Characterization of Pound-Drever-Hall Techniques for Transmon Qubits

The circuit QED architecture for superconducting qubits relies on using the frequency of a microwave resonator to infer the state of a qubit. Currently, this is carried out by using a homodyne or heterodyne interferometer to measure the amplitude or phase of a microwave tone at the resonator frequency. This method, while extremely effective, is inherently sensitive to path length fluctuations in the measurement apparatus and to the phase stability of the microwave generators, necessitating high phase-stability generators and high-performance clock synchronization between both generators and digitizers. The Pound-Drever-Hall (PDH) method, which is common in optical-frequency laser-locking applications [1, 2], uses interference between multiple co-propagating tones to measure the detuning from cavity resonance, and has the potential to enhance readout signals using off-resonant tones. Recently it has been shown that PDH can improve measurement speeds in superconducting resonators enabling better characterization of TLS loss [3,4,5], and can reduce the sensitivity of readout to microwave-generator phase stability [6]. In this talk, we present characterization of PDH-style readout of a transmon qubit and the effect of off-resonant side-band tones on the transmon qubit.

[1] R. W. Drever et al., Appl. Phys. B, 31, 97–105 (1983).

[2] E. D. Black, Am. J. Phys., 69, 79–87 (2001).

[3] T. Lindström et al., Rev. Sci. Instrum., 82(10), 104706 (2011).

[4] S. E. de Graaf et al., IEEE Trans. Appl. Supercond., 24(1), (2014).

[5] John Pitten, Jim Phillips, Brandon Boiko, Josh Mutus, and Corey Rae McRae, “Rapid characterization of superconducting microwave resonators using the Pound-Drever-Hall technique,” APS March Meeting 2023.

[6] I. A. Adisa, M. Ritter, A. J. Kollár, “Pound-Drever-Hall Readout for Superconducting Qubits,” APS March Meeting 2024.