Quantum control of hybrid nuclear-electronic qubits

Pulsed magnetic resonance is a wide-reaching technology allowing the quantum state of electronic and nuclear spins to be controlled on the timescale of nanoseconds and microseconds respectively. The time required to flip either dilute electronic or nuclear spins is orders of magnitude shorter than their decoherence times, leading to several schemes for quantum information processing with spin qubits. We investigate instead the novel regime where the eigenstates approximate 50:50 superpositions of the electronic and nuclear spin states forming "hybrid nuclear-electronic" qubits. Here we demonstrate quantum control of these states for the first time, using bismuth-doped silicon, in just 32 ns: this is orders of magnitude faster than previous experiments where pure nuclear states were used. The coherence times of our states are five orders of magnitude longer, reaching 4 ms, and are limited by the naturally-occurring 29Si nuclear spin impurities. There is quantitative agreement between our experiments and no-free-parameter analytical theory for the resonance positions, as well as their relative intensities and relative Rabi oscillation frequencies. In experiments where the slow manipulation of some of the qubits is the rate limiting step, quantum computations would benefit from faster operation in the hybrid regime.Comment: 20 pages, 8 figures, new data and simulation

Electron spin coherence exceeding seconds in high purity silicon

Silicon is undoubtedly one of the most promising semiconductor materials for spin-based information processing devices. Its highly advanced fabrication technology facilitates the transition from individual devices to large-scale processors, and the availability of an isotopically-purified $^{28}$Si form with no magnetic nuclei overcomes what is a main source of spin decoherence in many other materials. Nevertheless, the coherence lifetimes of electron spins in the solid state have typically remained several orders of magnitude lower than what can be achieved in isolated high-vacuum systems such as trapped ions. Here we examine electron spin coherence of donors in very pure $^{28}$Si material, with a residual $^{29}$Si concentration of less than 50 ppm and donor densities of $10^{14-15}$ per cm$^3$. We elucidate three separate mechanisms for spin decoherence, active at different temperatures, and extract a coherence lifetime $T_2$ up to 2 seconds. In this regime, we find the electron spin is sensitive to interactions with other donor electron spins separated by ~200 nm. We apply a magnetic field gradient in order to suppress such interactions and obtain an extrapolated electron spin $T_2$ of 10 seconds at 1.8 K. These coherence lifetimes are without peer in the solid state by several orders of magnitude and comparable with high-vacuum qubits, making electron spins of donors in silicon ideal components of a quantum computer, or quantum memories for systems such as superconducting qubits.Comment: 18 pages, 4 figures, supplementary informatio

Self-Trapped Excitons in Ionic-Covalent Silver Halide Crystals and Nanostructures: High-Frequency EPR, ESE, ENDOR and ODMR Studies

Silver halides have unique features in solid state physics because their properties are considered to be of borderline nature between ionic and covalent bonding. In AgCl, the self-trapped hole (STH) is centered and partly trapped in the cationic sublattice, forming an Ag2+ ion inside of a (AgCl6)4− complex as a result of the Jahn–Teller distortion. The STH in AgCl can capture an electron from the conduction band forming the self-trapped exciton (STE). Recent results of a study of STE by means of high-frequency electron paramagnetic resonance, electron spin echo, electron–nuclear double resonance (ENDOR) and optically detected magnetic resonance (ODMR) are reviewed. The properties of the STE in AgCl crystals, such as exchange coupling, the ordering of the triplet and singlet sublevels, the dynamical properties of the singlet and triplet states, and the hyperfine interaction with the Ag and Cl (Br) nuclei are discussed. Direct information about the spatial distribution of the wave function of STE unpaired electrons was obtained by ENDOR. From a comparison with the results of an ENDOR study of the shallow electron center and STH, it is concluded that the electron is mainly contained in a hydrogen-like 1s orbital with a Bohr radius of 15.1 ± 0.6 Å, but near its center the electron density reflects the charge distribution of the hole. The hole of the STE is virtually identical to an isolated STH center. For AgCl nanocrystals embedded into the KCl crystalline matrix, the anisotropy of the g-factor of STE and STH was found to be substantially reduced compared with that of bulk AgCl crystals, which can be explained by a considerable suppression of the Jahn–Teller effect in nanoparticles. A study of ODMR in AgBr nanocrystals in KBr revealed spatial confinement effects and allowed estimating the nanocrystal size from the shape of the ODMR spectra

Spectroscopic Studies of the Iron and Manganese Reconstituted Tyrosyl Radical in Bacillus Cereus Ribonucleotide Reductase R2 Protein

Ribonucleotide reductase (RNR) catalyzes the rate limiting step in DNA synthesis where ribonucleotides are reduced to the corresponding deoxyribonucleotides. Class Ib RNRs consist of two homodimeric subunits: R1E, which houses the active site; and R2F, which contains a metallo cofactor and a tyrosyl radical that initiates the ribonucleotide reduction reaction. We studied the R2F subunit of B. cereus reconstituted with iron or alternatively with manganese ions, then subsequently reacted with molecular oxygen to generate two tyrosyl-radicals. The two similar X-band EPR spectra did not change significantly over 4 to 50 K. From the 285 GHz EPR spectrum of the iron form, a g1-value of 2.0090 for the tyrosyl radical was extracted. This g1-value is similar to that observed in class Ia E. coli R2 and class Ib R2Fs with iron-oxygen cluster, suggesting the absence of hydrogen bond to the phenoxyl group. This was confirmed by resonance Raman spectroscopy, where the stretching vibration associated to the radical (C-O, ν7a = 1500 cm−1) was found to be insensitive to deuterium-oxide exchange. Additionally, the 18O-sensitive Fe-O-Fe symmetric stretching (483 cm−1) of the metallo-cofactor was also insensitive to deuterium-oxide exchange indicating no hydrogen bonding to the di-iron-oxygen cluster, and thus, different from mouse R2 with a hydrogen bonded cluster. The HF-EPR spectrum of the manganese reconstituted RNR R2F gave a g1-value of ∼2.0094. The tyrosyl radical microwave power saturation behavior of the iron-oxygen cluster form was as observed in class Ia R2, with diamagnetic di-ferric cluster ground state, while the properties of the manganese reconstituted form indicated a magnetic ground state of the manganese-cluster. The recent activity measurements (Crona et al., (2011) J Biol Chem 286: 33053–33060) indicates that both the manganese and iron reconstituted RNR R2F could be functional. The manganese form might be very important, as it has 8 times higher activity

The initialization and manipulation of quantum information stored in silicon by bismuth dopants

A prerequisite for exploiting spins for quantum data storage and processing is long spin coherence times. Phosphorus dopants in silicon (Si:P) have been favoured1, 2, 3, 4, 5, 6, 7, 8, 9, 10 as hosts for such spins because of measured electron spin coherence times (T2) longer than any other electron spin in the solid state: 14 ms at 7 K with isotopically purified silicon11. Heavier impurities such as bismuth in silicon (Si:Bi) could be used in conjunction with Si:P for quantum information proposals that require two separately addressable spin species12, 13, 14, 15. However, the question of whether the incorporation of the much less soluble Bi into Si leads to defect species that destroy coherence has not been addressed. Here we show that schemes involving Si:Bi are indeed feasible as the electron spin coherence time T2 is at least as long as for Si:P with non-isotopically purified silicon. We polarized the Si:Bi electrons and hyperpolarized the I=9/2 nuclear spin of 209Bi, manipulating both with pulsed magnetic resonance. The larger nuclear spin means that a Si:Bi dopant provides a 20-dimensional Hilbert space rather than the four-dimensional Hilbert space of an I=1/2 Si:P dopant