Preparation and detection of a mechanical resonator near the ground state of motion


Cold, macroscopic mechanical systems are expected to behave contrary to our usual classical understanding of reality; the most striking and counterintuitive predictions involve the existence of states in which the mechanical system is located in two places simultaneously. Various schemes have been proposed to generate and detect such states1,2, and all require starting from mechanical states that are close to the lowest energy eigenstate, the mechanical ground state. Here we report the cooling of the motion of a radio-frequency nanomechanical resonator by parametric coupling to a driven, microwave-frequency superconducting resonator. Starting from a thermal occupation of 480 quanta, we have observed occupation factors as low as 3.8 ± 1.3 and expect the mechanical resonator to be found with probability 0.21 in the quantum ground state of motion. Further cooling is limited by random excitation of the microwave resonator and heating of the dissipative mechanical bath. This level of cooling is expected to make possible a series of fundamental quantum mechanical observations including direct measurement of the Heisenberg uncertainty principle and quantum entanglement with qubits.

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Figure 1: Nanomechanical device, measurement diagram and thermal calibration.
Figure 2: Measured noise spectra.
Figure 3: Nanomechanical heating rate and superconducting-resonator occupation versus pump strength.
Figure 4: Mechanical linewidth broadening and cooling versus pump strength.


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We acknowledge conversations with M. Blencowe, M. Aspelmeyer, R. Ilic, M. Skvarla, M. Metzler and M. Shaw and assistance from M. Savva, S. Rosenthal and M. Corbett. This work has been supported by the Fundamental Questions Institute ( (RFP2-08-27) and the US National Science Foundation (NSF) (DMR-0804567). Device fabrication was performed at the Cornell Nanoscale Facility, a member of the US National Nanotechnology Infrastructure Network (NSF grant ECS-0335765).

Author Contributions T.R. and T.N. contributed equally to device fabrication and measurements. C.M. built key apparatus and assisted in experimental set-up. J.B.H. assisted in planning and analysis. A.A.C. provided theoretical analysis. K.C.S. initiated and oversaw the work.

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Correspondence to K. C. Schwab.

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The authors declare no competing financial interests.

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Rocheleau, T., Ndukum, T., Macklin, C. et al. Preparation and detection of a mechanical resonator near the ground state of motion. Nature 463, 72–75 (2010).

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