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Exact Solution of Two-Axis-Twisting Hamiltonian in Bose-Einstein Condensate

Duger Ulam-Orgikh, Purevdorj Munkhbaatar

Published Mar 13, 2022• 0 citations
Publisher

Abstract

In this Paper, we have dealt with two-axis twisting Hamiltonian for spin squeezing, which is experimentally implementable in Bose-Einstein Condensate, and have found an exact solution by two alternative methods. Many other important nonlinear Hamiltonians could also be solved exactly in a similar way.
DOI
10.22353/physics.v11i224.103

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In two-component Bose-Einstein condensates, the one-axis twisting Hamiltonian leads to spin squeezing with a limitation that scales with the number of atoms as ${N}^{\ensuremath{-}2/3}$. We propose a scheme to transform the one-axis twisting Hamiltonian into a two-axis twisting Hamiltonian, resulting in enhanced spin squeezing proportional to ${N}^{\ensuremath{-}1}$ approaching the Heisenberg limit. Instead of pulse sequences, only one continuous driving field is required to realize such a transformation, thus the scheme is promising for experimental realization of a two-axis twisting Hamiltonian. Quantum information processing and quantum metrology may benefit from this method in the future.
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We propose a scheme for spin squeezing in the orbital motion of a Bose-Einstein condensate in a toroidal trap. A circular lattice couples two counterrotating modes and squeezing is generated by the nonlinear interaction spatially modulated at half the lattice period. By varying the amplitude and phase of the modulation, various cases of the twisting tensor can be directly realized, leading to different squeezing regimes. These include the one-axis twisting and two-axis countertwisting that are often discussed as the most important paradigms for spin squeezing. Our scheme naturally realizes the Lipkin-Meshkov-Glick model with the freedom to vary all its parameters simultaneously.
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