Study of Phase Method in Tantalum Superconducting Qubit T₂ ^*Measurements

In this paper, the phase method is proposed to measure the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T_{2}^{*}$</tex> dephasing time in a Tantalum-based superconducting qubit. In the regular Ramsey method for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T_{2}^{*}$</tex> measurement, a superposition state precesses on the equatorial plane of the Bloch-sphere due to detuning. The dephasing during the precession is recorded. In the phase method, rapid rotation is applied to rotate the superposition state on the equatorial plane through various angles (phases) to extract the dephasing during an idle time right before the rotation. While the phase method has been used in atomic physics, it has not been commonly used to characterize <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T_{2}^{*}$</tex> in superconducting qubits. Compared to the traditional Ramsey method, the phase method does not require prior knowledge of the dephasing envelope, enabling it to capture the dynamic de-phasing behavior of a qubit during the measurement more easily. It also does not rely on detuning and, thus, is insensitive to any detuning error. In this paper, a Tantalum-based superconducting qubit with a high <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T_{1}(\sim 220\mu s)$</tex> is used. After careful calibrations, extensive dephasing experiments were conducted using both the Ramsey and the phase methods to extract <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T_{2}^*$</tex>. We show that the phase method is insensitive to detuning and works well even with a very sparse phase sampling (with a step size as large as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\frac{\pi}{2}$</tex>). We also show that, statistically, it is equivalent to the Ramsey method within ±10%. Therefore, if both the Ramsey method and the phase method are used together, it is expected a more accurate and reliable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T_{2}^{*}$</tex> extraction is possible.