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arXiv:1012.1078 · Europhysics Letters (EPL)

Manipulation and decoherence of acceptor states in silicon

Y. P. Song, B. Golding

Published Jul 26, 2011• 9 citations
arXivHTMLPDF

Abstract

Dielectric constant and absorption measurements on boron-doped silicon samples show that transitions between the acceptor energy levels can be induced by an applied resonant AC electric field and the Stark tuning of level spacing with an external DC electric field. The relatively longer decoherence times, T 2 =2.6 μs and T 1 =7.4 μs, were observed by the electric echo measurement in a low boron dopant concentration Si sample (8×10 −12 cm −3 ). The scalable acceptor-based system is a promising candidate of the charge qubit for quantum computing.

DOI
10.1209/0295-5075/95/47004

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Dielectric constant and absorption measurements on boron-doped silicon samples show that transitions between the acceptor energy levels can be induced by an applied resonant AC electric field and the Stark tuning of level spacing with an external DC electric field. The relatively longer decoherence times, T 2 =2.6 μs and T 1 =7.4 μs, were observed by the electric echo measurement in a low boron dopant concentration Si sample (8×10 −12 cm −3 ). The scalable acceptor-based system is a promising candidate of the charge qubit for quantum computing.
A solid-state quantum computer with dipolar coupling between qubits is proposed. The qubits are formed by the low-lying states of an isolated acceptor in silicon. The system has the scalability inherent to spin-based solid state systems, but the spatial separation between the qubits is an order of magnitude larger. Despite strong dipolar inter-qubit coupling, the decoherence rate, as measured by electric dipolar echoes at an energy splitting of 1.5 GHz, is less than 1 kHz at low temperatures. For inter-acceptor distances of 100 nm and for modest microwave field amplitudes (50 V/cm) the clock frequency of the quantum computer is 0.1 GHz, which yields a quality factor of 105. This paper describes ideas for detection and operation of the quantum computer, and examines limitations imposed by noise sources.
We study theoretically the phonon-induced relaxation and decoherence processes in the hybrid qubit in silicon. A hybrid qubit behaves as a charge qubit when the detuning is close to zero and as a spin qubit for large detuning values. It is realized starting from an electrostatically defined double quantum dot where three electrons are confined and manipulated through only electrical tuning. By employing a three-level effective model for the qubit and describing the environment bath as a series of harmonic oscillators in the thermal equilibrium states, we extract the relaxation and decoherence times as a function of the bath spectral density and of the bath temperature using the Bloch-Redfield theory. For Si quantum dots the energy dispersion is strongly affected by the physics of the valley, i.e., the conduction band minima, so we also included the contribution of the valley excitations in our analysis. Our results offer fundamental information on the system decoherence properties when the unavoidable interaction with the environment is included and temperature effects are considered.
The performance of superconducting quantum circuits is primarily limited by dielectric loss due to interactions with two-level systems (TLSs). State-of-the-art circuits with engineered material interfaces are approaching a limit where dielectric loss from bulk substrates plays an important role. However, a microscopic understanding of dielectric loss in crystalline substrates is still lacking. In this work, we show that boron acceptors in silicon constitute a TLS bath that leads to an energy dissipation channel for superconducting circuits. We discuss how the electronic structure of boron acceptors leads to an effective TLS response in silicon. We sweep the boron concentration in silicon and demonstrate the bulk dielectric loss limit from boron acceptors. We show that boron-induced dielectric loss can be reduced in a magnetic field due to the spin-orbit structure of boron. This work provides the first detailed microscopic description of a TLS bath for superconducting circuits and demonstrates the need for ultrahigh-purity substrates for next-generation superconducting quantum processors. Published by the American Physical Society 2024
Several solid-state quantum information processor proposals are based on silicon [16-18, 20, 52], including the original architecture conceived by Kane in 1998 [22], in which the quantum information was stored in the spin states of 31P donors. The interest raised by silicon in the field of quantum information is twofold. On the one hand, it represents the main semiconductor used for large- scale fabrication. On the other hand, it owns interesting physical properties suitable for preserving andmanipulating quantum states, such as long coherence times and relatively low disturbance of nuclear spins, which are further enhanced by employing purified 28Si. The employment of individual donors in silicon covers all the aspects of quantum information encoding and processing, like quantumbit (qubit) storage, implementation of quantum logic gates, coherent transfer of quantum states, and readout schemes. This chapter is devoted to the physics of few dopants in nanometric silicon devices and their applications to quantum information processing purposes. In the first part, an overview of the physics of themost common donors and acceptors in silicon is presented. Next, the quantum information key concepts and their implementation in donor-based architectures are discussed. Finally, decoherence effects and the concept of measurement of quantum states are presented for the case of electron states bound to donors in silicon. Between the sixties and the early eighties of the twentieth century, all the theoretical and experimental aspects related to the doping of bulk silicon have been investigated and explained. A silicon crystal consists of a diamond lattice constituted by two interleaved cubic lattices (face-centered cubic, FCC), the second of which has the origin in the center of the tetrahedron given by the origin (0,0,0) and the centers of the faces 100. Each Si atom has four valence electrons, which create a covalent bond with the shared electrons of four other Si atoms. The substitution of silicon atoms with atoms of a group V element (indicated as donors, typically P, As, and Sb in silicon) generates an n-doped silicon crystal (n-Si). Each donor introduces an eccess electron in the crystal, and it provides new energy levels in the band gap, close to the conduction band edge. Similarly, substituting silicon atoms with atoms of a group III element (an acceptor, typically B in silicon) generates a p-doped silicon crystal (p-Si). Each acceptor introduces an electron hole in the crystal, and it provides new energy levels in the band gap, close to the valence band. The diffusion of impurities in semiconductors alters the conduction properties from an insulating to a metallic regime. Depending on the different doping concentration, the wavefunction of the electron (hole) states introduced by each donor (acceptor) may overlap negligibly or substantially with those of neighboring sites. Such a transition from low doping to high doping as a function of the average distance between neighboring sites is described in terms of an Anderson-Mott transition and produces additional impurity bands (Hubbard bands) below the conduction band edge at sufficiently high concentration [1, 34]. The transport is governed by mechanisms based on localized states at low density, while it is based on delocalized states at high density. Four conventional regimes of impurity concentration are defined [50]. The dilute concentration of impurities holds for n < 1 · 1016 cm−3. There, the problem of the donor is that of a hydrogen atom with a scaled Rydberg and radius. Between the densities n of 1 ·1016 cm−3 and 2 · 1017 cm−3 (rNN = 11.9 nm), respectively, the regime is called semidilute, and it is characterized by formation of pairs. Above 2 · 1017 cm−3 and below the metallic behavior, which occurs at 3.7 · 1018 cm−3, the regime is called intermediate, and the formation of random clusters leads to effects generally accounted by the Hubbard band formation. Above n > 3.7 · 1018 cm−3, silicon is treated as a metal. In this section the physics of the first three regimes of donor concentration and the Anderson-Mott transition are described. The Anderson-Mott transition has been observed down to microscopic scale by employing arrays of few deterministically implanted As ions (see chapter 5) in Si transistors [39]. Analogous arguments and treatment can be given to acceptor concentration regimes.
Fast quantum oscillations of a charge qubit in a double quantum dot fabricated in a Si/SiGe heterostructure are demonstrated and characterized experimentally. The measured inhomogeneous dephasing time T2∗{T}_{2}^{*}T2∗​ ranges from 127 ps to 2.1 ns; it depends substantially on how the energy difference of the two qubit states varies with external voltages, consistent with a decoherence process that is dominated by detuning noise (charge noise that changes the asymmetry of the qubit's double-well potential). In the regime with the shortest T2∗{T}_{2}^{*}T2∗​, applying a charge-echo pulse sequence increases the measured inhomogeneous decoherence time from 127 to 760 ps, demonstrating that low-frequency noise processes are an important dephasing mechanism.
Neutrally charged divacancies in silicon carbide (SiC) are paramagnetic color centers whose long coherence times and near-telecom operating wavelengths make them promising for scalable quantum communication technologies compatible with existing fiber optic networks. However, local strain inhomogeneity can randomly perturb their optical transition frequencies, which degrades the indistinguishability of photons emitted from separate defects and hinders their coupling to optical cavities. Here, we show that electric fields can be used to tune the optical transition frequencies of single neutral divacancy defects in 4H-SiC over a range of several GHz via the DC Stark effect. The same technique can also control the charge state of the defect on microsecond timescales, which we use to stabilize unstable or non-neutral divacancies into their neutral charge state. Using fluorescence-based charge state detection, we show that both 975 nm and 1130 nm excitation can prepare their neutral charge state with near unity efficiency.