Fundamentals of Laser Cooling of Rare-Earth-Ion Doped Solids and its Enhancement Using Nanopowders.

Abstract

The Fermi golden rule is applied as the primary theory for laser cooling of solids, by recognizing that the absorption is a photon-induced, phonon-assisted, electronic transition. The limiting factors are identified as the coupling and population of the energy carriers (photon, electron, and phonon), which include the photon-electron coupling, electron-phonon coupling, ion-dopant concentration, phonon density of states, and the photon population. The photon-electron and electron-vibration coupling rates for ion-doped materials are calculated using ab initio methods for the first time. Using the calculated first-principle wavefunctions, the electric transition dipole moment between the ground and excited states is determined by its definition. The electron-phonon coupling is calculated by taking into account the modification of the electronic wavefunction in response to the nuclei motion, and the modifications of the vibrational modes before and after the transition. This ab initio approach does not require any fitting to experiment, providing a theoretical foundation for the optimal selection of laser cooling materials (both dopant and host). Nanostructure is proposed for the first time to enhance laser cooling performance, through the optimization of carrier populations using nanopowders. The concept of optimum dopant concentration is established and determined using the energy transfer theory, and is found to be larger than that currently used. The phonon density of states of nanopowders, calculated using molecular dynamics simulations, exhibits broadened modes, and extended tails at low and high frequencies. This is advantageous over the bulk material since more phonon modes are available in the desired range. The pumping field energy is calculated by solving the Maxwell equations in random nanopowder media. Photons are multiply scattered and do not propagate through the medium, and large field enhancement is observed. This leads to the trapping of more photons in nanopowder media, compared to the bulk material, implying more efficient absorption and cooling performance. Due to these enhancement effects, thermal predictions show that nanopowders can be cooled to the cryogenic temperature range, for the first time.