Historically, the completeness of quantum theory has been questioned using the concept of bipartite continuous-variable entanglement1. The non-classical correlations (entanglement) between the two subsystems imply that the observables of one subsystem are determined by the measurement choice on the other, regardless of the distance between the subsystems. Nowadays, continuous-variable entanglement is regarded as an essential resource, allowing for quantum enhanced measurement resolution2, the realization of quantum teleportation3,4,5 and quantum memories3,6, or the demonstration of the Einstein–Podolsky–Rosen paradox1,7,8,9. These applications rely on techniques to manipulate and detect coherences of quantum fields, the quadratures. Whereas in optics coherent homodyne detection10 of quadratures is a standard technique, for massive particles a corresponding method was missing. Here we report the realization of an atomic analogue to homodyne detection for the measurement of matter-wave quadratures. The application of this technique to a quantum state produced by spin-changing collisions in a Bose–Einstein condensate11,12 reveals continuous-variable entanglement, as well as the twin-atom character of the state13. Our results provide a rare example of continuous-variable entanglement of massive particles6,14. The direct detection of atomic quadratures has applications not only in experimental quantum atom optics, but also for the measurement of fields in many-body systems of massive particles15.
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We acknowledge discussions with P. Grangier, A. Aspect, A. J. Ferris, M. J. Davis and B. C. Sanders. This work was supported by the Forschergruppe FOR760, the Deutsche Forschungsgemeinschaft, the German–Israeli Foundation, the Heidelberg Center for Quantum Dynamics, Landesstiftung Baden-Württemberg, the ExtreMe Matter Institute and the European Commission Future and Emerging Technologies Open Scheme project MIDAS (Macroscopic Interference Devices for Atomic and Solid-State Systems). G.K. acknowledges support from the Humboldt-Meitner Award and the Deutsche-Israelische Projektgruppe (DIP).
The authors declare no competing financial interests.
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Gross, C., Strobel, H., Nicklas, E. et al. Atomic homodyne detection of continuous-variable entangled twin-atom states. Nature 480, 219–223 (2011). https://doi.org/10.1038/nature10654
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