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Title

Entanglement, number fluctuations and optimized interferometric phase measurement

Author(s)

He, Q. Y.;  Vaughan, T. G.;  Drummond, P. D.;  Reid, M. D.

Abstract

We derive a phase-entanglement criterion for two bosonic modes that is immune to number fluctuations, using the generalized Moore-Penrose inverse to normalize the phase-quadrature operator. We also obtain a phase-squeezing criterion that is immune to number fluctuations using similar techniques. These are used to obtain an operational definition of relative phase-measurement sensitivity via the analysis of phase measurement in interferometry. We show that these criteria are proportional to the enhanced phase-measurement sensitivity. The phase-entanglement criterion is the hallmark of a new type of quantum-squeezing, namely planar quantum-squeezing. This has the property that it squeezes simultaneously two orthogonal spin directions, which is possible owing to the fact that the SU(2) group that describes spin symmetry has a three-dimensional parameter space of higher dimension than the group for photonic quadratures. A practical advantage of planar quantum-squeezing is that, unlike conventional spin-squeezing, it allows noise reduction over all phase angles simultaneously. The application of this type of squeezing is to the quantum measurement of an unknown phase. We show that a completely unknown phase requires two orthogonal measurements and that with planar quantum-squeezing it is possible to reduce the measurement uncertainty independently of the unknown phase value. This is a different type of squeezing compared to the usual spin-squeezing interferometric criterion, which is applicable only when the measured phase is already known to a good approximation or can be measured iteratively. As an example, we calculate the phase entanglement of the ground state of a two-well, coupled Bose-Einstein condensate, similarly to recent experiments. This system demonstrates planar squeezing in both the attractive and the repulsive interaction regime.

Publication type

Journal article

Research centre

Swinburne University of Technology. Faculty of Engineering and Industrial Sciences. Centre for Atom Optics and Ultrafast Spectroscopy

Source

New Journal of Physics, Vol. 14 (Sep 2012), article no. 093012

Publication year

2012

FOR Code(s)

02 Physical Sciences

Keyword(s)

Interferometry;  Number fluctuations;  Phase-entanglement;  Phase measurement;  Phase sensitivity;  Planar squeezing

Publisher

Institute of Physics Publishing

ISSN

1367-2630

Publisher URL

http://dx.doi.org/10.1088/1367-2630/14/9/093012

Copyright

Copyright © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercialShareAlike 3.0 licence (http://creativecommons.org/licenses/by-nc-sa/3.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. The published version is reproduced in accordance with this policy.

Full text

Peer reviewed