# Femtosecond Laser Direct Writing of Integrated Photonic Quantum Chips for Generating Path-Encoded Bell States

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## Abstract

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## 1. Introduction

## 2. Design of the Photonic Quantum Chip

## 3. Experimental and Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the photonic quantum chip and the directional coupler (DC). (

**a**) Schematic representation of a photonic chip composed of one H and one CNOT gate to generate path-encoded Bell states. The DC in the red dashed box represents an H gate. (

**b**) Schematic representation of a waveguide directional coupler; IN1 and IN2 are the input ports, whereas OUT1 and OUT2 are the output ports of the device; L is the interaction length and d is the interaction distance in the coupling region of two adjacent waveguides.

**Figure 2.**Optical micrograph and mode distributions of a fabricated straight waveguide. (

**a**) Micrograph of the cross section of the waveguide. (

**b**) Mode of the fiber in H polarization; (

**c**) mode of the waveguide in H polarization; (

**d**) mode of the fiber in V polarization; (

**e**) mode of the waveguide in V polarization. The wavelength of the injected CW laser is 785 nm.

**Figure 3.**Experimental reflectivity and transmission of fabricated DCs. (

**a**) Measured reflectivity R and transmission T of the DCs with different interaction length L at fixed interaction distance d = 8 μm as well as fitting curves for R and T. (

**b**) Fitting for linear relation between coupling phase $\phi $ and interaction length L ranging from 0–1 mm.

**Figure 4.**Experimental setup for quantum characterization. Through Type-I spontaneous parametric down-conversion (SPDC) process, 808 nm photon pairs are generated by pumping the BBO crystal using 140 mW, 404 nm CW diode laser. Long pass filter (LPF) from 650 nm and interference filter (IF) at 808 nm with 3 nm bandwidth are used to ensure spectral indistinguishability. Half-wave plate (HWP) and polarization controller (PC) are used to control the polarization state of photons in fiber. A delay line is inserted into one way to control the relative arrival time of photons to ensure temporal indistinguishability. Photons are injected into waveguides in the chip through fiber array and then collected at the output by another fiber array. Single photon counting modules (SPCMs) and the Time to Digital Converter (TDC) are used to conduct coincidence counting of different output-photon combinations.

**Figure 5.**Coincidence counts in 30 s of post-selected output-photon combinations x′y′ denoted as Cx′y′ for different input-photon combinations xy denoted as x.y. INPUT as a function of the relative delay of photons input in x and y ports: (

**a**) input (1,3); (

**b**) input (1,4); (

**c**) input (2,3); (

**d**) input (2,4). From the interference curve with a deep dip, the HOM interference visibilities are (

**a**) 98.5 $\pm $ 1.2%, (

**b**) 97.8 $\pm $ 1.8%, (

**c**) 98.2 $\pm $ 1.8%, (

**d**) 99.5 $\pm $ 0.5%, respectively.

**Figure 6.**Reconstructed truth table of combined chip composed of one H gate and one CNOT gate. The labels on the Input axis represent $\left|{C}_{q}{T}_{q}\right.\u232a$, and the labels on the Output axis represent $\left|{C}_{q}^{\prime}{T}_{q}^{\prime}\right.\u232a$. P represents the probability for each input-output combination. The empty bars stand for the theoretical values, and the filled pink bars represent the experimental data. The average fidelity is as high as 98.8 $\pm $ 0.3%.

**Table 1.**Theoretical prediction of the ratio of output power for each output port y′(0′–5′) when laser is injected into each input port x (0–5).

Theory | 0′ | 1′ | 2′ | 3′ | 4′ | 5′ |
---|---|---|---|---|---|---|

0 | 1/3 | 2/3 | ||||

1 | 1/3 | 1/6 | 1/6 | 1/6 | 1/6 | |

2 | 1/3 | 1/6 | 1/6 | 1/6 | 1/6 | |

3 | 1/3 | 0 | 1/3 | 1/3 | ||

4 | 1/3 | 1/3 | 0 | 1/3 | ||

5 | 1/3 | 1/3 | 1/3 |

Experiment | 0′ | 1′ | 2′ | 3′ | 4′ | 5′ | F |
---|---|---|---|---|---|---|---|

0 | 0.350 | 0.650 | 0.999 | ||||

1 | 0.352 | 0.181 | 0.159 | 0.156 | 0.153 | 0.999 | |

2 | 0.355 | 0.180 | 0.155 | 0.155 | 0.155 | 0.999 | |

3 | 0.297 | 0.030 | 0.318 | 0.355 | 0.984 | ||

4 | 0.301 | 0.306 | 0.028 | 0.365 | 0.985 | ||

5 | 0.348 | 0.375 | 0.277 | 0.998 |

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**MDPI and ACS Style**

Li, M.; Zhang, Q.; Chen, Y.; Ren, X.; Gong, Q.; Li, Y.
Femtosecond Laser Direct Writing of Integrated Photonic Quantum Chips for Generating Path-Encoded Bell States. *Micromachines* **2020**, *11*, 1111.
https://doi.org/10.3390/mi11121111

**AMA Style**

Li M, Zhang Q, Chen Y, Ren X, Gong Q, Li Y.
Femtosecond Laser Direct Writing of Integrated Photonic Quantum Chips for Generating Path-Encoded Bell States. *Micromachines*. 2020; 11(12):1111.
https://doi.org/10.3390/mi11121111

**Chicago/Turabian Style**

Li, Meng, Qian Zhang, Yang Chen, Xifeng Ren, Qihuang Gong, and Yan Li.
2020. "Femtosecond Laser Direct Writing of Integrated Photonic Quantum Chips for Generating Path-Encoded Bell States" *Micromachines* 11, no. 12: 1111.
https://doi.org/10.3390/mi11121111