Erasing the orbital angular momentum information of a photon

Quantum erasers with paths in the form of physical slits have been studied extensively and proven instrumental in probing wave-particle duality in quantum mechanics. Here we replace physical paths (slits) with abstract paths of orbital angular momentum (OAM). Using spin-orbit hybrid entanglement of photons, we show that the OAM content of a photon can be erased with a complementary polarization projection of one of the entangled pair. The result is the (dis)appearance of azimuthal fringes based on whether the “which-OAM” information was erased. We extend this concept to a delayed measurement scheme and show that the OAM information and fringe visibility are complementary.

Figure 1

(a) Schematic of a quantum eraser that uses polarization-entangled photons using a physical double slit, as reported by Walborn et al. [13]. The two slits ($s_1, s_2$) are marked with orthogonal horizontal (H) and vertical (V) linear polarizers to distinguish the two paths. The polarizer (P) in arm $A$ acts as the eraser. (b) The proposed quantum eraser using geometric phase control to perform OAM-polarization conversion. The polarization control (P) of photon $A$ sets the OAM interference of photon $B$. (c) An example of two independent OAM abstract paths ($\left|\ell =5\right.〉$ and $\left|-5\right.〉$) and their superposition $\left|5\right.〉+\left|-5\right.〉$, having $2\ell$ azimuthal spatial fringes analogous to path-interference fringes in the double-slit experiment.

Figure 2

(a) Experimental setup for the hybrid entanglement-based quantum eraser. The SPDC state was prepared at the plane of the nonlinear crystal (PPKTP) and imaged onto the spatial light modulator (SLM) in arm $B$. The same imaging system was replicated in arm $A$, where the crystal plane was imaged onto the polarizer, while the OAM-to-spin (polarization) conversion was obtained through the geometric phase control of photon $A$ using a $q$ plate ($q=0.5$). The imaging system consisted of lenses $f_1=100$ and $f_2=300$ mm. Lenses $f_3=500$ and $f_4=2$ mm were used to couple the photons into single-mode fibers (SMFs). Note that the photons passed through 10 nm bandwidth interference filters (IFs) prior to collection. The SMFs were coupled to avalanche photon diodes (APDs) which detected the down-converted photons in coincidence. Furthermore, we performed a delayed-measure-type eraser by extending arm $A$ by 2.3 m, corresponding to a relative delay time of 7.66 ns with the polarizer placed after the lens $f_3$. (b) Angular phase masks that were encoded on the SLM and rotated by an angle $\theta$, serving as an azimuthal scanner to detect the spatial fringes.

Figure 3

Comparison of theory and experiment for a OAM quantum eraser. (a) Interference measurements where the OAM path information of photon $B$ is distinguished (squares) and erased (circles) by marking the path with a polarization choice on photon $A$. (b) Visibility of interference fringes with a variation of the polarizer angle ($\alpha$) in the range 0 to $\pi /4$. Similarly, (c) delayed-choice measurement results where the OAM path is distinguished (squares) and erased (circles), and subsequence measurements of the fringe visibility (d) with the polarizer angle. In all panels, experimental data are shown as symbols with error bars and theoretical calculations as dashed curves. In some frames, the error bars are of similar scale to the symbols.