlled by a motorized actuator. Half-wave plates (HWP) in each path realize the weak polarization measurement through a small rotation of polarization. A microscope glass slide oriented at Brewster's angle implements the weak measurement of presence through its probabilistic rejection of one polarization component. After the two beams are recombined, a polarizing beam splitter (PBS) postselects the horizontally polarized component. Idler and signal photons are captured by fiber-coupling lenses (labeled $A$ and $B$, respectively) and transmitted via multimode fiber-optic cables to single-photon counting modules (not shown).

Figure 2

Photon counts (per 5 s) when weak measurements of presence are performed inside the interferometer by filtering one of the arms, shown as a function of the position of the actuator that adjusts the relative phase between the two arms of the interferometer. The measurement is implemented by a Brewster-angle glass slide oriented to probabilistically reject either horizontal or vertical polarization. In agreement with theoretical predictions, the count rates are substantially affected only by a measurement of presence in arm 2.

Figure 3

Photon counts (per 5 s) when a weak measurement of circular polarization is performed in (a) arm 2 and (b) arm 1 of the interferometer, shown as a function of actuator position (relative phase). The measurement is implemented through a small polarization rotation by an angle ${\theta }_k$ in arm $k$. Solid lines are sinusoidal fits. In agreement with theoretical predictions, the visibility of the interference pattern is substantially affected only by the measurement in arm 1.

Figure 4

Photon counts (per 5 s) for simultaneous weak measurements of presence and circular polarization, shown as a function of actuator position (relative phase). Solid lines are sinusoidal fits. (a) Presence measurement in arm 1 and polarization measurement in arm 2. (b) Presence measurement in arm 2 and polarization measurement in arm 1.