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Resonator filter spectroscopy

This experiment measures the resonator's Purcell filter frequency when the qubit is in the ground state.

Description

The standard cQED setup of dispersive measurement introduces an undesirable decay channel for the qubit due to energy leakage through the resonator into the transmission line1. (See Resonator Spectroscopy for more details on dispersive measurement.) This process, known as the Purcell effect, limits the fidelity of qubit readout.

To suppress this effect, a second resonator of frequency \(\omega_{f}\) can be coupled to the readout resonator (which has frequency \(\omega_r\)). This second resonator acts as a Purcell filter, inhibiting the propagation of photons emitted at the qubit frequency.

Experiment steps

  1. The frequency applied to the filter resonator is swept over a range of values defined around the expected Purcell filter frequency, \(\omega_f\), and its transmission is measured for each value.

Analysis steps

  1. The amplitude of the filter resonator's signal is calculated as \(\sqrt{I^2 + Q^2}\), where \(I\) and \(Q\) are the in-phase and quadrature components of the transmitted signal, respectively.

  2. This amplitude is plotted as a function of the applied frequency, and the Purcell filter frequency, \(\omega_f\), is extracted from the centre of a Fano line shape fit to the data.

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  1. Eyob A. Sete, John M. Martinis, and Alexander N. Korotkov. Quantum theory of a bandpass purcell filter for qubit readout. Phys. Rev. A, 92:012325, Jul 2015. doi:10.1103/PhysRevA.92.012325. ↩