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cQED is one of the most active research fields because of its application in quantum computing (QC) as the superconducting (SC) quantum circuit. In this approach of QC, the “artificial atom” is constructed by adding the nonlinear Josephson junction to the carefully-designed, low-loss, linear circuits made by superconductor. Thanks to the nonlinearity, (usually the lowest) two energy levels could be selected out as the qubit for the purpose of QC. Because of the fully artificial construction and highly controllable behavior, the cQED system is one of the most competitive platforms of QC, showing the advantages in flexibility, operation, readout, and scaling up. However, the advantages of cQED system are also accompanied by challenges: the strong coupling to the environment makes cQED system susceptible to the noise and interference. Both the advantages and challenges indicate that, there is grand space to explore in the cQED system.
2DES is a research field in condensed matter physics with long history. Under the magnetic field, the continuous density of states of a 2DES is quantized into discrete energy levels called Landau levels (LLs). Depending on the filling factor which is the amount of filled LLs below the Fermi energy, the 2DES shows rich phases at low temperature. Following the discovery of the integer quantum Hall effect (IQHE), fractional quantum Hall effect (FQHE), magnetic-field-induced quantum Wigner crystal (WC), composite fermion (CF), striped/nematic phase, skyrmion, etc., have been observed/confirmed by experiments successively. Besides the IQHE which could be explained by a single-electron picture, most of the exotic phases of 2DES have many-body origin. The studies on those many-body phases of 2DES not only help us to understand the physics of highly correlated system, but also unveil the potential, impactful applications such as QC.