Laser cooling and electromagnetic traps have led to a revolution in atomic physics, yielding dramatic discoveries ranging from Bose-Einstein condensation to the quantum control of single atoms. Of particular interest, because they can be used in the quantum control of one atom by another, are excited Rydberg states, where wavefunctions are expanded from their ground-state extents of less than 0.1 nm to several nanometres and even beyond; this allows atoms far enough apart to be non-interacting in their ground states to strongly interact in their excited states. For eventual application of such states, a solid-state implementation is very desirable. Here we demonstrate the coherent control of impurity wavefunctions in the most ubiquitous donor in a semiconductor, namely phosphorus-doped silicon. In our experiments, we use a free-electron laser to stimulate and observe photon echoes, the orbital analogue of the Hahn spin echo, and Rabi oscillations familiar from magnetic resonance spectroscopy. As well as extending atomic physicists' explorations of quantum phenomena to the solid state, our work adds coherent terahertz radiation, as a particularly precise regulator of orbitals in solids, to the list of controls, such as pressure and chemical composition, already familiar to materials scientists.

Abstract. Because it is sensitive to fluctuations occurring over femtoseconds to picoseconds, gigahertz-to-terahertz dielectric relaxation spectroscopy can provide a valuable window into water's most rapid intermolecular motions. In response, we have built a vector network analyzer dielectric spectrometer capable of measuring absorbance and index of refraction in this frequency regime with unprecedented precision. Using this to determine the complex dielectric response of water and aqueous salt solutions from 5.9GHz to 1.12 THz (which we provide in the SI), we have obtained strong new constraints on theories of water's collective dynamics. For example, while the salt-dependencies we observe for water's two slower relaxations (8 and 1 ps) are easily reconciled with suggestions that they arise due to rotations of fully and partially hydrogen bonded molecules, respectively, the salt-dependence of the fastest relaxation (180 fs) appears difficult to reconcile with its prior assignment to liberations of single hydrogen bonds.

Decades of molecular dynamics and normal mode calculations suggest that the largest-scale collective vibrational modes of proteins span the picosecond to nanosecond time scale. Experimental investigation of these harmonic, low-amplitude motions, however, has proven challenging. In response, we have developed a vector network analyzer-based spectrometer that supports the accurate measurement of both the absorbance and refractive index of solvated biomolecules over the corresponding gigahertz to terahertz frequency regime, thus providing experimental information regarding their largest-scale, lowest frequency harmonic motions. We have used this spectrometer to measure the complex dielectric response of lysozyme solutions over the range 65 to 700 GHz and an effective medium model to separate the dielectric response of the solvated protein from that of its buffer. In doing so, we find that each lysozyme is surrounded by a tightly bound layer of 165 ± 15 water molecules that, in terms of their picosecond dynamics, behave as if they are an integral part of the protein. We also find that existing computational descriptions of the protein's dynamics compare poorly with the results of our experiment. Specifically, published normal mode and molecular dynamics simulations do not explain the measured dielectric response unless we introduce a cutoff frequency of 250 GHz below which the density of vibrational modes drops to zero. This cutoff is physically plausible, given the known size of the protein and the known speed of sound in proteins, raising questions as to why it is not apparent in computational models of the protein's motions.