title: Theory of single-shot phase contrast imaging in spinor Bose-Einstein condensates.
abstract: We introduce a theoretical framework for single-shot phase contrast imaging (PCI) measurements of spinor Bose-Einstein condensates (BECs). Our model allows for the simple calculation of the quantum backaction resulting from the measurement, and the amount of information that is read out. We find that there is an optimum time Gτ ∼ 1/N for the light-matter interaction (G is the ac Stark shift frequency, N is the number of particles in the BEC), where the maximum amount of information can be read out from the BEC. A universal information-disturbance tradeoff law ε(F)ε(G) ∝ 1/N(2) is found where ε(F) is the amount of backaction and ε(G) is the estimation error. The PCI measurement can also be found to be a direct probe of the quantum fluctuations of the BEC, via the noise of the PCI signal.
authors: National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan and Department of Physics, School of Science, Federal University of Technology, P. M. B. 1526, Owerri, Imo State 460001, Nigeria.
authors: Ebubechukwu O
authors: EO
authors: Ilo-Okeke
authors: National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan.
authors: Tim
authors: T
authors: Byrnes