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

TL;DR

This paper demonstrates that a broad class of $U(1)$-symmetric spin Hamiltonians with axial symmetry can generate robust spin squeezing, linking their eigenstate structure to the Anderson tower of states and the dynamics of the planar-rotor model.

Contribution

It reveals that $U(1)$-symmetric Hamiltonians with Anderson's tower of states produce persistent spin squeezing similar to the one-axis-twisting model, expanding the understanding of squeezing in quantum systems.

Findings

Robust spin squeezing is generated by a large class of $U(1)$-symmetric Hamiltonians.

The eigenstates form an Anderson tower related to spontaneous symmetry breaking.

Squeezing dynamics resemble the planar-rotor model, especially for interactions decaying as $r^{-eta}$ with $eta<5d/3$.

Abstract

Spin squeezing - a central resource for quantum metrology - can be generated via the non-linear, entangling evolution of an initially factorized spin state. Here we show that robust (i.e. persistent) 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, for models with sufficiently high connectivity, 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. Our central insight is 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 of the planar-rotor model 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.