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The zone-center $E_{2g}$ modes play a crucial role in MgB$_2$, controllingthe scattering mechanisms in the normal state as well the superconductingpairing. Here, we demonstrate via first-principles quantum-field theorycalculations that, due to the anisotropic electron-phonon interaction, a$hot$-$phonon$ regime where the $E_{2g}$ phonons can achieve significantlylarger effective populations than other modes, is triggered in MgB$_2$ by theinteraction with an ultra-short laser pulse. Spectral signatures of thisscenario in ultrafast pump-probe Raman spectroscopy are discussed in detail,revealing also a fundamental role of nonadiabatic processes in the opticalfeatures of the $E_{2g}$ mode.

Ultrafast Hot Phonon Dynamics in MgB$_2$ Driven by Anisotropic Electron-Phonon Coupling