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Optomechanical Bell Test Delft University of Technology Optomechanical Bell Test Marinković, Igor; Wallucks, Andreas; Riedinger, Ralf; Hong, Sungkun; Aspelmeyer, Markus; Gröblacher, Simon DOI 10.1103/PhysRevLett.121.220404 Publication date 2018 Document Version Final published version Published in Physical Review Letters Citation (APA) Marinković, I., Wallucks, A., Riedinger, R., Hong, S., Aspelmeyer, M., & Gröblacher, S. (2018). Optomechanical Bell Test. Physical Review Letters, 121(22), [220404]. https://doi.org/10.1103/PhysRevLett.121.220404 Important note To cite this publication, please use the final published version (if applicable). Please check the document version above. Copyright Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy Please contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. This work is downloaded from Delft University of Technology. For technical reasons the number of authors shown on this cover page is limited to a maximum of 10. PHYSICAL REVIEW LETTERS 121, 220404 (2018) Editors' Suggestion Featured in Physics Optomechanical Bell Test † Igor Marinković,1,* Andreas Wallucks,1,* Ralf Riedinger,2 Sungkun Hong,2 Markus Aspelmeyer,2 and Simon Gröblacher1, 1Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2628CJ Delft, Netherlands 2Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, A-1090 Vienna, Austria (Received 18 June 2018; published 29 November 2018) Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from some of the most fundamental concepts of classical physics—in particular that properties of an object are well-defined independent of measurements (realism) and only affected by local interactions (locality). The violation of these bounds unambiguously shows that the measured system does not behave classically, void of any assumption on the validity of quantum theory. It has also found applications in quantum technologies for certifying the suitability of devices for generating quantum randomness, distributing secret keys and for quantum computing. Here we report on the violation of a Bell inequality involving a massive, macroscopic mechanical system. We create light-matter entanglement between the vibrational motion of two silicon optomechanical oscillators, each comprising approx. 1010 atoms, and two optical modes. This state allows us to violate a Bell inequality by more than 4 standard deviations, directly confirming the nonclassical behavior of our optomechanical system under the fair sampling assumption. DOI: 10.1103/PhysRevLett.121.220404 Bell’s theorem [1] predicts that any local realistic theory scale. Recent experiments have demonstrated quantum is at variance with quantum mechanics. It was originally control of such mechanical systems, including mechanical conceived to settle an argument between Einstein [2] and squeezing [24], single-phonon manipulation [25–28],as Bohr [3] on locality in physics, and to investigate the well as entanglement between light and mechanics [29] and axioms of quantum physics. First tests of the Clauser- entanglement between two mechanical modes [30–32]. Horne-Shimony-Holt (CHSH) inequality [4], an experi- However, explaining the observed results in these experi- mentally testable version of Bell’s original inequality, were ments required assuming the validity of quantum theory at performed with photons from cascaded decays of atoms some level. A Bell test, in contrast, is a genuine test of [5,6] and parametric down-conversion [7–9]. Subsequent nonclassicality without quantum assumptions. experiments reduced the set of assumptions required for the Here we report on the first Bell test using correlations falsification of classical theories, closing, e.g., the locality between light and microfabricated mechanical resonators, [10] and detection loopholes [11], first individually and which constitute massive macroscopic objects, hence recently simultaneously [12–15]. In addition to the funda- verifying nonclassical behavior of our system without mental importance of these experiments, the violation of a relying on the quantum formalism. Bell tests do not require Bell-type inequality has very practical implications—in assumptions about the physical implementation of a quan- particular, it has become the most important benchmark for tum system such as the dimension of the underlying Hilbert thrust-worthily verifying entanglement in various systems space or the fundamental interactions involved in state [16,17], including mesoscopic superconducting circuits preparation and measurement [33]. The violation of a Bell [18], for certifying randomness [19,20], secret keys [21], inequality is hence the most unambiguous demonstration and quantum computing [22]. of entanglement with numerous important implications. While the standard form of quantum theory does not From a fundamental perspective, the robust entanglement impose any limits on the mass or size of a quantum system between flying optical photons and a stored mechanical [23], the potential persistence of quantum effects on a state rules out local hidden variables, which can be used for macroscopic scale seems to contradict the human experi- further tests of quantum mechanics at even larger mass ence of classical physics. Over the past years, quantum scales [34,35]. From an application perspective, the pre- optomechanics has emerged as a new research field, sented measurements also imply that optomechanics is a coupling mechanical oscillators to optical fields. While promising technique to be used for quantum information these systems are very promising for quantum information processing tasks including teleportation, quantum memo- applications due to their complete engineerability, they also ries, and the possibility of quantum communication with hold great potential to test quantum physics on a new mass device-independent security [21]. 0031-9007=18=121(22)=220404(6) 220404-1 © 2018 American Physical Society PHYSICAL REVIEW LETTERS 121, 220404 (2018) (a) (b) A blue detuned, ∼40 ns long laser pulse with frequency νb ¼ νo þ νm (νo optical resonance, νm mechanical reso- nance) generates photon-phonon pairs. The interaction in ˆ pffiffiffiffiffi † ˆ † this case is described by Hb ¼ −ℏg0 nbaˆ b þ H:c:, with the intracavity photon number nb, the optomechanical (c) single photon coupling g0 and the optical (mechanical) creation operators aˆ † (bˆ †). This correlates the number of mechanical and optical excitations in each of the arms of the interferometer as jψi ∝ ½j00i þ ϵj11i þ Oðϵ2Þ ð Þ om om ; 1 where o denotes the optical and m the mechanical mode, while p ¼ ϵ2 is the excitation probability. For small p ≪ 1, FIG. 1. (a) Schematic of the setup: blue detuned drive pulses states with multiple excitations are unlikely to occur, and A B interact with the mechanical resonators (devices and ) can therefore be neglected in the statistical analysis. producing entangled photon-phonon pairs. The light-matter entanglement is in the path basis (A or B), corresponding to Driving the devices simultaneously and postselecting on the device in which the Stokes scattering event took place. The trials with a successful detection of both the Stokes photon generated photons are detected in single-photon detectors giving and the phonon, we approximate the combined state as the measurement results ab1 and ab2. The detection of the 1 ϕ phonons is done by transferring their states to another optical jΨi¼pffiffiffi ðj11i j00i þ i b j00i j11i Þ A B e A B mode by using a red drive after some time Δτ and, subsequently, 2 obtaining the results a 1 and a 2. Note that for technical reasons r r 1 ϕ ¼ pffiffiffi ðjAAi þ ei b jBBi Þ; ð2Þ the photons created by the blue and red drives are detected on the 2 om om same pair of detectors, but with a time delay Δτ ¼ 200 ns. Therefore we have time separation of the two parties of the Bell again neglecting higher order excitations. Here ϕ is the test instead of space separation (as commonly done). BS1=2 b phase difference that the blue drives acquire in the two represent beam splitter 1=2. (b) Scanning electron microscope image of one of the optomechanical devices, represented with a interferometer paths A and B, including the phase shift of the star symbol in (a) and (c), next to the coupling waveguide (top). first beam splitter. Expressing the state in a path basis j i ¼j10i (c) Illustration of our experimental sequence: one party of the Bell A x AB, where x is o for the photonic and m for test measures in which detector path the Stokes photon is found at the phononic subsystem in arms A and B,allowsusto time t ¼ 0, while the other performs the same measurement for identify the Bell state, similarly to polarization entanglement the anti-Stokes photon after a time t ¼ Δτ. We probe their in optical down-conversion experiments. Unlike the two correlations in order to violate the CHSH inequality. Since the mode entangled mechanical state in Ref. [31],thisfour-mode two photons never interacted directly (only through the mechan- entangled optomechanical state allows
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