Coherent control of Rydberg states in silicon.

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.

Coherent superpositions of three states for phosphorous donors in silicon prepared using THz radiation.

Superposition of orbital eigenstates is crucial to quantum technology utilizing atoms, such as atomic clocks and quantum computers, and control over the interaction between atoms and their neighbours is an essential ingredient for both gating and readout. The simplest coherent wavefunction control uses a two-eigenstate admixture, but more control over the spatial distribution of the wavefunction can be obtained by increasing the number of states in the wavepacket. Here we demonstrate THz laser pulse control of Si:P orbitals using multiple orbital state admixtures, observing beat patterns produced by Zeeman splitting. The beats are an observable signature of the ability to control the path of the electron, which implies we can now control the strength and duration of the interaction of the atom with different neighbours. This could simplify surface code networks which require spatially controlled interaction between atoms, and we propose an architecture that might take advantage of this.

Coherent creation and destruction of orbital wavepackets in Si:P with electrical and optical read-out.

The ability to control dynamics of quantum states by optical interference, and subsequent electrical read-out, is crucial for solid state quantum technologies. Ramsey interference has been successfully observed for spins in silicon and nitrogen vacancy centres in diamond, and for orbital motion in InAs quantum dots. Here we demonstrate terahertz optical excitation, manipulation and destruction via Ramsey interference of orbital wavepackets in Si:P with electrical read-out. We show milliradian control over the wavefunction phase for the two-level system formed by the 1s and 2p states. The results have been verified by all-optical echo detection methods, sensitive only to coherent excitations in the sample. The experiments open a route to exploitation of donors in silicon for atom trap physics, with concomitant potential for quantum computing schemes, which rely on orbital superpositions to, for example, gate the magnetic exchange interactions between impurities.

Classical versus quantum coherence.

Quantum dots are structures engineered to have desirable quantum-mechanical properties. Much of their potential usefulness stems from the ability to design such structures so that their passive properties can be exploited. However, there are many plans to use dots as the basis of a more active quantum engineering, in which the detailed quantum states of the dot's components are manipulated by externally imposed fields. This leads to a new requirement: our ability to model the time development of individual driven quantum systems. I shall discuss some of the problems which arise when single systems, rather than ensembles, are considered and give examples which illustrate the effects of classical and quantum incoherences. I propose a new classification of incoherent processes, based on their effect on individual wave functions.