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.

Experimental determination of the Rashba coefficient in InSb/InAlSb quantum wells at zero magnetic field and elevated temperatures.

We report the optical measurement of the spin dynamics at elevated temperatures and in zero magnetic field for two types of degenerately doped n-InSb quantum wells (QWs), one asymmetric (sample A) and one symmetric (sample B) with regards to the electrostatic potential across the QW. Making use of three directly determined experimental parameters: the spin lifetime, τ(s), the sheet carrier concentration, n, and the electron mobility, µ, we directly extract the zero-field spin splitting. For the asymmetric sample where the Rashba interaction is the dominant source of spin splitting, we deduce a room temperature Rashba parameter of α = 0.09 ± 0.1 eV Å which is in good agreement with calculations and we estimate the Rashba coefficient α(0) (a figure of merit for the ease with which electron spins can be modulated via an electric field). We review the merits/limitations of this approach and the implications of our findings for spintronic devices.

The multi-photon induced Fano effect.

The ordinary Fano effect occurs in many-electron atoms and requires an autoionizing state. With such a state, photo-ionization may proceed via pathways that interfere, and the characteristic asymmetric resonance structures appear in the continuum. Here we demonstrate that Fano structure may also be induced without need of auto-ionization, by dressing the continuum with an ordinary bound state in any atom by a coupling laser. Using multi-photon processes gives complete, ultra-fast control over the interference. We show that a line-shape index q near unity (maximum asymmetry) may be produced in hydrogenic silicon donors with a relatively weak beam. Since the Fano lineshape has both constructive and destructive interference, the laser control opens the possibility of state-selective detection with enhancement on one side of resonance and invisibility on the other. We discuss a variety of atomic and molecular spectroscopies, and in the case of silicon donors we provide a calculation for a qubit readout application.

Spin preservation during THz orbital pumping of shallow donors in silicon.

We investigate the spin relaxation under conditions of optical excitation between the Rydberg orbital states of phosphorus donor impurities in silicon. Here we show that the spin relaxation is less than a few percent, even after multiple excitation/relaxation cycles. The observed high level of spin preservation may be useful for readout cycling or in quantum information schemes where coupling of neighbor qubits is via orbital excitation.

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.

Optical pumping and readout of bismuth hyperfine states in silicon for atomic clock applications.

The push for a semiconductor-based quantum information technology has renewed interest in the spin states and optical transitions of shallow donors in silicon, including the donor bound exciton transitions in the near-infrared and the Rydberg, or hydrogenic, transitions in the mid-infrared. The deepest group V donor in silicon, bismuth, has a large zero-field ground state hyperfine splitting, comparable to that of rubidium, upon which the now-ubiquitous rubidium atomic clock time standard is based. Here we show that the ground state hyperfine populations of bismuth can be read out using the mid-infrared Rydberg transitions, analogous to the optical readout of the rubidium ground state populations upon which rubidium clock technology is based. We further use these transitions to demonstrate strong population pumping by resonant excitation of the bound exciton transitions, suggesting several possible approaches to a solid-state atomic clock using bismuth in silicon, or eventually in enriched (28)Si.

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.

Si:P as a laboratory analogue for hydrogen on high magnetic field white dwarf stars.

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.

Continuous voltage tunability of intersubband relaxation times in coupled SiGe quantum well structures using ultrafast spectroscopy.

We demonstrate continuous voltage control of the nonradiative transition lifetime in semiconductor heterostructures. The results were obtained by picosecond time-resolved experiments on biased SiGe valence band quantum well structures using a free electron laser. By varying the applied voltage, the intersubband hole relaxation times for quantum well structures were varied by a factor of 2 as the wave functions and their overlaps were tuned. The range of magnitudes for the lifetime indicates a possible route to silicon-based quantum cascade lasers.

Spin relaxation by transient monopolar and bipolar optical orientation.

We have used two-color time-resolved spectroscopy to measure the relaxation of electron spin polarizations in a bulk semiconductor. The circularly polarized pump beam induces a polarization either by direct excitation from the valence band, or by free-carrier (Drude) absorption when tuned to an energy below the band gap. We find that the spin relaxation time, measured with picosecond time resolution by resonant induced Faraday rotation in both cases, increases in the presence of photogenerated holes. In the case of the material chosen, n-InSb, the increase was from 14 to 38 ps.