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Roton-type excitations usually emerge from strong correlations or long-rangeinteractions, as in superfluid helium or dipolar ultracold atoms. However, inweakly short-range interacting quantum gas, the recently synthesized spin-orbit(SO) coupling can lead to various unconventional phases of superfluidity, andgive rise to an excitation spectrum of roton-maxon character. Using Braggspectroscopy we study a SO coupled Bose-Einstein condensate of $^{87}$Rb atoms,and show that the excitation spectrum in a "magnetized" phase clearly possessesa two-branch and roton-maxon structure. As Raman coupling strength $\Omega$ isdecreased, a roton-mode softening is observed, as a precursor of the phasetransition to a stripe phase that spontaneously breaks spatially translationalsymmetry. The measured roton gaps agree well with theoretical calculations.Further, we determine sound velocities both in the magnetized and thenon-magnetized phase, and a phonon-mode softening is observed around the phasetransition in between. The validity of the $f$-sum rule is examined.

Softening of Roton and Phonon Modes in a Bose-Einstein Condensate with Spin-Orbit Coupling