Scalable spin squeezing from spontaneous breaking of a continuous symmetry

TL;DR

This paper demonstrates that adiabatic processes in quantum spin models with continuous symmetry breaking can produce highly spin-squeezed states with minimal uncertainty, scalable with system size, useful for quantum metrology.

Contribution

It shows that spontaneous symmetry breaking in XXZ models enables adiabatic creation of near-minimal spin uncertainty states with a specific N^{-3/4} scaling.

Findings

Spin squeezing achieved through symmetry breaking.

Minimum phase uncertainty scales as N^{-3/4}.

Preparation time scales linearly with the number of spins.

Abstract

Spontaneous symmetry breaking (SSB) is a property of Hamiltonian equilibrium states which, in the thermodynamic limit, retain a finite average value of an order parameter even after a field coupled to it is adiabatically turned off. In the case of quantum spin models with continuous symmetry, we show that this adiabatic process is also accompanied by the suppression of the fluctuations of the symmetry generator -- namely, the collective spin component along an axis of symmetry. In systems of $S=1/2$ spins or qubits, the combination of the suppression of fluctuations along one direction and of the persistence of transverse magnetization leads to spin squeezing -- a much sought-after property of quantum states, both for the purpose of entanglement detection as well as for metrological uses. Focusing on the case of XXZ models spontaneously breaking a U(1) (or even SU(2)) symmetry, we show that the adiabatically prepared states have nearly minimal spin uncertainty; that the minimum phase uncertainty that one can achieve with these states scales as $N^{-3/4}$ with the number of spins $N$; and that this scaling is attained after an adiabatic preparation time scaling linearly with $N$. Our findings open the door to the adiabatic preparation of strongly spin-squeezed states in a large variety of quantum many-body devices including e.g. optical lattice clocks.