38 The฀Australian฀Research฀Council฀Centre฀of฀Excellence฀for฀Quantum-Atom฀Optics฀ Annual฀Report฀for฀the฀year฀2005 Macroscopic entanglement and the Einstein-Podolsky-Rosen Paradox M. D. Reid 1 , E. Cavalcanti 1 , P. D. Drummond 1 , P.K. Lam 2 , H.-A. Bachor 2 , K. Dechoum 3 1 ACQAO, School of Physical Sciences, The University of Queensland, QLD 4072, Australia 2 ACQAO, Department of Physics, The Australian National University, ACT, Australia. 3 Instituto de F´ ısica da Universidade Federal Fluminense, Rio de Janeiro, Brazil The aim of this project is to provide a strategy for detecting mesoscopic or macroscopic quantum superpositions in mixed states that better represent the output of physical systems that can be used to generate entanglement. This is a fundamental scientific question in both quantum and atom optics, and the experimental groups in the ACQAO Centre are competitively placed to investigate these issues, with world-class squeezing and entanglement. Crucial to the field of quantum information is the concept of quantum entanglement. Einstein, Podolsky and Rosen [1] first pointed to the paradoxes of spatially separated quantum entangled state in their now famous EPR argument of 1935. Schr¨ odinger in his essay [2] that same year made particular mention of the paradox of macroscopic entanglement, where we have a quantum superposition of two macroscopically distinguishable states. A paradox arises because the system cannot be interpreted as being in one state or the other, prior to measurement. Experiments [3, 4] in quantum optics are at the forefront in experimentally confirming quantum en- tanglement. These involve measurements performed on fields generated by parametric amplification, which can have macroscopic output intensities. An article summarising the criteria used to detect the entanglement of the EPR paradox has been published [5] and a review incorporating experimental achievement is being written by invitation, to be submitted to Reviews of Modern Physics. The criteria have recently been applied [6] to give predictions of measurable entanglement in the near-threshold regime of the parametric amplification experiments. In addition, a type of near-threshold universal spatial entanglement has been identified in a planar parametric amplifier [7]. The challenge to generate and detect any macroscopic quantum entanglement in these macroscopic fields still remains however. In practice some loss is unavoidable, and the sensitivity of pure macro- scopic superposition states to decoherence poses a significant problem to their detection. At best one would hope for a mixture of both microscopic and mesoscopic (or macroscopic) superpositions. We have derived criteria for the detection of macroscopic quantum superpositions that are based on the measurable variances of output probability distributions. The criteria are applicable to both discrete and continuous variable measurements, and to macroscopic quantum entangled states that are of current interest experimentally, namely the two-mode squeezed state and the higher-spin and atomic squeezed states. We have shown how these new signatures give a macroscopic version of the Einstein-Podolsky-Rosen paradox and a Schr¨ odinger’s paradox, through the proven failure of certain macroscopic quantum mixtures. The work has been presented as part of two invited papers and is now published [8], with further papers submitted for publication. References [1] A. Einstein, B. Podolsky, and N. Rosen, Phys.Rev. 47, 777, (1935). [2] A. E. Schr¨ odinger, Naturwissenschaften 23, 807 (1935). [3] W. P. Bowen, R. Schnabel, P. K. Lam, and T. C.Ralph, Phys.Rev. Lett. 90 (4), 043601 (2003). [4] C. Silberhorn, P. K. Lam, O. Weiss, F. Koenig, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001). [5] M. D. Reid, Einstein-Podolsky-Rosen Correlations, Entanglement and Quantum Cryptography, in: Quantum Squeezing, edited by P. D. Drummond and Z. Ficek (Springer Verlag, Berlin, 2004). [6] K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, Phys.Rev. A 70, 053807 (2004). [7] P. D. Drummond and K. Dechoum, Phys. Rev. Lett. 95, 083601 (2005). [8] M. D. Reid and E. Cavalcanti, J. Modern Optics 52, 2245 (2005).