Dynamically encircling exceptional points for robust eigenstate generation and all-optical logic operations in a three-dimensional photonic chip

Open Access

Dynamically encircling exceptional points for robust eigenstate generation and all-optical logic operations in a three-dimensional photonic chip

Chu Li, Meng Li, Ruiqi Wang, Yang Chen, Xifeng Ren, Linyu Yan, Qiang Li, Qihuang Gong, and Yan Li

Phys. Rev. Research 6, 013203 – Published 26 February 2024

Abstract

Dynamically encircling exceptional points (EEPs) in non-Hermitian systems have been utilized to realize robust on-chip mode conversions by taking the advantage that the output states are usually fixed and independent of the input states. This highly protects one of the specific eigenstates, but restricts their practical applications requiring superposition states. Here, we realize an on-chip robust eigenstate generator using a depth-varying 3D waveguide to overpass the EEP system. It not only preserves the robustness of the EEP system to generate one determinate eigenstate, but also generates another two-level eigenstate and arbitrary superposition states. Furthermore, by ingeniously combining two identical generators with a symmetric Y combiner, both the all-optical XOR and OR logic operations insensitive to the variations in the input light are realized by the destructive or constructive interference between the two generators' near-neighboring output signals. This paper paves the way for applications of EEP systems to highly robust state manipulations and information processing in integrated photonic and quantum devices.

Received 11 October 2023
Accepted 1 February 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.013203

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Integrated optics Optics & lasers Photonics Topological effects in photonic systems

Non-Hermitian systems Waveguides

Atomic, Molecular & Optical

Authors & Affiliations

Chu Li^1,2, Meng Li ^1,2, Ruiqi Wang ^1,2, Yang Chen ^3,4, Xifeng Ren^3,4, Linyu Yan^1,2, Qiang Li ^1,2, Qihuang Gong ^1,2,5,6,7, and Yan Li ^1,2,5,6,7,*

¹State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
²Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing 100871, China
³CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
⁴CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
⁵Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
⁶Hefei National Laboratory, Hefei 230088, China
⁷Peking University Yangtze Delta Institute of Optoelectronics, Nantong 226010, China

^*li@pku.edu.cn

Article Text

Click to Expand

References

Click to Expand

Issue

Vol. 6, Iss. 1 — February - April 2024

Subject Areas

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
State transformation in the EEP system. (a) Schematic of the EEP system. For the CCW encircling direction, both the states $| 0 〉$ from the input port 0 and $| 1 〉$ from the input port 1 are transformed into the antisymmetric state $| - 〉$ . For an arbitrary input state $C_{0} | 0 〉 + C_{1} | 1 〉$ , it is still transformed into the antisymmetric state $| - 〉$ with amplitude $C^{'}$ . (b) Design parameters of the EEP system. The loss $g_{I} (z)$ varies along the z direction in WG I and the propagation constant $β_{I I} (z)$ varies in WG II. (c) The CCW encirclement of EP in parameter space, corresponding to the forward propagation of light. (d) The eigenvalues swap with each other after a whole encirclement path. The red curve is the trajectory of the $E_{I I}$ to $E_{I}$ path and the blue curve is the trajectory of the $E_{I}$ to $E_{I I}$ path. (e) Normalized power ratios of symmetric (red curve) and antisymmetric (blue curve) states when light is injected into the WG I.
Reuse & Permissions
Figure 2
Working principle of the eigenstate generator. (a) Schematic of the two-level eigenstate generator, which is a 3D integration of the EEP system and the overpass waveguide. The blue and red arrows represent the independent paths of the input state $| 0 〉$ and $| 1 〉$ , respectively. When the input state is $| 0 〉$ , it enters into the EEP system and is transformed into the antisymmetric state $| - 〉$ , then the state $| - 〉$ maintains as an eigenstate until it is eventually outputted. While the input state is $| 1 〉$ , it first enters into the overpass waveguide and turns into the auxiliary state $| A 〉$ , then the state $| A 〉$ is transformed into the symmetric state $| + 〉$ during the coupling between the overpass waveguide and the two identical neighboring symmetrically arranged waveguides. (b) The micrographs of the EEP system with different depth of focus, which demonstrates that the depth-varying waveguide overpasses EEP system without crossing. (c) The intensity of the states $| A 〉$ and $| + 〉$ during the coupling between the overpass waveguide and the two identical neighboring symmetrically arranged waveguides.
Reuse & Permissions
Figure 3
Experimental results. (a) The experimental setup. (b) Experimental results of single port input. The dashed bars represent the theoretical results. (c) The evolution of normalized intensity of port 0' and port 1' with different values of $φ$ . (d) Experimental results of vertically polarized 785 nm light input and both the horizontally and vertically polarized 808 nm light input. The horizontal (vertical) arrow represents horizontal (vertical) polarization. (Coupling lens, CL; beam splitter, BS; power attenuator, PA; delay line, DL; polarization controller, PC; objective lens, OL.)
Reuse & Permissions
Figure 4
On-chip robust XOR and OR operations. (a) Schematic diagram of the structure that combines two generators with a Y-shaped combiner. The multiplexing of the XOR and OR operations are shown in the right column. [(b),(c)] The output intensity distributions for both single and superposition inputs at ports A0(A1) and B0(B1), which indicate a XOR(OR) operation. (d) The output intensity for both the horizontally and the vertically polarized light input cases with the wavelength of 785 nm and 808 nm. The top (bottom) four columns represent the case where A0 and B0 (A1 and B1) are the input ports, corresponds to the XOR (OR) operation. The horizontal (vertical) arrow represents horizontal (vertical) polarization.
Reuse & Permissions
Figure 5
Schematic of the systems to obtain the fitted parameters and the results. (a) The schematic of the systems to measure the coupling strength, the propagation constants and the extra loss. (b) The relationship between the coupling strength and the distance. (c) The relationship between the propagation constant and the writing speed. (d) The relationship between the total additional loss and the number of scatterers in a 20 mm waveguide.
Reuse & Permissions
Figure 6
Results of different coupling strength and length of the EEP system. (a) The trajectories of the loops for three different coupling strengths. (b) The normalized power ratios of the antisymmetric states when light is injected into the WG I for three different coupling strengths. (c) and (d) are the normalized power ratios of the symmetric and antisymmetric states when light is injected into the WG I for $L = 12 mm$ and $L = 20 mm$ , respectively.
Reuse & Permissions

Physical Review Research