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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.

The quantum cascade laser provides one possible method of realizing high efficiency light emitters in indirect band gap materials such as silicon. Electroluminescence results from Si/SiGe quantum cascade emitters are presented demonstrating edge emission from heavy-hole to heavy-hole transitions and light-hole to heavy-hole transitions. In surface-normal emission, only light-hole to heavy-hole electroluminescence is observed as predicted by theory. Intersubband emission is demonstrated at 2.9 THz ͑103 m wavelength͒, 8.9 THz ͑33.7 m͒, and 16.2 THz ͑18.5 m͒ from the Si/SiGe quantum cascade heterostructures.

One of the great successes of quantum physics is the description of the long-lived Rydberg states of atoms and ions. The Bohr model is equally applicable to donor impurity atoms in semiconductor physics, where the conduction band corresponds to the vacuum, and the loosely bound electron orbiting a singly charged core has a hydrogen-like spectrum according to the usual Bohr-Sommerfeld formula, shifted to the far-infrared because of the small effective mass and high dielectric constant. Manipulation of Rydberg states in free atoms and ions by single and multiphoton processes has been tremendously productive since the development of pulsed visible laser spectroscopy. The analogous manipulations have not been conducted for donor impurities in silicon. Here, we use the FELIX pulsed free electron laser to perform time-domain measurements of the Rydberg state dynamics in phosphorus-and arsenicdoped silicon and we have obtained lifetimes consistent with frequency domain linewidths for isotopically purified silicon. This implies that the dominant decoherence mechanism for excited Rydberg states is lifetime broadening, just as for atoms in ion traps. The experiments are important because they represent a step toward coherent control and manipulation of atomic-like quantum levels in the most common semiconductor and complement magnetic resonance experiments in the literature, which show extraordinarily long spin lattice relaxation times-key to many well known schemes for quantum computing qubits-for the same impurities. Our results, taken together with the magnetic resonance data and progress in precise placement of single impurities, suggest that doped silicon, the basis for modern microelectronics, is also a model ion trap.coherence ͉ free electron laser ͉ quantum information ͉ picosecond population dynamics ͉ hydrogenic donor impurity H omogenous lifetime-broadened two-level atoms in ion traps (1) have become favorite objects of study for quantum optics with a view toward both fundamental physics and the eventual development of a quantum computer. Among the many schemes proposed (2), the states of ions in trap systems are attractive for the realization of quantum information ''qubits'' (quantum bits) because they are well isolated from the decohering effects of the environment and can be coherently controlled by lasers. The Bohr model is equally applicable to donor impurity atoms in semiconductor physics, where the conduction band corresponds to the vacuum, and the loosely bound electron orbiting a singly charged core has a hydrogen-like spectrum according to the usual Bohr-Sommerfeld formula, shifted to the far-infrared because of the small effective mass and high dielectric constant. As with atoms in traps the ground states are tightly confined and well isolated from the environment, giving rise to extraordinarily sharp transitions (3-5) and very long spin coherence times (6, 7), measured with magnetic resonance experiments. There are several proposals for quantum information processing based on the spin of silicon do...

Under oblique incidence of circularly polarized infrared radiation the spin-galvanic effect has been unambiguously observed in (001)-grown n-type GaAs quantum well (QW) structures in the absence of any external magnetic field. Resonant inter-subband transitions have been obtained making use of the tunability of the free-electron laser FELIX. It is shown that a helicity dependent photocurrent along one of the 110 axes is predominantly contributed by the spin-galvanic effect while that along the perpendicular in-plane axis is mainly due to the circular photogalvanic effect. This strong non-equivalence of the [110] and [110] directions is determined by the interplay between bulk and structural inversion asymmetries. A microscopic theory of the spin-galvanic effect for direct inter-subband optical transitions has been developed being in good agreement with experimental findings.

Pump-probe transmission experiments have been performed on PbSe above the fundamental absorption edge near 4 m in the temperature range 30 to 300 K, using the Dutch ps free-electron laser. For temperatures below 200 K and carrier densities above the threshold for stimulated emission, stimulated recombination represents the most efficient recombination mechanism with relatively fast kinetics in the 50-100-ps regime, in good agreement with earlier reports of photoluminescent emission. Above this temperature Auger recombination dominates, and the Auger coefficient C is determined from the pump-probe decay curves. In the lowtemperature regime the Auger coefficient is determined from the decay curves at times beyond 100 ps. The Auger coefficient is approximately constant ͑with a value of about 8ϫ10 Ϫ28 cm 6 s Ϫ1) between 300 and 70 K, and then drops a value of about 1ϫ10 Ϫ28 cm 6 s Ϫ1 at 30 K, in good agreement with the theory for nonparabolic near-mirror bands and nondegenerate statistics. It is found that C for PbSe is between one and two orders of magnitude lower than for Hg 1Ϫx Cd x Te of comparable band gap. ͓S0163-1829͑98͒07243-9͔

Laboratory spectroscopy of atomic hydrogen in a magnetic flux density of 10 5 T (1 gigagauss), the maximum observed on high-field magnetic white dwarfs, is impossible because practically available fields are about a thousand times less. In this regime, the cyclotron and binding energies become equal. Here we demonstrate Lyman series spectra for phosphorus impurities in silicon up to the equivalent field, which is scaled to 32.8 T by the effective mass and dielectric constant. The spectra reproduce the high-field theory for free hydrogen, with quadratic Zeeman splitting and strong mixing of spherical harmonics. They show the way for experiments on He and H 2 analogues, and for investigation of He 2 , a bound molecule predicted under extreme field conditions.

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