Superconducting-circuit based Aulter-Towns splitting effect

Abstract

The superconducting quantum bit(qubit) based on Josephson junction is a macroscopic artificial atom. The basic parameters of the artificial atom can be changed by micro and nano machining. The three-dimensional (3D) Transmon qubit is a kind of qubit with the longer decoherence time. It is coupled with a 3D superconducting cavity by means of capacitance. It is a man-made coupling system between atom and cavity field, which can verify the effects of atomic physics, quantum mechanics, quantum optics and cavity quantum electrodynamics. In this paper, transmon qubits are prepared by the double angle evaporation method, and coupled with aluminum based 3D superconducting resonator to form 3D transmon qubits. The basic parameters of 3D transmon are characterized at an ultra-low temperature of 10 mK. The 3D transmon parameters are <i>E</i><sub>C</sub> = 348.74 MHz and <i>E</i><sub>J</sub> = 11.556 GHz. The coupling coefficient <i>g</i><sup>2</sup>/<i>Δ</i> between qubit and the 3D cavity is 43 MHz, which is located in the dispersive regime. The first transition frequency of qubit is <i>f</i><sub>01</sub><italic/> = 9.2709 GHz, and the second transition frequency is <i>f</i><sub>12</sub> = 9.0100 GHz. The 3D resonator is made of the material 6061T6 aluminum, the loaded quality factor is 4.8 × 10<sup>5</sup>, and the bare frequency of the resonator is 8.108 GHz. The Jaynes-Cummings readout method is used to find the optimal readout power to distinguish among the qubit in the ground state <inline-formula><tex-math id="M1">\begin{document}$ \left| {\rm{0}} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M1.png"/></alternatives></inline-formula>, qubit in the superposition state of <inline-formula><tex-math id="M2">\begin{document}$ \left| {\rm{0}} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M2.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ \left| {\rm{1}} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M3.png"/></alternatives></inline-formula>, and qubit in the superposition state of <inline-formula><tex-math id="M4">\begin{document}$ \left| {\rm{0}} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M4.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ \left| {\rm{1}} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M5.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ \left| {\rm{2}} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200796_M6.png"/></alternatives></inline-formula>. Then, the Aulter-Townes splitting (ATS) experiment can be fulfilled in this system. Unlike the method given by Novikov et al. [Novikov S, Robinson J E, Keane Z K, et al. 2013 <i>Phys. Rev. B</i> <b>88</b> 060503], our method only needs to apply continuous microwave excitation signal to the qubit, and does not need to carry out precise timing test on the qubit, thus reducing the test complexity of observing ATS effect. The ATS effect in resonance and non-resonance regime are observed. In the resonance ATS experiment, in order to obtain the peak value and frequency of resonance peak, Lorentz curve can be used for fitting peaks, and the ATS curve of double peak can be fitted by adding two Lorentz curves together. In the non-resonance ATS experiment, the detection signal is scanned, and the ATS double peak will shift with the different coupling signal detuning, forming an anti-crossing structure. The two curves formed by crossing free structure give two eigenvalues of Hamiltonian. By solving the equation, the experimental results can also be found to be consistent with the theoretical results.