Ground-state chiral currents in the synthetic Hall tube

Hall tube is an important model to simulate the quantum effect. However it hasn't been realized in superconducting circuits which have emerged as a promising platform for macro-controlling Taking advantage of fine tunability circuits, three-chain transmon qubits with periodic boundary condition are designed this paper. For constructing synthetic tube, ac magnetic fluxes introduced drive each qubit. The gauge field can be tuned independently by properly choosing driving phases. Then ground-state chiral currents discovered Meissner current on <inline-formula><tex-math id="M1">\begin{document}$xy$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220293_M1.jpg"/><graphic xlink:href="16-20220293_M1.png"/></alternatives></inline-formula> plane (<inline-formula><tex-math id="M2">\begin{document}$xy$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M2.jpg"/><graphic xlink:href="16-20220293_M2.png"/></alternatives></inline-formula>-M), vortex id="M3">\begin{document}$xy$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M3.jpg"/><graphic xlink:href="16-20220293_M3.png"/></alternatives></inline-formula> id="M4">\begin{document}$xy$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M4.jpg"/><graphic xlink:href="16-20220293_M4.png"/></alternatives></inline-formula>-V), id="M5">\begin{document}$xz$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M5.jpg"/><graphic xlink:href="16-20220293_M5.png"/></alternatives></inline-formula> id="M6">\begin{document}$xz$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M6.jpg"/><graphic xlink:href="16-20220293_M6.png"/></alternatives></inline-formula>-V), and both id="M7">\begin{document}$xy$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M7.jpg"/><graphic xlink:href="16-20220293_M7.png"/></alternatives></inline-formula> id="M8">\begin{document}$xz$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M8.jpg"/><graphic xlink:href="16-20220293_M8.png"/></alternatives></inline-formula> planes (DV). distinguishing these currents, four order parameters id="M9">\begin{document}$J_{C//}$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M9.jpg"/><graphic xlink:href="16-20220293_M9.png"/></alternatives></inline-formula>, id="M10">\begin{document}$J_{AB}$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M10.jpg"/><graphic xlink:href="16-20220293_M10.png"/></alternatives></inline-formula> id="M11">\begin{document}$J_{BC}$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M11.jpg"/><graphic xlink:href="16-20220293_M11.png"/></alternatives></inline-formula>), id="M12">\begin{document}$J_{CA}$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M12.jpg"/><graphic xlink:href="16-20220293_M12.png"/></alternatives></inline-formula> defined. phase diagrams mapped out. emergence different phases due competition between coupling strengths id="M13">\begin{document}$\tilde{t}$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M13.jpg"/><graphic xlink:href="16-20220293_M13.png"/></alternatives></inline-formula> id="M14">\begin{document}$t_{CA}$\end{document}</tex-math><alternatives><graphic xlink:href="16-20220293_M14.jpg"/><graphic xlink:href="16-20220293_M14.png"/></alternatives></inline-formula>. emerging also emerge type II superconductor, generate opposite weaken influence applied field. Thus used diamagnet. At last we consider imperfections device fabrication. We proof when strength imperfection not large enough, shown paper remain valid. Moreover, possible experimental observations addressed. ground state generated applying microwave pulses. corresponding density matrix constructed tomography. After matrix, obtained calculating trace. These results enrich provide new route explore novel