Purcell effect with microwave drive: Suppression of qubit relaxation rate

Abstract

We analyze the Purcell relaxation rate of a superconducting qubit coupled to a resonator, which is coupled to a transmission line and pumped by an external microwave drive. Considering the typical regime of the qubit measurement, we focus on the case when the qubit frequency is significantly detuned from the resonator frequency. Surprisingly, the Purcell rate decreases when the strength of the microwave drive is increased. This suppression becomes significant in the nonlinear regime.In the presence of the microwave drive, the loss of photons to the transmission line also causes excitation of the qubit; however, the excitation rate is typically much smaller than the relaxation rate. Our analysis also applies to a more general case of a two-level quantum system coupled to a cavity.

Quantum theory of a bandpass Purcell filter for qubit readout

“…The effect is similar to what was discussed in Ref. [23] for the standard setup without the filter, and can be crudely understood as being due to the ac Stark shift of the qubit frequency, which increases the resonator-qubit detuning ∆ rq . Since the Purcell rate with the filter scales with ∆ rq crudely as ∆ rq in the standard setup, the Purcell rate suppression due to microwaves is stronger in the case with the filter.…”

“…In the presence of strong microwave drive, the Purcell rate is further suppressed with increasing drive strength. We have found that this suppression is stronger than that obtained without a filter [23].…”

“…In this section we discuss the quantum derivation of the Purcell rate in the presence of the bandpass filter in the regime when the resonators are not driven or driven sufficiently weakly to neglect dependence of the Purcell rate on the number of photons in the resonator [23]. More precisely, we consider the quantum evolution in the singleexcitation (and zero-excitation) subspace.…”

“…The Purcell rate may decrease when the measurement microwave drive is added [23]. A simple physical reason is the ac Stark shift, which in the typical setup increases the absolute value of detuning between the qubit and readout resonator with increasing number of photons in the resonator, thus reducing the Purcell rate.…”

“…[23] for the case without the Purcell filter and using the two-level approximation for the qubit. It was shown that in this case the suppression factor Γ(n)/Γ(0) is approximately [(1 +n/n crit ) −1/2 + (1 +n/n crit )…”