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arXiv:2006.03852 · Physical Review Research

Two-axis two-spin squeezed states

Jonas Kitzinger, Manish Chaudhary, Manikandan Kondappan, Valentin Ivannikov, Tim Byrnes

Published Sep 28, 2020• 24 citations
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Abstract

This paper examines the properties of the states generated by the two-spin generalization of the two-axis countertwisting Hamiltonian. The spin squeezing produces correlations for arbitrary spin directions, and can violate the Bell-CHSH inequality with quadratic spin correlators
DOI
10.1103/physrevresearch.2.033504

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The basic concept of squeezed spin states is established and the principles for their generation are discussed. Two proposed mechanisms, referred to as one-axis twisting and two-axis countertwisting, are shown to reduce the standard quantum noise S/2 of the coherent S-spin state down to 1/2(S/3)1/3{)}^{1/3})1/3 and 1/2, respectively. Implementations of spin squeezing in interferometers are also discussed.
There is currently much interest in the two-axis countertwisting spin squeezing Hamiltonian suggested originally by Kitagawa and Ueda, since it is useful for interferometry and metrology. No analytical solution valid for arbitrary spin values seems to be available. In this article we systematically consider the issue of the analytical solvability of this Hamiltonian for various specific spin values. We show that the spin squeezing dynamics can be considered to be analytically solved for angular momentum values upto 21/221/221/2, i.e. for 212121 spin half particles. We also identify the properties of the system responsible for yielding analytic solutions for much higher spin values than based on naive expectations. Our work is relevant for analytic characterization of squeezing experiments with low spin values, and semi-analytic modeling of higher values of spins.
We propose a feedback scheme for the production of two-mode spin squeezing. We determine a general expression for the optimal feedback, which is also applicable to the case of single-mode spin squeezing. The two-mode spin squeezed states obtained via this feedback are optimal for j=1/2j=1/2j=1/2 and are very close to optimal for j>1/2.j>1/2.j>1/2. In addition, the master equation suggests a Hamiltonian that would produce two-mode spin squeezing without feedback, and is analogous to the two-axis countertwisting Hamiltonian in the single-mode case.