  Spin-orbit (SO) coupling has led to numerously exciting phenomena in electron
systems, for instance, the recently discovered topological insulator. The
synthesized SO coupling with ultracold neutral atoms opens a new avenue of
quantum simulation, and gives us an opportunity to study SO coupling in bosonic
systems. Indeed, SO coupling leads to many new phenomena of boson superfluidity
and various condensate phases that spontaneously break different symmetries. A
richer structure of symmetry breaking always results in a nontrivial
finite-temperature phase diagram. While the thermodynamics of the SO coupled
Bose gas at finite temperature is still unknown either in theory or experiment.
In this work, we experimentally generate the SO coupling in ultracold Rb-87 gas
to explore in a large temperature range and get most key features. We discover
a novel phase transition between the stripe ordered phase and the magnetized
phase, which is reminiscent of temperature-driven transition from the B phase
to the A phase in super- fluid Helium-3 and from spin-density-wave to spin
nematic transition in iron pnictide. We also observe that the magnetic phase
transition and the Bose condensate transition occur simultaneously as
temperature decreases. Our work determines the entire finite-temperature phase
diagram of SO coupled Bose gas and further demonstrate the power of quantum
simulation.
