Generation of twin-Fock states for precision measurement beyond the standard quantum limit

The highest precision achievable for a two-mode (two-path) classical interferometer is bounded by 1/√N (with NN</span/2) in each mode). In the past, either through optical spontaneous parametric-down-conversion or through quantum-gate operations on trapped ions, twin-Fock states consisting of no more than 10 photons or ions have been realized. In recent years, twin-Fock states made up of a few thousand atoms have been generated using spin-mixing dynamics in spinor Bose-Einstein condensates (BECs). However, these twin-Fock states exhibit huge fluctuation in particle numbers, thereby limiting their potential applications. We recently generated twin-Fock states of about 11000 atoms in a deterministic manner by driving a spin-1 BEC through quantum critical points (QCPs) slowly. Even though substantial excitations occur while crossing the QCP regions during the drive, this method is capable of generating highly entangled twin-Fock states because of the very different structures of the system's low-lying eigenstates across the QCPs. The samples we prepare feature a number squeezing of 10.7±0.6 decibels and a normalized collective spin length of 0.99±0.01. Together, they infer a minimum entanglement cluster (or entanglement breadth) of 910 atoms. This article introduces the background and advancement of this research.