Compact component for integrated quantum optic processing

Quantum interference is indispensable to derive integrated quantum optic technologies (1–2). For further progress in large scale integration of quantum optic circuit, we have introduced first time two mode interference (TMI) coupler as an ultra compact component. The quantum interference varying with coupling length corresponding to the coupling ratio is studied and the larger HOM dip with peak visibility ~0.963 ± 0.009 is found at half coupling length of TMI coupler. Our results also demonstrate complex quantum interference with high fabrication tolerance and quantum visibility in TMI coupler.

where T 11 , T 12 , T 21 and T 22 are matrix elements depending on phase changes of two excited modes (fundamental mode and first order mode) propagated through TMI region of length L. The phase difference θ ∆ is written as β β ( − )L 00 01 , where, β 00 and β 01 are propagation constants of fundamental mode and first order mode respectively. The special characteristic of the linear quantum device is that the coupling between two photons is achieved by using quantum interference. In this direction, the state of two photons in which one is in input c 1 and other photon is in input c 2 is described as ψ = 1 1 . If the photons are entered through two input ports c 1 and c 2 , the coincidence probability for detecting one photon in each of the outputs d 1 and d 2 is written as 16,17 ,  =  +  P  T T  T T   12  12  11 22  12 21  2 . Quantum interference arises due to the indistinguishability of the photons depending mainly on polarization and arrival time. As TMI coupler is polarization independent, the polarization states of two photons in TMI region are considered to be same. Here, the indistinguishability of two photons is studied by varying arrival time of the photons which is taken to be parametric down conversion anti-correlated photons following Gaussian spectral density distribution 18,19 . Since, the coincidence measurement corresponds to coincidence probability P 12 12 , the expected number of the photon coincidence is then written as = overlap integral representing degree of distinguishability of two photons 18 , ω ∆ = difference between two central frequencies of Gaussian spectral distribution, τ = Δ x/c = time lag between the arrivals of two photons at the ports of TMI coupler and t c = coherence time which corresponds to coherence length l c = c.t c and K is a constant which is determined from incident number photons. For quantum mechanically indistinguishable photons (τ → 0), the expected number of the photon coincidence is written as, For classically distinguishable (τ → ∞), the photon coincidence, Depending on phase θ ∆ , the photon coincidence is obtained for different beam splitting ratio of TMI coupler. After obtaining coincidence counts theoretically for quantum mechanically indistinguishable photons and classically distinguishable photons, we have demonstrated quantum interference in compact two mode interference coupler fabricated by using SiON/SiO 2 technology. Here, we have also estimated HOM dip visibilities varying with coupling length of TMI coupler.

Results
The 2 × 2 TMI couplers of different beam splitting ratio were designed with index contrast ∆n = 0.05 and core index of 1.5 by using a commercial available BPM package (Fig. 1b shows designed 3dB 2 × 2 TMI coupler). For all the designs and simulations, a wavelength of 0.804 μ m and TE mode operation are taken. The deviation of design based on TM mode from that based on TE mode is within 0.25%, because of polarization independent property of TMI device. These devices were fabricated by using SiO 2 /SiON material. Figure 1c shows SEM photograph of 50:50 TMI coupler with coupling length ~11.5 μ m. Figure 2 shows the coincidence count rate versus relative delay in arrival time of photons (represented in terms of ∆x), measured simultaneously at both outputs d 1 and d 2 of TMI coupler by using the detectors with computer control. The Hong Ou Mandel (HOM) dip 20 is found and centered on zero path difference, confirming occurrence of quantum interference. The behaviour of HOM dip varying with splitting ratio is well explained theoretically in the figure. The largest and lowest HOM dip are obtained (theoretically with the equation 3) for TMI coupler with splitting ratio 50:50 and 10:90 respectively. The degree of quantum interference is quantified by quantum interference visibility V which is written as  (4). It is seen that the peak visibility V obtained at half power length of 11.5 μ m is 0.963 ± 0.009 which is more than that of 2 × 2 MMI device demonstrated by previous authors 13 . This is due to the fact that the jitter produced in TMI coupler is less than that of MMI coupler as fewer numbers of modes (2 modes) is propagated in TMI coupler than that of MMI coupler. These results shows high visibility quantum interference occurred in the TMI coupling length of 11.5 μ m which is 90 times lower than that of MMI coupler. The figure also confirms high visibility quantum interference even with small variation of coupling ratio near to peak region of visibility.

Two-photon quantum interference.
For bending loss < 0.01 dB 21 , the transition length L T of the access waveguide (along z direction) having bending radius R and separation 2 H T between access waveguides of TMI coupler (Fig. 1)  . Experimental measurement confirmed the insertion loss ~1.5 dB obtained by considering same transition length of the access waveguide. The overall length of 50:50 TMI beam splitter is obtained as ~100.8 μ m which is ~29.5 times less than that of directional coupler reported by previous authors 22 . Due to fabrication errors, there may be slight deviation of core and cladding refractive index which leads to degradation of quantum interference visibility in 50:50 TMI coupler and 50:50 MMI coupler. Figure 4 shows less quantum interference visibility reduction in TMI coupler than that in MMI coupler. . The solid line obtained theoretically by using the equation (3) for ω ∆ = 0.986 × 10 12 s −1 , λ = 0.804 μ m, n 1 = 1.5, n 2 = 1.45 and w = 1.5 μ m also represents same evidence. The figure also shows coincidence versus ∆x obtained theoretically by using the equation (3) for TMI coupler with splitting ratio 40:60, 30:70, 20:80 and 10:90. The degree of quantum interference for 40:60 splitting ratio is almost close to that of 50:50 splitting ratio.
TMI coupler has not only offered as an ultra compact component but also a high quantum interference visibility component for large scale quantum optic circuit. The TMI couplers promise to develop miniaturization and prototyping of complex quantum logic devices. Due to having fewer number of fabrication parameters, TMI couplers of splitting ratio from 50:50 to 40:60 provides almost same high quantum interference visibility. So this paves practical way for miniaturizing, scaling, and improving the performance for future quantum optic processing and network.

Methods
Devices. On silicon substrate, embedded waveguide having TMI region of width 2w ~ 3 μ m and length ~12 μ m with silicon oxinitride core of refractive index 1.5 and silica cladding of refractive index 1.45 were fabricated on silicon substrate by combination of plasma enhanced chemical vapor deposition (PECVD), photolithography and reactive ion etching (RIE) and. The overall length of the chip from input to output was ~100.8 μ m.  Experiment. The quantum interference experiments were performed by launching two photons into inputs (one into c 1 and other into c 2 ), generated by spontaneous down parametric conversion crystal made of type-I phase matched bismuth borate (BiB 3 O 6 ) pumped with 0.402 μ m wavelength pulse laser diode. The photon pairs made by BiB 3 O 6 crystal are traveled through 3 nm interference filter which allows each photon with coherence length of l c = λ 2 /Δ λ ~ 215 μ m. The photon were collected from the device outputs into butt-coupled single mode polarization maintaining fiber (PMF) and coupled to silicon single photon avalanche photodiodes (APDs) 13 . In case of low average pump power the state 1 1 c c 2 1 was produced at rate of 100 s −1 for two photon quantum interference.