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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum control in silicon using coherent THz pulses

Stephen A. Lynch, P. Thornton Greenland, Alexander F. G. van der Meer, Benedict N Murdin, C. R. Pidgeon, Britta Redlich, N. Q. Vinh, G. Aeppli

Published Oct 15, 2012• 0 citations
Publisher

Abstract

It has long been known that shallow donors such as phosphorous and the other group-V elements, have a hydrogen-like optical spectrum. The main difference is that while the spectrum of atomic hydrogen lies in the visible band, the spectrum of shallow donors in silicon is downshifted to the THz frequency band. This is a direct consequence of the reduced Coulomb attraction seen by the loosely bound electron because the core electrons shield the positive donor atom nucleus, and because the electron is now moving in a dielectric material. While spectroscopy has already revealed much about the energy level structure, very little was known about the temporal dynamics of the system until now. We have used THz pulses from the FELIX free electron laser to probe these hydrogen-like levels. By exploiting the well-known pump-probe technique we have measured the characteristic lifetimes of the excited Rydberg states and found them to be of the order 200 ps. Then, by making subtle changes to the geometry of the pump-probe experimental setup we demonstrate the existence of a THz photon echo. The photon echo is a purely quantum phenomenon with no classical analogue, and it allows us to study the quantum state of the donor electron. We then show, using the photon echo, that it is possible to create a coherent superposition of the ground and excited state of the donor. Measuring the photon echo is important because it can also be used to measure a second important characteristic lifetime of the silicon-donor system, the phase decoherence time.

DOI
10.1117/12.928571

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It has long been known that shallow donors such as phosphorous and the other group-V elements, have a hydrogen-like optical spectrum. The main difference is that while the spectrum of atomic hydrogen lies in the visible band, the spectrum of shallow donors in silicon is downshifted to the THz frequency band. This is a direct consequence of the reduced Coulomb attraction seen by the loosely bound electron because the core electrons shield the positive donor atom nucleus, and because the electron is now moving in a dielectric material. While spectroscopy has already revealed much about the energy level structure, very little was known about the temporal dynamics of the system until now. We have used THz pulses from the FELIX free electron laser to probe these hydrogen-like levels. By exploiting the well-known pump-probe technique we have measured the characteristic lifetimes of the excited Rydberg states and found them to be of the order 200 ps. Then, by making subtle changes to the geometry of the pump-probe experimental setup we demonstrate the existence of a THz photon echo. The photon echo is a purely quantum phenomenon with no classical analogue, and it allows us to study the quantum state of the donor electron. We then show, using the photon echo, that it is possible to create a coherent superposition of the ground and excited state of the donor. Measuring the photon echo is important because it can also be used to measure a second important characteristic lifetime of the silicon-donor system, the phase decoherence time.
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 arsenic-doped 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.
Quantum computation holds the promise of efficient solutions to currently formidable problems. A prospective technology is that of computing using quantum states, which may dramatically speed up or otherwise reduce the complexity for the solution of some hard problems. Of the many different schemes proposed, shallow substitutional donors in Silicon hold great attractiveness for the detailed study of the medium, high industrial capacity, and ubiquity of raw materials. We develop control over the quantum orbital and spin states of bound electrons using the THz ultrafast laser FELIX. \nManipulation of orbital states is studied using interferometric methods to produce Ramsey fringes, read out using optical and electrical methods. Contactless electrical measurement of free charge carriers is implemented, and the details of its advantages and limitations are explored. Both types of readout are used to demonstrate a coherent 3-level orbital manipulation, otherwise known as a quantum beat. The work constitutes a nontrivial control over the spatial distribution of the wavefunction of the atom which may enable error correcting surface code implementations. \nSpin dynamics are then explored in the presence of FELIX using donor-bound exciton techniques, which allow a sensitive and fast control over the electron spin states. The implementation is used to probe whether orbital excitation has a strong effect upon the spin states of the donor electrons, and it is shown that any modification of the spin is negligible. Experimental measurements of optically gated spin-exchange coupling are enabled by this methodology, and a roadmap to future implementation is discussed in the context of the present work. \nOverall, the work advances the state of spin and orbital control of neutral donor states for the purposes of optically gated quantum computing. Combined spin and orbital manipulations are now possible in the system, which will allow a more advanced implementation of quantum computation using orbital states than was previously possible.
In this thesis the reasons for pursuing an optically addressable quantum object in silicon are outlined before introducing some possible technological applications. Chalcogen donor electron systems in silicon are then discussed as a candidate for these quantum technologies. The chalcogen donor complexes in silicon allow the solid-state analogues of hydrogen and helium to be studied. The time-resolved Fourier transform technique was employed to measure the photoluminescence from a selenium doped silicon sample when pumped above band gap at the temperatures 10 K, 80 K and 300 K. The excited state lifetime of the 2p0 state was found to be 28.2 ns for atomic centres and 66.4 ns for molecular centres at 10 K. The lifetimes were seen to be similar across large emission bands indicating a rate limiting step. A multi-colour pump-probe experiment, using time-resolved Fourier transform spectroscopy, was performed at the FELIX institute to determine the excited state lifetimes of the 2p0 and 1s(T2) to be <2.5 ns and 10.62 ns respectively. A system of 5 coupled rate equations was then implemented to verify the experimental results. The lifetimes were theoretically determined from three sets of initial conditions. Carriers were initially positioned in the conduction band, modelling the photoluminescence experiment, the 2p and 1s states, imitating the FELIX experiment. The 2p state was shown to have two decay lifetimes, one 15.1 ps and the second of 7.24 ns. The first fast decay is due to the pure 2p state relaxation while the second long lifetime is a result of the 1s(T2) state in uencing the 2p excited state lifetime. The 1s(T2) excited state lifetime that back-fills the 2p state elongates the 2p excited state lifetime, causing the lifetime to appear longer than the true lifetime. This research implies that silicon has the potential to be an accessible test bed for quantum experiments by showing that it could be possible to create isolated non-interacting donor centres that are individually optically addressable by mid-IR laser light.
An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.
Each cycle of a quantum computation requires a quantum state initialisation. For semiconductor-based quantum platforms, initialisation is typically performed via slow microwave processes and usually requires cooling to temperatures where only the lowest quantum level is occupied. In silicon, boron atoms are the most common impurities. They bind holes in orbitals including an effective spin-3/2 ground state as well as excited states analogous to the Rydberg series for hydrogen. Here we show that initialisation temperature demands may be relaxed and speeds increased over a thousand-fold by importing, from atomic physics, the procedure of optical pumping via excited orbital states to preferentially occupy a target ground state spin. Spin relaxation within the orbital ground state of unstrained silicon is too fast to measure for conventional pulsed microwave technology, except at temperatures below 2 K, implying a need not only for fast state preparation but also fast state readout. Circularly polarised ~10 THz photon pulses from a free electron laser meet both needs at temperatures above 3 K: a 9 ps pulse enhances the population of one spin eigenstate for the "1s"-like ground state orbital, and the second interrogates this imbalance in spin population. Using parameters given by our data, we calculate that it should be possible to initialise 99% of spins for boron in strained silicon within 250 ps at 3 K. The speedup of both state preparation and measurement gained for THz rather than microwave photons should be explored for the many other solid state quantum systems hosting THz excitations potentially useful as intermediate states.