Quantum entanglement for systems of identical bosons: I. General features

dc.contributor.authorDalton, B. J.
dc.contributor.authorGoold, J.
dc.contributor.authorGarraway, B. M.
dc.contributor.authorReid, M. D.
dc.contributor.funderScience Foundation Ireland
dc.contributor.funderEngineering and Physical Sciences Research Council
dc.contributor.funderAustralian Research Council
dc.description.abstractThese two accompanying papers are concerned with two mode entanglement for systems of identical massive bosons and the relationship to spin squeezing and other quantum correlation effects. Entanglement is a key quantum feature of composite systems in which the probabilities for joint measurements on the composite sub-systems are no longer determined from measurement probabilities on the separate sub-systems. There are many aspects of entanglement that can be studied. This two-part review focuses on the meaning of entanglement, the quantum paradoxes associated with entangled states, and the important tests that allow an experimentalist to determine whether a quantum state-in particular, one for massive bosons is entangled. An overall outcome of the review is to distinguish criteria (and hence experiments) for entanglement that fully utilize the symmetrization principle and the super-selection rules that can be applied to bosonic massive particles. In the first paper (I), the background is given for the meaning of entanglement in the context of systems of identical particles. For such systems, the requirement is that the relevant quantum density operators must satisfy the symmetrization principle and that global and local super-selection rules prohibit states in which there are coherences between differing particle numbers. The justification for these requirements is fully discussed. In the second quantization approach that is used, both the system and the sub-systems are modes (or sets of modes) rather than particles, particles being associated with different occupancies of the modes. The definition of entangled states is based on first defining the non-entangled states-after specifying which modes constitute the sub-systems. This work mainly focuses on the two mode entanglement for massive bosons, but is put in the context of tests of local hidden variable theories, where one may not be able to make the above restrictions. The review provides the detailed arguments necessary for the conclusions of a recent paper, where the question of how to rigorously demonstrate the entanglement of a two-mode Bose-Einstein condensate (BEC) has been examined. In the accompanying review paper (II), we consider spin squeezing and other tests for entanglement that have been proposed for two-mode bosonic systems. We apply the approach of review (I) to determine which tests, and which modifications of the tests, are useful for detecting entanglement in massive bosonic (BEC), as opposed to photonic, systems. Several new inequalities are derived, a theory for the required two-mode interferometry is presented, and key experiments to date are analyzed.en
dc.description.sponsorshipScience Foundation Ireland (E T S Walton Visiting Fellowship, 11/W.1/11959); Engineering and Physical Sciences Research Council (EP/1010394/1); Australian Research Council (Discovery Project Grant)en
dc.description.statusPeer revieweden
dc.description.versionPublished Versionen
dc.identifier.citationDalton, B. J., Goold, J., Garraway, B. M. and Reid, M. D. (2017) 'Quantum entanglement for systems of identical bosons: I. General features', Physica Scripta, 92(2), 023004 (36pp). doi: 10.1088/1402-4896/92/2/023004en
dc.identifier.journaltitlePhysica Scriptaen
dc.publisherIOP Publishing Ltd.en
dc.rights© 2017, Royal Swedish Academy of Sciences. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.en
dc.subjectIdentical massive bosonsen
dc.subjectSuper-selection rulesen
dc.subjectSpin squeezingen
dc.subjectQuadrature squeezingen
dc.subjectPhase referenceen
dc.titleQuantum entanglement for systems of identical bosons: I. General featuresen
dc.typeArticle (peer-reviewed)en
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