Three-dimensional transmon coherence measurement method based on network analyser

Abstract

<sec>Three-dimensional(3D) transmon is a kind of superconducting qubit with long decoherence time, which has important applications in superconducting quantum computation, quantum optics, cavity quantum electrodynamics, et al. Rabi oscillation is a vital method to characterize the decoherence time of quantum system, and it is also a basic experiment to demonstrate the energy level evolution of quantum system. In order to test the Rabi oscillation of 3D transmon, strict timing control is necessary, and the process of testing and debugging is complicated. In this paper, 3D transmon samples are fabricated and their basic parameters <i>E_C</i> = 348.74 MHz and <i>E_J</i> = 11.556 GHz are tested and characterized. The coupling coefficient <i>g²</i>/Δ between qubit and the 3D cavity is 43 MHz, which is located in the dispersive regime. The qubit’s first transition frequency <i>f</i>₀₁<italic/> = 9.2709 GHz, and the second transition frequency <i>f</i>₁₂ = 9.0100 GHz. The 3D resonator is fabricated by the material 6061T6 aluminum, the loaded quality factor is 4.8 × 10⁵, and the bare frequency of the resonator is 8.108 GHz.</sec><sec>Through comparison, it is found that the Rabi oscillation time obtained by the proposed method is shorter than by the Jaynes-Cummings method. The main reasons are as follows. First, the measurement of network analyzer is a continuous measurement, and the test signal always affects the decoherence process of 3D transmon. Second, the quantum bit is in the ground state after decoherence, and the ground state measured by the network analyzer accounts for a relatively high proportion, which causes the curve measured by the network analyzer to be one-sided attenuation oscillation. Third, the dispersive readout method is related to the quality factor of the superconducting cavity. The storage time of microwave photons in the superconducting cavity is longer than the decoherence time of 3D transmon, so the quantum information is partially decohered before leaving the superconducting cavity, which will shorten the Rabi oscillation time.</sec><sec>An innovative Rabi oscillation test method based on network analyzer is presented. The test system based on this method is simple to build and can be used as a new way to quickly verify whether 3D transmon has quantum characteristics. This method can also be extended to other quantum systems for preliminarily verifying the time domain characteristics.</sec>