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arXiv:2201.01744 · Physical Review Applied

Extreme Spin Squeezing via Optimized One-Axis Twisting and Rotations

Sebastian Camilo Carrasco, Michael H. Goerz, Zeyang Li, Simone Colombo, Vladan Vuletić, Vladimir S. Malinovsky

Published Jun 27, 2022• 28 citations
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Abstract

We propose a scheme for the generation of optimal squeezed states for Ramsey interferometry. The scheme consists of an alternating series of one-axis twisting pulses and rotations, both of which are straightforward to implement experimentally. The resulting states show a metrological gain proportional to the Heisenberg limit. We demonstrate that the Heisenberg scaling is maintained even when placing constraints on the amplitude of the pulses implementing the one-axis twisting and when taking into account realistic losses due to photon scattering.

DOI
10.1103/physrevapplied.17.064050

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Spin squeezing provides crucial quantum resource for quantum metrology and quantum information science. Here we propose that one axis-twisted (OAT) spin squeezing can be generated from free evolution under a general coupled-spin model with collective spin-spin interactions. We further propose pulse schemes to recover squeezing from parameter imperfections, and reach the extreme squeezing with Heisenberg-limited measurement precision scaling as 1/N1/N1/N for NNN particles. This work provides a feasible method for generating extreme spin squeezing.
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.
Considering the unique energy level structure of the one-axis twisting Hamiltonian in combination with standard rotations, we propose the implementation of a rapid adiabatic passage scheme on the Dicke state basis. The method permits to drive Dicke states of the many-atom system into entangled states with maximum quantum Fisher information. The designed states allow us to overcome the classical limit of phase sensitivity in quantum metrology and sensing. We show how to generate superpositions of Dicke states, which maximize metrological gain for a Ramsey interferometric measurement. The proposed scheme is remarkably robust to variations of the driving field and has favorable time scaling, especially for a small to moderate (∼1000) number of atoms, where the total time does not depend on the number of atoms.
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We consider a large class of Ramsey interferometry protocols which are enhanced by squeezing and un-squeezing operations before and after a phase signal is imprinted on the collective spin of N particles. We report an analytical optimization for any given particle number and strengths of (un-)squeezing. These results can be applied even when experimentally relevant decoherence processes during the squeezing and un-squeezing interactions are included. Noise between the two interactions is however not considered in this work. This provides a generalized characterization of squeezing echo protocols, recovering a number of known quantum metrological protocols as local sensitivity maxima, thereby proving their optimality. We discover a single new protocol. Its sensitivity enhancement relies on a double inversion of squeezing. In the general class of echo protocols, the newly found over-un-twisting protocol is singled out due to its Heisenberg scaling even at strong collective dephasing.