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Spin Squeezing and Non-linear Atom Interferometry with Bose-Einstein Condensates pp 5–23Cite as

Spin Squeezing, Entanglement and Quantum Metrology

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Abstract

Spin squeezing is a quantum strategy introduced in 1993 by Kitagawa and Ueda [1] which aims to redistribute the fluctuations of two conjugate spin directions among each other. In 1994 it was theoretically shown that spin squeezed states are useful quantum resources to enhance the precision of atom interferometers [2] and in 2001 the connection between spin squeezing and entanglement was pointed out [3].

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Notes

  1. 1.

    In this thesis we deal with large spins such that we often approximate \(\sqrt{\mathcal{J}(\mathcal{J}+1)}\approx{\mathcal {J}}.\)

  2. 2.

    Above we give an example for the mean spin in \(J_{x}\) direction, however for the purpose of better illustration we have chosen a different direction in the figure.

  3. 3.

    The general expression is \({\frac{4\Updelta\hat{J}_k^2}{N}} \geq 1 - {\frac{4\langle\hat{J}_k\rangle^2}{N^2}}\) [19].

  4. 4.

    Since criterion (2.15) can be related to a gain in interferometric precision (see Sect. 2.4), it measures the “usefulness" of spin squeezed states as a quantum resource in a known experimental protocol.

  5. 5.

    As already mentioned a spin \(S=1/2\) can not be squeezed at all.

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  1. University of Heidelberg, Heidelberg, Germany

    Christian Groß

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  1. Christian Groß
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Groß, C. (2012). Spin Squeezing, Entanglement and Quantum Metrology. In: Spin Squeezing and Non-linear Atom Interferometry with Bose-Einstein Condensates. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25637-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-25637-0_2

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