How to best probe quantum mechanical effects in mechanical resonators is a long-standing open problem. The usual position-measurement method is ultimately limited by the always-present "zero-point motion" fluctuations in the quantum regime. Here, we propose a spectroscopic approach to probe the vibrating motion of a nanomechanical resonator (NAMR) by indirectly coupling it to a superconducting transmission line resonator (TLR), via a Josephson qubit. The classical (quantum mechanical) vibrations of the NAMR induce symmetric (asymmetric) Stark shifts of the qubit levels, which can be measured by the voltage fluctuations in the TLR. Thus, the motion of the NAMR, including if it is quantum mechanical or not, could be probed by detecting the voltage-fluctuation spectra of the TLR.
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