Hong-Ou-Mandel interference of entangled Hermite-Gauss modes

Hong-Ou-Mandel (HOM) interference is demonstrated experimentally for entangled photon pairs in the Hermite-Gauss (HG) basis. We use two Dove prisms in one of the paths of the photons to manipulate the entangled quantum state that enters the HOM interferometer. It is demonstrated that, when entangled photon pairs are in a symmetric Bell state in the Laguerre-Gauss (LG) basis, they will remain symmetric after decomposing them into the HG basis, thereby resulting in no coincidence events after the HOM interference. On the other hand, if the photon pairs are in an antisymmetric Bell state in the LG basis, then they will also be antisymmetric in the HG basis, thereby producing only coincidence events as a result of the HOM interference.

Figure 1

Diagram of experimental setup to observe HOM interference of photons in the HG basis (imaging lenses not shown). BBO: $\beta$-barium borate crystal; APD: avalanche photodiode; CC: coincidence counter; SMF: single-mode optical fiber; SLM: spatial light modulator; IF: interference filter and BS: nonpolarizing 50:50 beam splitter.

Figure 2

Coincidence counts measured for a spectrum of HG modes when the Dove prisms are at $0^{\circ }$ to each other. (a) shows the coincidence counts measured when the path length is unequal, and (b) shows the coincidence counts decrease to almost zero when there is equal path length.

Figure 3

Coincidence counts measured for a spectrum of HG modes when the Dove prisms are at ${45}^{\circ }$ to each other. (a) shows the coincidence counts measured when the path length is unequal, and (b) shows that some of the modes have coincidence counts that decrease to zero while others double when there is equal path length.

Figure 4

Coincidence rate measured against the path-length difference between paths A and B showing the HOM interference dip measured for signal and idler photons in the ${\mathrm{HG}}_{02}$ and ${\mathrm{HG}}_{04}$ and ${\mathrm{HG}}_{11}$ and ${\mathrm{HG}}_{11}$ modes when the Dove prisms are at $0^{\circ }$. Due to the high coincidence rate, error from Poisson statistics is mostly negligible; therefore, error bars are not shown.

Figure 5

Coincidence rate measured against the path-length difference between paths A and B showing the HOM interference dip or peak measured for signal and idler photons in the ${\mathrm{HG}}_{01}$ and ${\mathrm{HG}}_{10}$ and ${\mathrm{HG}}_{04}$ and ${\mathrm{HG}}_{20}$ modes for when the Dove prisms are at ${45}^{\circ }$. Due to the high coincidence rate, error from Poisson statistics is mostly negligible; therefore, error bars are not shown.