Quantum back-action-evading measurement of motion in a negative mass reference frame


Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random quantum back-action (QBA) perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty on the measurement of motion1,2. As a consequence of this randomness, and in accordance with the Heisenberg uncertainty principle, the QBA3,4 puts a limitation—the so-called standard quantum limit—on the precision of sensing of position, velocity and acceleration. Here we show that QBA5 on a macroscopic mechanical oscillator can be evaded if the measurement of motion is conducted in the reference frame of an atomic spin oscillator6,7. The collective quantum measurement on this hybrid system of two distant and disparate oscillators is performed with light. The mechanical oscillator is a vibrational ‘drum’ mode of a millimetre-sized dielectric membrane8, and the spin oscillator is an atomic ensemble in a magnetic field9,10. The spin oriented along the field corresponds to an energetically inverted spin population and realizes a negative-effective-mass oscillator, while the opposite orientation corresponds to an oscillator with positive effective mass. The QBA is suppressed by −1.8 decibels in the negative-mass setting and enhanced by 2.4 decibels in the positive-mass case. This hybrid quantum system paves the way to entanglement generation and distant quantum communication between mechanical and spin systems and to sensing of force, motion and gravity beyond the standard quantum limit.

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Figure 1: Mechanical and spin oscillators.
Figure 2: Experimental set-up and observation of QBA for the spin and mechanical oscillators.
Figure 3: QBA interference for the mechanical and spin oscillators with equal central frequencies.
Figure 4: QBA evasion for the optimally detuned mechanical and spin oscillators.


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We acknowledge discussions with F. Khalili. This work was supported by the European Union Seventh Framework Program (ERC grant INTERFACE, projects SIQS and iQUOEMS), the European Union’s Horizon 2020 research and innovation programme (ERC grant Q-CEOM, grant agreement no. 638765), a Sapere Aude starting grant from the Danish Council for Independent Research, and the DARPA project QUASAR. R.A.T. is funded by the program Science without Borders of the Brazilian Federal Government. E.Z. is supported by the Carlsberg Foundation. K.H. and E.Z. acknowledge support from DFG through SFB 1227 (DQ-mat). We acknowledge help from M. Gaudesius at the early stage of the experimental development.

Author information




E.S.P. conceived and led the project. C.B.M., R.A.T. and G.V. built the experiment with the help of K.J., Y.T. and A.S. The membrane resonator was designed and fabricated by Y.T. M.B. fabricated caesium cells with spin protecting coating. C.B.M., R.A.T., G.V. and E.S.P. took the data. E.Z. and K.H. developed the theory with input from A.S. and E.S.P. The paper was written by E.S.P., K.H., E.Z., R.A.T., C.B.M. and G.V. with contributions from other authors. A.S., K.H. and E.S.P. supervised the research.

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Correspondence to Eugene S. Polzik.

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Reviewer Information Nature thanks W. Bowen and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Detailed schematic of the experimental set-up.

The atomic spin system is pictured in the black–orange dashed box (left), along with its B field and optical pumping (blue and olive arrows; bottom); the optomechanical membrane-in-the-middle set-up is in the blue box (right). Circled numerals indicate sections with specific functions. The hybrid system is probed via a travelling optical mode (pink lines and arrows). The atomic system, driven by local oscillator 1 (LO1) with linear polarization angle set by section (0), has its output polarization filtered in section (1) and is recombined with the correct phase with LO2 in section (2), set electronically via suitable detection in D1; the apparatus in section (3) ensures that both local oscillator and the filtered atomic response have the same polarization. The optomechanical system is probed by LO2 in reflection and phase-sensitive detection is done via homodyning with LO3 in D2. Probing the remaining cavity port in reflection with LOPDH, the optomechanical system is frequency stabilized using the Pound–Drever–Hall (PDH) technique on the signal of detector DPDH. HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarizing beamsplitter; EOM, electro-optic modulator. See Methods for details.

Extended Data Figure 2 Theoretical schematic of the set-up.

The atomic spin (in the spin cell, blue box at left) is driven by light noise XL,in and spin noise FS. Output light of the spin system is channelled to the optomechanical system. En route, it experiences losses characterized by a transmissivity η1 associated with additional light noise V1,in and a phase rotation by an angle φ, resulting in a driving field of the optomechanical system. The optomechanical cavity (shown blue at right) is two-sided, with decay rates κ1 and κ2. The optomechanical system is driven in addition by light noise Vin and a thermal force F. The output field of the optomechanical system experiences further losses, with transmissivity η2 associated with additional light noise V2,in. All unwanted additional noise sources are indicated with dashed lines.

Extended Data Table 1 Summary of notation and experimental parameters

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Møller, C., Thomas, R., Vasilakis, G. et al. Quantum back-action-evading measurement of motion in a negative mass reference frame. Nature 547, 191–195 (2017). https://doi.org/10.1038/nature22980

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