Partial polarization by quantum distinguishability

We establish that a connection exists between wave-particle duality of photons and partial polarization of a light beam. We perform a two-path lowest-order (single photon) interference experiment and demonstrate both theoretically and experimentally that the degree of polarization of the light beam emerging from an output of the interferometer depends on path distinguishability. In our experiment, we are able to change the quantum state of the emerging photon from a pure state to a fully mixed state without any direct interaction with the photon. Although most lowest-order interference experiments can be explained by classical theory, our experiment has no genuine classical analog. Our results show that a case exists where the cause of partial polarization is beyond the scope of classical theory.

Figure 1

Two identical sources, $Q_1$ and $Q_2$, emit identical linearly polarized photons. The photons from $Q_1$ are sent through a polarization rotator, $\mathrm{\Gamma }$, and then superposed with the photons generated by $Q_2$ by a beam splitter, BS. The beam emerging from one of the outputs of BS is sent through a polarizer, $\mathrm{\Theta }$, and then detected by a photodetector, D. The device, M, attached to $Q_1$ determines with probability $1-{\mathcal{M}}^2$ whether $Q_1$ has emitted.

Figure 2

Pump beams $P_1$ and $P_2$ (dotted lines) are generated by a CW laser source (532 nm). The crystals, NL1 and NL2, produce linearly polarized signal ($S_1, S_2$; solid line; 810 nm) and idler ($I_1, I_2$; dashed line; 1550 nm) photons. A neutral density filter, $A$, is placed on the path of $I_1$ between NL1 and NL2. Initially, $S_1$ and $S_2$ are polarized in the same direction $x$. $S_1$ is sent through a half-wave plate, $\mathrm{\Gamma }$. $S_1$ and $S_2$ are superposed by a nonpolarizing beam splitter, BS. The detection-system (inside dotted box) used for polarization state tomography consists of a quarter-wave plate, q, a polarizer, $\mathrm{\Theta }$, and an avalanche photo detector, D; detection time 15 s. The mirror, $M_S$, is placed on a piezo-driven stage; DM1, DM2 and DM3 are dichroic mirrors.

Figure 3

Dependence of the degree of polarization $P$ on inerasable path distinguishability: (a) Experimentally observed dependence of $P$ on $\left|T\right|$ for various values of $\gamma$, and computed curves considering experimental imperfections (solid lines). Data points are represented by filled circles with error bars including both systematic and statistical errors. (b) Dependence of $P$ on $\mathcal{M}$ for various values of $\gamma$ predicted by the thought experiment [Eq. (2)]. The difference with the experimentally obtained results is because BS is slightly polarizing and $I_1$ beam suffers losses at the various optical components.