letters to nature electrons could be employed to probe atoms and molecules ................................................................. remotely while minimizing the perturbing in¯uences of a nearby Experimental test of quantum local probeÐthese unwanted interactions might be chemical in nature or result from electric or magnetic ®elds emanating from an nonlocality in three-photon STM tip or other probe device. Our results also suggest altered geometries such as ellipsoids con®ning bulk electrons, or specially Greenberger±Horne±Zeilinger shaped electron mirrors (such as parabolic re¯ectors) electronically coupling two or more points. One might additionally envision entanglement performing other types of `spectroscopy-at-a-distance' beyond electronic structure measurements, for example, detecting Jian-Wei Pan*, Dik Bouwmeester², Matthew Daniell*, vibrational16 or magnetic excitations. Harald Weinfurter³ & Anton Zeilinger* We conclude with some remaining questions. Our calculations show that ellipses have a class of eigenmodes that possess strongly * Institut fuÈr Experimentalphysik, UniversitaÈt Wien, Boltzmanngasse 5, peaked probability amplitude near the classical foci (Fig. 3e and f are 1090 Wien, Austria good examples). Our experiments reveal that the strongest mirages ² Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK ³ Sektion Physik, Ludwig-Maximilians-UniversitaÈtofMuÈnchen, occur when one of these eigenmodes is at EF and therefore at the energy of the Kondo resonance. When perturbed by a focal atom, Schellingstrasse 4/III, D-80799 MuÈnchen, Germany this eigenmode still has substantial density surrounding both foci; it .............................................................................................................................................. is therefore plausible that this quantum state `samples' the Kondo Bell's theorem1 states that certain statistical correlations predicted resonance on the real atom and transmits that signal to the other by quantum physics for measurements on two-particle systems focus. The physics behind this process is not completely under- cannot be understood within a realistic picture based on local stood. Also, given that a Kondo signature is detected at the empty properties of each individual particleÐeven if the two particles focus, does this imply that a measurement there is simply providing are separated by large distances. Einstein, Podolsky and Rosen us with a remote probe of the Co atom with the intervening two- ®rst recognized2 the fundamental signi®cance of these quantum dimensional electrons acting essentially like a wire? Or, as the Kondo correlations (termed `entanglement' by SchroÈdinger3) and the effect on the Co atom requires a net spin polarization of the surrounding electron gas, does the projection of the Kondo reso- D nance imply a modi®ed spin polarization at the empty focus? We D1 2 speculate that both interpretations are actually correct. Full answers to these questions, however, await further experimental and theo- F F retical efforts. λ /4 D POL POL 3 Received 12 October; accepted 14 December 1999. T 1. Spector, J., Stormer, H. L., Baldwin, K. W., Pfeiffer, L. N. & West, K. W. Electron focusing in two- F F dimensional systems by means of an electrostatic lens. Appl. Phys. Lett. 56, 1290±1292 (1990). PBS 2. Crommie, M. F., Lutz, C. P. & Eigler, D. M. Con®nement of electrons to quantum corrals on a metal λ/4 surface. Science 262, 218±220 (1993). λ/2 POL 3. Heremans, J. J., von MolnaÂr, S., Awschalom, D. D. & Gossard, A. C. Ballistic electron focusing by elliptic re¯ecting barriers. Appl. Phys. Lett. 74, 1281±1283 (1999). 4. Kondo, J. Resistance minimum in dilute magnetic alloys. Prog. Theor. Phys. 32, 37±49 (1964). BS 5. Li, J., Schneider, W.-D., Berndt, R. & Delley, B. Kondo scattering observed at a single magnetic PBS impurity. Phys. Rev. Lett. 80, 2893±2896 (1998). 6. Madhavan, V., Chen, W., Jamneala, T., Crommie, M. F. & Wingreen, N. S. Tunnelling into a single ab magnetic atom: Spectroscopic evidence of the Kondo resonance. Science 280, 567±569 (1998). 7. Kittel, C. Quantum Theory of Solids (Wiley, New York, 1963). BBO 8. Hewson, A. C. The Kondo Problem to Heavy Fermions (Cambridge Univ. Press, Cambridge, 1997). 9. Fano, U. Effects of con®guration interaction on intensities and phase shifts. Phys. Rev. 124, 1866±1878 (1961). Pulse 10. Crommie, M. F., Lutz, C. P.& Eigler, D. M. Imaging standing waves in a two-dimensional electron gas. Nature 363, 524±527 (1993). 11. Hasegawa, Y. & Avouris, P. Direct observation of standing wave formation at surface steps using scanning tunneling spectroscopy. Phys. Rev. Lett. 71, 1071±1074 (1993). 12. Eigler, D. M. & Schweizer, E. K. Positioning single atoms with a scanning tunnelling microscope. Nature 344, 524±526 (1990). Figure 1 Experimental set-up for Greenberger±Horne±Zeilinger (GHZ) tests of quantum 13. Stroscio, J. A. & Eigler, D. M. Atomic and molecular manipulation with the scanning tunneling nonlocality. Pairs of polarization-entangled photons28 (one photon H polarized and the microscope. Science 254, 1319±1326 (1991). 14. Tomsovic, S. & Heller, E. J. Semiclassical construction of chaotic eigenstates. Phys. Rev. Lett. 70, 1405± other V ) are generated by a short pulse of ultraviolet light (, 200 fs, l = 394 nm). 1408 (1993). Observation of the desired GHZ correlations requires fourfold coincidence and therefore 15. Chan, Y. S. & Heller, E. J. Scanning tunnel microscopy surface state electron scattering: Two-tip results two pairs29. The photon registered at T is always H and thus its partner in b must be V. The from one-tip data. Phys. Rev. Lett. 78, 2570±2572 (1997). 16. Stipe, B. C., Rezaei, M. A. & Ho, W. Single-molecule vibrational spectroscopy and microscopy. Science photon re¯ected at the polarizing beam-splitter (PBS) in arm a is always V, being turned 280, 1732±1735 (1998). into equal superposition of V and H by the l/2 plate, and its partner in arm b must be H. 17. Lang, N. D. Spectroscopy of single atoms in the scanning tunneling microscope. Phys. Rev. B 34, 5947± Thus if all four detectors register at the same time, the two photons in D1 and D2 must 5950 (1986). either both have been VVand re¯ected by the last PBS or HH and transmitted. The photon 18. Everson, M. P., Jaklevic, R. C. & Shen, W. Measurement of the local density of states on a metal surface: Scanning tunneling spectroscopic imaging of Au(111). J. Vac. Sci. Technol. A 8, 3662±3665 (1990). at D3 was therefore H or V, respectively. Both possibilities are made indistinguishable by 19. Kittel, C. Indirect exchange interactions in metals. Solid State Phys. 22, 1±26 (1968). having equal path lengths via a and b to D1 (D2) and by using narrow bandwidth ®lters (F < 4 nm) to stretch the coherence time to about 500 fs, substantially larger than the pulse length30. This effectively erases the prior correlation information and, owing to indis- Acknowledgements tinguishability, the three photons registered at D1,D2 and D3 exhibit the desired GHZ We thank B. A. Jones, E. J. Heller, J. S. Hersch, G. Fiete, A. J. Heinrich and C. T. Rettner for correlations predicted by the state of equation (1), where for simplicity we assume the helpful discussions, and L. Folks for expert assistance with image preparation. polarizations at D3 to be de®ned at right angles relative to the others. Polarizers oriented at Correspondence and requests for materials should be addressed to H.C.M. 458 and l/4 plates in front of the detectors allow measurement of linear H9/V 9 (circular (e-mail: [email protected]). R/L) polarization. NATURE | VOL 403 | 3 FEBRUARY 2000 | www.nature.com © 2000 Macmillan Magazines Ltd 515 letters to nature two-particle quantum predictions have found ever-increasing ization. Then by the third term in equation (4), photon 3 will experimental support4. A more striking con¯ict between quantum de®nitely be V9 polarized. mechanical and local realistic predictions (for perfect correla- By cyclic permutation, we can obtain analogous expressions for tions) has been discovered5,6; but experimental veri®cation has any experiment measuring circular polarization on two photons been dif®cult, as it requires entanglement between at least three and H9/V9 linear polarization on the remaining one. Thus, in every particles. Here we report experimental con®rmation of this one of the three yyx, yxy, and xyy experiments, any individual con¯ict, using our recently developed method7 to observe three- measurement resultÐboth for circular polarization and for linear photon entanglement, or `Greenberger±Horne±Zeilinger' (GHZ) H9/V9 polarizationÐcan be predicted with certainty for every states. The results of three speci®c experiments, involving photon given the corresponding measurement results of the other measurements of polarization correlations between three two. photons, lead to predictions for a fourth experiment; quantum Now we will analyse the implications for local realism. As these physical predictions are mutually contradictory with expectations predictions are independent both of the spatial separation and of based on local realism. We ®nd the results of the fourth experi- the relative time order of the three measurements, we consider them ment to be in agreement with the quantum prediction and in performed simultaneously in a given reference frameÐsay, for striking con¯ict with local realism. conceptual simplicity, in the reference frame of the source. Then, We ®rst analyse certain quantum predictions for the