Telecommunication technologies

Design of spatial mode beamsplitter.

(a) Si₃N₄ dispersion for a multi-mode waveguide with 190 nm height. Horizontal red line shows phase matching for waveguides with different widths for spatial mode multiplexing. Vertical red line shows phase matching between modes in a single waveguide for the spatial mode beamsplitter. (b) Symmetric grating structure for coupling the TE0 and TE2 modes. The period is defined by the difference in effective index between the modes in a particular waveguide. The period (Λ) is 6.675 μm and the grating depth, d, is 24 nm. The width, w, is 1,600 nm and the height is 190 nm. Inset: SEM of fabricated grating structure. Scale bar, 200 nm. (c) Simulation of mode conversion in a 50:50 splitter for η=0.5, where N=20 periods and all other dimensions are the same as in b.


Equation:
The attenuation of a waveguide path can be calculated using the following equation:
A = 10 log10 (1 - |Γ|^2) dB

where A is the attenuation in decibels, and Γ is the reflection coefficient. The reflection coefficient is a function of the dimensions and material properties of the waveguide and the frequency of the wave.

NOON interference visibility measurements

Finally, to show these structures can be cascaded and actively tuned, we fabricate a Mach–Zehnder structure to create a NOON state interferometer based on our spatial mode beamsplitter. The HOM interferometer and phase shifter produces the NOON state described by:  where φ is the phase between the two modes of the interferometer, and the subscripts 1 and 2 refer to the different modes. NOON states are more generally written as  and provide increased phase sensitivity, φ, by  for quantum metrology over the standard quantum limit of  . In our experiment, the Mach–Zehnder structure consists of two gratings separated by a phase shifter, a length of waveguide and heater (Methods; Supplementary Fig. 1). Within the phase shifter, the waveguide is tapered out to 10 μm width that gives a larger differential in phase shift between the fundamental and higher-order modes as the heater is tuned. In Fig. 5d–f, we show measurements of the classical interference by inputting a single arm of the SPDC source into the device and measuring the single counts of both output arms, which show the classical Mach–Zehnder fringe as expected. This specific device (η_exp=0.66) has a classical visibility of 82±8% with a period of about 1.3±0.082 W, which corresponds to the power of the heater. The relatively high powers required to achieve a differential phase shift between the higher-order modes requires further optimization. Simulations and extended discussion on this point are included in Supplementary Note 3 and Supplementary Figs 2 and 3. We then measure the two-photon interference, or NOON state interference, by measuring coincidences when both arms of the SPDC source are input into the device with no path delay. We observe a visibility of 86±1% with a period of 0.64±0.005 W, about half of the classical interference. In addition to the increased phase sensitivity, this demonstrates the active tunability of this device, which could be useful in state preparation for quantum simulators