Optomechanical state reconstruction and nonclassicality verification beyond the resolved-sideband regime

Farid Shahandeh1,2 and Martin Ringbauer3,4

1Centre for Quantum Computation and Communication Technology, School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072, Australia
2Department of Physics, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom
3Centre for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072, Australia
4Institute for Experimental Physics, University of Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria

Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices. Yet, the challenge of reconstructing and verifying the quantum state of mechanical systems has remained a major roadblock in the field. Here, we present a novel approach that allows for tomographic reconstruction of the quantum state of a mechanical system without the need for extremely high quality optical cavities. We show that, without relying on the usual state transfer presumption between light an mechanics, the full optomechanical Hamiltonian can be exploited to imprint mechanical tomograms on a strong optical coherent pulse, which can then be read out using well-established techniques. Furthermore, with only a small number of measurements, our method can be used to witness nonclassical features of mechanical systems without requiring full tomography. By relaxing the experimental requirements, our technique thus opens a feasible route towards verifying the quantum state of mechanical resonators and their nonclassical behaviour in a wide range of optomechanical systems.

Quantum optomechanics exploits the interaction between light and massive mechanical resonators to engineer and control their quantum state of motion. Such systems hold the promise to ultra-sensitive force sensors and tests of fundamental physics. Over recent years, the field has made great progress—from the preparation of nonclassical states of mechanical motion to the violation of Bell’s inequality using mechanical systems. Despite all these achievements, the reconstruction of the state of motion of a mechanical system has remained an outstanding challenge.

Here, we introduce a new technique for optomechanical quantum state tomography and nonclassicality verification with the potential to avoid much of the experimental challenges typically associated with this task. While previous approaches mostly aimed at completely transferring the mechanical state of motion onto a single photon, our method works more like taking two-dimensional snapshots of the three-dimensional phase-space distribution of the mechanical system, using strong pulses of light. From these snapshots the state of motion can be reconstructed using standard procedures. Due to the significantly reduced experimental requirements, this method can be applied to a wide range of state-of-the-art optomechanical experiments. Furthermore, it makes it possible to certify that a certain state of motion is nonclassical without having to reconstruct the state and using only a small number of noisy measurements.

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[2] P. Warszawski, A. Szorkovszky, W. P. Bowen, and A. C. Doherty, "Tomography of an optomechanical oscillator via parametrically amplified position measurement", arXiv:1811.08444 (2018).

[3] Martin Koppenhöfer, Christoph Bruder, and Niels Lörch, "Unraveling nonclassicality in the optomechanical instability", Physical Review A 97 6, 063812 (2018).

[4] L. A. Howard, T. J. Weinhold, J. Combes, F. Shahandeh, M. R. Vanner, M. Ringbauer, and A. G. White, "Hypercube States for Sub-Planck Sensing", arXiv:1811.03011 (2018).

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