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# Universal spin squeezing from the tower of states of $U(1)$-symmetric spin Hamiltonians

Abstract : Spin squeezing -- a central resource for quantum metrology -- results from the non-linear, entangling evolution of an initially factorized spin state. Here we show that universal squeezing dynamics is generated by a very large class of $S=1/2$ spin Hamiltonians with axial symmetry, in relationship with the existence of a peculiar structure of the low-lying Hamiltonian eigenstates -- the so-called Anderson's tower of states. Such states are fundamentally related to the appearance of spontaneous symmetry breaking in quantum systems, and they are parametrically close to the eigenstates of a planar rotor (Dicke states), in that they feature an anomalously large value of the total angular momentum. We show that, starting from a coherent spin state, a generic $U(1)$-symmetric Hamiltonian featuring the Anderson's tower of states generates the same squeezing evolution at short times as the one governed by the paradigmatic one-axis-twisting (or planar rotor) model of squeezing dynamics. The full squeezing evolution is seemingly reproduced for interactions decaying with distance $r$ as $r^{-\alpha}$ when $\alpha < 5d/3$ in $d$ dimensions. Our results connect quantum simulation with quantum metrology by unveiling the squeezing power of a large variety of Hamiltonian dynamics that are currently implemented by different quantum simulation platforms.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal-ens-lyon.archives-ouvertes.fr/ensl-03366113
Contributor : Fabio Mezzacapo Connect in order to contact the contributor
Submitted on : Tuesday, October 5, 2021 - 3:09:09 PM
Last modification on : Wednesday, October 6, 2021 - 3:28:54 AM

### Identifiers

• HAL Id : ensl-03366113, version 1
• ARXIV : 2103.07354

### Citation

Tommaso Comparin, Fabio Mezzacapo, Tommaso Roscilde. Universal spin squeezing from the tower of states of $U(1)$-symmetric spin Hamiltonians. 2021. ⟨ensl-03366113⟩

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