We present a quantitative study of the efficiency of degenerate THz transient four-wave mixing in germanium doped by shallow impurities using the Dutch free electron laser FELIX. We derive the third order nonlinear sheet susceptibility and find values at low temperature that exceed those of any other material and wavelength range reported to date.

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.

We have performed high field magnetoabsorption spectroscopy on silicon doped with a variety of single and double donor species. The magnetic field provides access to an experimental magnetic length, and the quadratic Zeeman effect, in particular, may be used to extract the wave-function radius without reliance on previously determined effective mass parameters. We were, therefore, able to determine the limits of validity for the standard one-band anisotropic effective mass model. We also provide improved parameters and use them for an independent check on the accuracy of effective mass theory. Finally, we show that the optically accessible excited-state wave functions have the attractive property that interactions with neighbors are far more forgiving of position errors than (say) the ground state.

The absorption of multiple photons when there is no resonant intermediate state is a well-known nonlinear process in atomic vapours, dyes and semiconductors. The N-photon absorption (NPA) rate for donors in semiconductors scales proportionally from hydrogenic atoms in vacuum with the dielectric constant and inversely with the effective mass, factors that carry exponents 6N and 4N, respectively, suggesting that extremely large enhancements are possible. We observed 1PA, 2PA and 3PA in Si:P with a terahertz free-electron laser. The 2PA coefficient for 1s–2s at 4.25 THz was 400,000,000 GM (=4 × 10−42 cm4 s), many orders of magnitude larger than is available in other systems. Such high cross-sections allow us to enter a regime where the NPA cross-section exceeds that of 1PA—that is, when the intensity approaches the binding energy per Bohr radius squared divided by the uncertainty time (only 3.84 MW cm−2 in silicon)—and will enable new kinds of terahertz quantum control. By using a terahertz free-electron laser, multiphoton transitions between impurity states in p-doped Si are investigated. The two- and three-photon integrated absorption cross-sections are found to be the highest ever reported for a discrete oscillator system.

Juerong Li, Nguyen H. Le, K. Litvinenko, S.K. Clowes, H. Engelkamp, S.G. Pavlov, H.3 W. Hübers, V.B. Shuman, L.М. Portsel, А.N. Lodygin, Yu.A. Astrov, N.V. 4 Abrosimov, C.R. Pidgeon, A. Fisher, Zaiping Zeng, Y-M Niquet, B.N. Murdin 5 Advanced Technology Institute, University of Surrey, Guildford, GU2 7XH, UK 6 High Field Magnet Laboratory (HFML-EMFL), Radboud University, Toernooiveld 7, 6525 ED Nijmegen, The 7

THz optical properties of lithium borate (LBO) crystals were measured using time-domain spectroscopy (TDS). The LBO crystal samples were of high optical quality and were cut and polished along the < 100 >, < 010 > and < 001 > axes. Two independent measurements were performed in order to confirm the reproducibility and consistency of results. The contradictions in the previously published data on the THz optical properties of LBO were clarified. It was shown that the birefringence order at THz frequencies is n(z) < n(x)< n(y), whereas at optical frequencies it is known to be n(x) < n(y) < nz. It was seen that nz, which has the highest value in the visible, has the lowest value at THz. This is explained in terms of ionic polarizability and is consistent with the fact that the THz absorption coefficient for a wave polarized along the Z-axis is more than an order of magnitude lower than for the X and Yaxes. Absorption as low as 0.2 cm(-1) was found at frequencies up to 0.5 THz for a wave polarized parallel to the Z-axis. A set of new dispersion equations was designed for the entire transparency range. (c) 2017 Elsevier B.V. All rights reserved.

We have measured the near-infrared photoluminescence spectrum of phosphorus doped silicon (Si:P) and extracted the donor-bound exciton (D0X) energy at magnetic fields up to 28 T. At high field the Zeeman effect is strongly nonlinear because of the diamagnetic shift, also known as the quadratic Zeeman effect (QZE). The magnitude of the QZE is determined by the spatial extent of the wave-function. High field data allows us to extract values for the radius of the neutral donor (D0) ground state, and the light and heavy hole D0X states, all with more than an order of magnitude better precision than previous work. Good agreement was found between the experimental state radius and an effective mass model for D0. The D0X results are much more surprising, and the radius of the mJ = ±3/2 heavy hole is found to be larger than that of the mJ = ±1/2 light hole.

Pump-probe spectroscopy is the most common time-resolved technique for investigation of electronic dynamics, and the results provide the incoherent population decay time ${T}_{1}$. Here we use a modified pump-probe experiment to investigate coherent dynamics, and we demonstrate this with a measurement of the inhomogeneous dephasing time ${T}_{2}^{*}$ for phosphorus impurities in silicon. The pulse sequence produces the same information as previous coherent all-optical (photon-echo-based) techniques but is simpler. The probe signal strength is first order in the pulse area but its effect on the target state is only second order, meaning that it does not demolish the quantum information. We propose simple extensions to the technique to measure the homogeneous dephasing time ${T}_{2}$, or to perform tomography of the target qubit.

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 1 s and 2 p 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.

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 28Si.

A silicon crystal provides an extremely clean environment within which electrons may orbit impurity atoms, analogous to isolated atoms held in vacuum traps1–4. The hyperfine splittings of alkali atoms in vacuum are widely used as microwave frequency standards5, while the push for semiconductor-based quantum information technologies has resulted in dramatic improvements of the coherence times for hyperfine states of shallow donors in silicon3,6. Magnetic resonance detection in alkali atoms is enabled by selective pumping of the D-lines7, but the hyperfine splittings of the equivalent transitions to the odd-parity excited states of shallow donors in semiconductors have so far eluded detection. Here we demonstrate well-resolved hyperfine splittings of these transitions in natural silicon doped with bismuth, and use these transitions to observe strong, controllable polarization of the hyperfine states by pumping the donor bound exciton transitions. Our results open the possibility of sub-ns pumping, and bring solid-state frequency standards and masers based on these donor transitions within reach. The last fifty years have been a period of outstanding developments in the field of atomic frequency standards, reaching frequency stabilities in the 10−16 range in hydrogen masers and accuracies better than 10−15 in cesium fountains5, ytterbium lasers8 and even 10−18 in a strontium lattice9. In many implementations, hydrogen or alkali-metal atoms with a single valence electron are used, and the resonance transition between the two hyperfine levels of the S1/2 ground-state serves as the frequency reference. The splitting, which is in the microwave range (1–10 GHz), is produced by the interaction between the electron spin and the nuclear spin. The splitting is much smaller than kBT (except at mK temperature), and a common characteristic of the preparation to enhance the detected magnetic resonance signal in those implementations is the use of state selection by means of optical pumping10. The simplest “intensity pumping” scheme involving a third, higher energy state, uses repeated cycles of selective excitation

Just as phosphorus in silicon produces a hydrogenic defect, the double donor selenium in silicon is an analog of helium. We have measured the impurity absorption spectrum at high magnetic field, and we show that the odd-parity excited states of Si:Se behave identically to those of Si:P. This fact allows us to isolate the electron-electron interactions (exchange and correlation) in the ground state from the quadratic Zeeman effect. The field tuning allows us to put upper limits on the strength of some of these interactions (e.g., at 30 T the electron-electron correlation interaction in the ground state of Se is less than about 40 \ensuremath{\mu}eV; at 30 T the quadratic Zeeman energy in the ground state of P is less than about 200 \ensuremath{\mu}eV).

K. L. Litvinenko,1,* M. Pang,1 Juerong Li,1 E. Bowyer,1 H. Engelkamp,2 V. B. Shuman,3 L. M. Portsel,3 A. N. Lodygin,3 Yu. A. Astrov,3 S. G. Pavlov,4 H.-W. Hübers,4,5 C. R. Pidgeon,6 and B. N. Murdin1 1Advanced Technology Institute and SEPNet, University of Surrey, Guildford GU2 7XH, United Kingdom 2High Field Magnet Laboratory, Institute for Molecules and Materials, Radboud University Nijmegen, Toernooiveld 7, NL-6525 ED Nijmegen, The Netherlands 3Ioffe Physical-Technical Institute, Politekhnicheskaya 26, 194021 St. Petersburg, Russia 4Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstraße 2, 12489 Berlin, Germany 5Technische Universität Berlin, Institut für Optik und Atomare Physik, Hardenbergstrasse 36, 10623 Berlin, Germany 6Institute of Photonics and Quantum Sciences, SUPA, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom (Received 30 June 2014; revised manuscript received 18 August 2014; published 8 September 2014)

We report the characteristics of a simple complementary metal-oxide-semiconductor compatible terahertz detector device with low response time (nanoseconds) determined using a short-pulse, high intensity free-electron laser. The noise equivalent power was 1 × 10−11 W Hz−1/2. The detector has an enhanced response over narrow bands, most notably at 9.5 THz, with a continuum response at higher frequencies. Using such a device, the dynamics of donors in silicon can be explored, a system which has great potential for quantum information processing.

Shallow donors in silicon are favorable candidates for the implementation of solid-state quantum computer architectures because of the promising combination of atomiclike coherence properties and scalability from the semiconductor manufacturing industry. Quantum processing schemes require (among other things) controlled information transfer for readout. Here we demonstrate controlled electron tunneling at 10 K from P to Sb impurities and vice versa with the assistance of resonant terahertz photons.

Shallow donor impurities in silicon, once frozen out at low temperature, share many properties in common with free hydrogen atoms [1]. They have long been the subject of spectroscopic investigation, but it is only very recently [2,3] that it has been possible to investigate the time-domain dynamics of orbital excitations such as the 1 s to 2p, due to the difficulty of obtaining short, intense pulses in the relevant wavelength range. These new techniques make shallow donors (and also acceptors [4]) attractive for studying atomic physics effects, and for applications in quantum information. We have measured the population dynamics of electrons orbiting around phosphorus impurities in commercially-available silicon, and shown that the lattice relaxation lifetime is about 200 ps, only 1 order of magnitude shorter than the radiative lifetime of free hydrogen.

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.

The low-temperature (similar to 5 K) phonon-assisted relaxation of the 2p(0) state of phosphorus donors in isotopically pure, monocrystalline Si-28 has been studied in the time domain using a pump-probe technique. The lifetime of the 2p(0) state in Si-28: P is found to be 235 ps, which is 16% larger than the lifetime of a reference Si:P sample with a natural isotope composition. The interaction of the 2p(0) state with intervalley g-type longitudinal acoustic and f-type transverse acoustic phonons determines its lifetime. This interaction, which depends on the homogeneity of the crystal, becomes weaker in Si-28 because of its more perfect crystal lattice compared to natural Si, and this leads to a longer lifetime. The difference between the linewidths of the 1s(A(1)) -> 2p(0) transition in Si-28:P and natural Si:P is more than a factor of two. It follows that linewidth broadening due to isotopic composition is an inhomogeneous process.