  Quantum wires with spin-orbit coupling provide a unique opportunity to
simultaneously control the coupling strength and the screened Coulomb
interactions where new exotic phases of matter can be explored. Here we report
on the observation of an exotic spin-orbit density wave in Pb-atomic wires on
Si(557) surfaces by mapping out the evolution of the modulated spin-texture at
various conditions with spin- and angle-resolved photoelectron spectroscopy.
The results are independently quantified by surface transport measurements. The
spin polarization, coherence length, spin dephasing rate, and the associated
quasiparticle gap decrease simultaneously as the screened Coulomb interaction
decreases with increasing excess coverage, providing a new mechanism for
generating and manipulating a spin-orbit entanglement effect via electronic
interaction. Despite clear evidence of spontaneous spin-rotation symmetry
breaking and modulation of spin-momentum structure as a function of excess
coverage, the average spin-polarization over the Brillouin zone vanishes,
indicating that time-reversal symmetry is intact as theoretically predicted.
