Hyperentangled photon sources in semiconductor waveguides

We propose and analyze the performance of a technique to generate mode and polarization hyperentangled photons in monolithic semiconductor waveguides using two concurrent type-II spontaneous parametric down-conversion (SPDC) processes. These two SPDC processes are achieved by waveguide engineering which allows for simultaneous modal phase matching with the pump beam in a higher-order mode. Paired photons generated in each process are cross polarized and guided by different guiding mechanisms, which produces entanglement in both polarization and spatial mode. Theoretical analysis shows that the output quantum state has a high quality of hyperentanglement by spectral filtering with a bandwidth of a few nanometers, while off-chip compensation is not needed. This technique offers a path to realize an electrically pumped hyperentangled photon source.

Figure 1

(a) Epitaxial structure of the waveguide, with layer thicknesses $t$ and aluminum concentrations $x$; (b) vertical refractive index profile at 775 nm; (c)–(e) modal intensity profiles for the pump TE${}_{40}$ mode, down-converted TE Bragg mode, and TE TIR mode, respectively. The TM Bragg and TM TIR modes have similar profiles and are not shown here.

Figure 2

(a) Dependence of effective index of each mode on the ridge width; (b) the same as (a) but zoomed in around the cross points; (c) difference of PM wavelengths of the two SPDC processes as a function of the core thickness.

Figure 3

(a) Spectral intensities of the four terms in Eq. (3) and (b) the corresponding relative phases as functions of signal wavelengths using cw pump, i.e., ${\left|\varphi \left(\omega \right)\right|}^2=\delta (\omega -2{\omega }_0)$.

Figure 4

Real (left) and imaginary (right) parts of the filtered and normalized density matrices corresponding to Eq. (4) for a filter bandwidth of 2 nm, 5 nm, and 10 nm, respectively.

Figure 5

Dependences of the FEF and the numbers of available photon pairs per pump photon via the two processes on the filter bandwidth.