  Squeezing a quantum state along a specific direction has long been recognized
as a crucial technique for enhancing the precision of quantum metrology by
reducing parameter uncertainty. However, practical quantum metrology often
involves the simultaneous estimation of multiple parameters, necessitating the
use of high-quality squeezed states along multiple orthogonal axes to surpass
the standard quantum limit for all relevant parameters. In addition, a
temporally stabilized squeezed state can provide an event-ready probe for
parameters, regardless of the initial state, and robust to the timing of the
state preparation process once stabilized. In this work, we generate and
stabilize a two-mode squeezed state along two secular motional modes in a
vibrating trapped ion with reservoir engineering, despite starting from a
thermal state of the motion. Leveraging this resource, we demonstrate an
estimation of two simultaneous collective displacements along the squeezed
axes, achieving improvements surpassing the classical limit by up to 6.9(3) and
7.0(3) decibels (dB), respectively. Our demonstration can be readily scaled to
squeezed states with even more modes. The practical implications of our
findings span a wide range of applications, including quantum sensing, quantum
imaging, and various fields that demand precise measurements of multiple
parameters.
