Simultaneous cooling by measuring one ancillary system

We present a simultaneous-cooling protocol for a double-resonator system via projective measurements on an ancillary $V$-type qutrit. Through repeated measurements on the ground state of the ancillary system, the two resonators can be cooled down to their respective ground states from thermal states. With respect to the measurement-based cooling, an optimized measurement-interval $τ_{\rm opt}$ is analytically obtained for the first time, which is inversely proportional to the collective thermal Rabi frequency $Ω_{\rm th}$ as a function of the resonators' average population of the last round. Under about only $20$ optimized measurements, the average population of the target resonators can be reduced by $6$ orders in magnitude. Our simultaneous or collective cooling protocol is scalable to the systems with more numbers of resonators and robust to the fluctuation in the resonator frequency.

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