Multimode Hong-Ou-Mandel Interference

We consider multimode two-photon interference at a beam splitter by photons created by spontaneous parametric down-conversion. The resulting interference pattern is shown to depend upon the transverse spatial symmetry of the pump beam. In an experiment, we employ the first-order Hermite-Gaussian modes in order to show that, by manipulating the pump beam, one can control the resulting two-photon interference behavior. We expect these results to play an important role in the engineering of quantum states of light for use in quantum information processing and quantum imaging.

Figure 1

HOM interferometer. SPDC-created photons are reflected through paths $s$ and $i$ onto a beam splitter (BS). The coordinate systems $x_t,y_t,z_t$ ($t=s,i$) are transmitted or reflected into coordinate systems $x_j,y_j,z_j$ ($j=1,2$). $x_p,y_p,z_p$ is the coordinate system of the pump field.

Figure 2

Experimental setup. The argon laser is used to pump a BBO ($\beta \mathrm{\text{−}}{\mathrm{B}\mathrm{a}\mathrm{B}}_2{\mathrm{O}}_4$) crystal cut for degenerate type II phase matching, generating noncollinear entangled photons by SPDC. The wire is used to generate Hermite-Gaussian (HG) modes (see text). The $L_s$ are spherical lenses ($f=500\mathrm{m}\mathrm{m}$) used to focus the pump beam in the plane of the detectors to increase the coincidence detection efficiency [7]. UV is an ultraviolet mirror used to block the laser beam. The down-converted photons are reflected through a system of mirrors and incident on a 50-50 beam splitter BS ($t=r\approx \sqrt{1/2}$). A computer-controlled stepper motor is used to control the path length difference by scanning mirror assembly $M_1$. HWP is a half-wave plate used to transform the polarization state. The detectors $D_1$ and $D_2$ are free space EG&G SPCM 200 photodetectors, equipped with interference filters (1 nm FWHM centered at 702 nm) and 2 mm circular collection apertures. Coincidence and single counts were registered using a personal computer.

Figure 3

Coincidence counts when the polarization state is symmetric and the pump beam is a first-order Hermite-Gaussian beam. Open circles (○) correspond to ${\mathcal{W}}_{10}$ and solid circles (●) correspond to ${\mathcal{W}}_{01}$.

Figure 4

Coincidence counts when the polarization state is antisymmetric and the pump beam is a first-order Hermite-Gaussian beam. Open circles (○) correspond to ${\mathcal{W}}_{10}$ and solid circles (●) correspond to ${\mathcal{W}}_{01}$.

Figure 5

Coincidence counts when the polarization state is symmetric and the pump beam is an equal superposition of Hermite-Gaussian modes ${\mathcal{W}}_{01}$ and ${\mathcal{W}}_{10}$.