Nonlinear Phonon-Assisted Up-Conversion Photoluminescence Under Vibrational Pumping at Liquid-Helium Temperatures

Optical refrigeration in semiconductors is driven by anti-Stokes photoluminescence (PL) arising from phonon-assisted up-conversion. In the conventional picture, lattice vibrations remain in thermal equilibrium and the relevant phonon population is pump independent, so the up-conversion rate scales approximately linearly with excitation power, which places a practical limit on cooling power density and predicts a rapid collapse of cooling efficiency at cryogenic temperatures. Because at liquid-helium temperatures (∼4  K), the occupation of optical phonons is vanishingly small, rendering phonon-assisted up-conversion, and thus laser cooling, effectively inaccessible; conversely, nonlinear up-conversion photoluminescence is typically attributed to multiphoton absorption and treated as parasitic heating. Here, we show that this paradigm fails in strongly polar semiconductors: under continuous-wave excitation at 4 K, Stokes Raman scattering pumps longitudinal optical phonons far out of equilibrium, creating a pump-power-dependent vibrational population that strengthens the Fröhlich-induced internal electric field and exponentially enhances field-assisted carrier tunneling, yielding nonlinear phonon-assisted up-conversion without invoking multiphoton processes. Using ZnTe nanobelts, we correlate power-dependent Raman signatures with up-conversion photoluminescence to establish the mechanism, and further theoretically demonstrate that vibrational pumping could broaden the cooling window and increase achievable cooling power, offering a route to enhanced semiconductor optical refrigeration.