Session A35: Focus Session: Spins in Semiconductors -- Hyperfine Interactions

Magnetic spin resonance of hydrogenic phosphorus donors in silicon

A variety of electron paramagnetic resonance (EPR) measurements of an ensemble of phosphorus donors in silicon has lead to following intriguing discoveries. Electrically detected magnetic resonance (EDMR) at low magnetic fields ($<$200G) has revealed transitions involving superposition states between phosphorus electron and nuclear spins. Such states emerge because the hyperfine term overwhelm the electron Zeeman term at such low magnetic fields. A continuous control of the degree of the superposition by applied magnetic field has been demonstrated. Extremely long coherence times $\sim $0.6 s at 2K of electron spins bound to phosphorus and $\sim $3 s at 6K of $^{31}$P nuclear spins have been obtained by pulse-EPR and ENDOR of an isotopically enriched $^{28}$Si single crystal (99.992{\%}). Making the Si crystal nearly monoisotopic led to elimination of docoherence due to $^{29}$Si nuclear spins. Not only the electron spin but also phosphorus nuclear spin decoherence time was found to depend strongly on the phosphorus concentration in the range 8x10$^{13}$-4x10$^{15}$ cm$^{-3}$. Unexpected observation of shifts in $^{31}$P nuclear transition energies (ENDOR peak positions) with the change in the background silicon isotopic composition is also reported. The four nearest neighbor silicon isotopes of phosphorus are shown to affect strongly the nuclear transition energy of $^{31}$P. Experimental results will be discussed in the context of isotope effect arising from differences in the nuclear mass and spins. This work has been performed in collaborations with S. Tojo, H. Morishita, M. Eto, L. S. Vlasenko, and groups lead by K. Semba, M. L. W. Thewalt, S. A. Lyon, J. J. L. Morton, and M. S. Brandt. Financial supports by Grant-in-Aid for Scientific Research {\#}18001002, NONOQUINE, JST-DFG Strategic Cooperative Program, and Global Center of Excellence at Keio University are greatly appreciated.   

Hyperfine interaction in silicon quantum dots

Spins in semiconductor nanostructures are promising qubit candidates for solid state quantum computing. For Si:P systems, the main factor that determines quantum coherence of donor electron spins is their hyperfine (HF) interactions with the host $^{29}$Si nuclei. The success of experimental studies of spin dynamics in gated semiconductors (in particular GaAs quantum dots - QDs) motivated several groups to perform similar experiments in gated QDs in Si. Gated QDs are more flexible and tunable than the Si:P system. We report results from a first- principles all-electron calculation of the HF interaction strength (both isotropic and anisotropic) for a single conduction electron in Si, which as far as we know has not been previously reported in the literature. We compare our theoretical values with previous experimental measurements to ascertain the reliability of our calculations. We discuss implications of our results on QD-confined electron spin decoherence and manipulation.   

Dynamic nuclear polarization in silicon

We report on our DNP experiments on silicon wafers and nanoparticles. The DNP mechanism in n-doped wafers depends on the doping concentration, and a broad range of DNP enhancements have been observed. The largest enhancements we have recorded (over 200) were for wafers with donor concentrations in the range of $1-3 \times 10^{17}$ cm$^{-3}$, where the DNP is mediated by exchange-coupled clusters of donors. The silicon polarization obtained was over 10\%. We have also characterized the DNP of silicon nanoparticles suspended in a frozen solution. Off-resonant microwave irradiation of paramagnetic electron defects at the silicon-silicon dioxide interface in the nanoparticles results in a hyperpolarization of both the silicon spins of the particle as well as the water protons at the surface of the particle.   

Optically Detected NMR of Optically Hyperpolarized $^{31}$P Nuclear Spins in $^{28}$Si

We have recently shown that the improved spectral resolution possible in highly enriched $^{28}$Si permits the optical measurement of the $^{31}$P electron and nuclear spin populations via the donor bound exciton transitions. We also demonstrated how the same optical transitions can be used to hyperpolarize both the electron and nuclear spins at low magnetic field. Here we combine these effects to measure the NMR of dilute $^{31}$P in a regime inaccessible to other methods.   

Optically detected hyperfine splitting and optical nuclear-spin hyperpolarization of the $^{209}$Bi donor in $^{\mathrm{nat}}$Si

Among the group-V donors in silicon, bismuth ($^{209}$Bi) has by far the largest hyperfine constant due to its large binding energy. So far, however, there has been no attempt to see the hyperfine splitting in the Bi bound exciton transition. We show a well-resolved zero-field hyperfine splitting, and while the hyperfine splitting under magnetic field is not well resolved an optical hyperpolarization of the Bi nuclear spin ($I$ = 9/2) is observed by studying the temperature dependence of the PL spectra. This nonresonant optical nuclear hyperpolarization is similar to one observed recently for $^{31}$P using EPR, and we propose a new model for its origin.   

Electrically Probing Nuclear Spin Polarization in an InSb Single Quantum Well

We perform tilted-magnetic-field and resistively detected nuclear magnetic resonance (RDNMR) measurements of a symmetrically doped InSb single quantum well. Two types of Landau level crossings are presented in magnetotransport spectra by tilting the quantum well, one is characterized by a collapse of longitudinal resistance minimum and another shows resistance spikes within persistent resistance minimum. A small rf field with the frequency sweeping through the Larmor resonance of individual nuclear isotopes is applied to probe the nuclear spin polarization at or near these crosses. By flowing a relatively large current, NMR signals of high nuclear spin isotopes of both In and Sb at the resistance spikes around filling factor 2 are detected using the RDNMR measurement. We interpret this as evidence that energetically degenerate domains with different pseudospin polarization are requisite for dynamic nuclear polarization at the cross.   

Phase-Sensitive Probes of Nuclear Polarization in Spin-Blockaded Quantum Dots

Semiconducting quantum dots provide a platform for investigating the quantum many-body dynamics of coupled electron and nuclear spins. The phenomenon of spin blockade, wherein the Pauli exclusion principle requires electrons to flip their spins in order to pass through the system [1], is an invaluable tool in this pursuit. We describe a new regime of coupled electron and nuclear spin dynamics in spin-blockaded quantum dots where the hyperfine coupling to nuclear spins competes with a purely electronic spin-flip mechanism, such as the spin-orbit interaction or coupling to an inhomogeneous Zeeman field [M. S. Rudner et al., arXiv:0909.0060]. We show that the long-lived coherence of the nuclear spin bath plays a crucial role and leads to a range of new surprising phenomena. In particular, a purely electrical detection of coherent nuclear precession can be realized. Recent results of Foletti et al. [arXiv:0801.3613] suggest that this interesting new regime is now within experimental reach. [1] K. Ono et al. Science 297, 1313 (2002).   

Electron spin dephasing by hyperfine interaction with nuclei in quantum dots

The problem of the dynamics of an electron spin coupled by hyperfine (hf) interaction to nuclear spins has been a focus of large theoretical attention, since the interaction with the nuclear bath is the most limiting decoherence mechanism in spin qubits based on quantum dots made of III-V materials. I will present a theory of pure dephasing decoherence which gives predictions for electron dynamics in narrowed state free induction decay, spin echo, and under higher order dynamical decoupling sequences [1,2]. In this theory we take advantage of the long-range character of hf-mediated interactions (which couple remote nuclei via virtual flip-flops with the electron spin), and we resum the leading terms in 1/N expansion of the decoherence time-evolution function (N being the large number of nuclei interacting appreciably with the electron spin). For the case of a thermal uncorrelated bath this approach is applicable as long as the electron Zeeman splitting is larger than the typical Overhauser shift of the electron energy (i.e.~magnetic field must be larger than a few mT in a large GaAs dot). For the spin echo evolution we show that the dominant decoherence process at low fields is due to interactions between nuclei having different Zeeman energies (i.e.~nuclei of As and two isotopes of Ga in GaAs). The robustness of this theory is verified by comparison with a numerical simulation of spin echo in a system with $N = 20$ nuclei. I will also discuss the application of our approach to singlet-triplet qubit in a double quantum dot. \\[4pt] [1] L. Cywinski, W.M. Witzel, and S. Das Sarma, Phys. Rev. Lett. {\bf 102}, 057601 (2009). \\[0pt] [2] L. Cywinski, W.M. Witzel, and S. Das Sarma, Phys. Rev. B {\bf 79}, 245314 (2009).   

Coherent optical manipulation of localized electron-nuclear spin systems in n-GaAs

We present studies on ensembles of single-electron systems in GaAs, realized by Si doping at very low concentration. This yields a gas of donor-bound electrons in hydrogen-like orbitals. The Bohr radius is large and each electron spin has hyperfine interaction with around 10$^5$ nuclear spins. We address this system with a resonant Raman scheme: The electron spin states both have a transition to a common donor-bound trion state. With polarization maintaining fibers to a cryogenic confocal microscope we study spin selective excitations in this medium in transmission. This is used for extending earlier observations of coherent population trapping [PRL 95, 187405 (2005)] to a direct demonstration of electromagnetically induced transparency. However, this requires a long electron spin coherence time, which is hindered by nuclear spin fluctuations. We use the optical control to drive dynamic nuclear polarization effects, which result in stable configurations of the electron-nuclear spin system that are homogeneous over the electron ensemble.   

Electron Shot Noise and Nuclear Spin Dynamics in Spin-Blockaded Quantum Dots

In the spin-blockade regime of double quantum dots [1], electron transport through the system constitutes a purely electrical means of probing and manipulating the dynamics of nuclear spins. Intense interest in this system as a platform to study spin coherence and many-body dynamics has spawned a wide range of experiments [2], which have revealed many complex dynamical phenomena. Here we identify a fundamental process in which nuclear spin dynamics can be driven by electron shot noise; fast electric current fluctuations generate much slower nuclear polarization dynamics, which in turn affect electron dynamics via the Overhauser field. The resulting extremely slow current fluctuations account for a variety of observed phenomena that were not previously understood. We propose a simple model for the coupled dynamics of electron and nuclear spins that captures much of the essential physics behind these experiments and validate the model by comparison with experimental data. [1] K. Ono et al. Science 297, 1313 (2002). [2] R. Hanson et al., Rev. Mod. Phys. 79, 1217 (2007).   

Optical Polarization of Nuclei in Bulk and Nanocrystalline Diamond

We present new results on the hyperpolarization of $^{13}$C nuclear spins in diamond through optically-oriented nitrogen vacancy (NV-) defects. Optical illumination of high NV- concentration diamonds at cryogenic temperatures and 9.4 Tesla results in a negative nuclear spin temperature with measured bulk-average polarization over 5$\%$, although local polarization may be higher. The negative spin-temperature is attributed to a population inversion within the dipolar energy levels of the NV- spin ensemble. In our quantitative model, nuclei near defects equilibrate with the NV- dipolar energy reservoir and polarization is transported to the bulk material via spin diffusion. We also investigate the nuclear hyperpolarization of NV- containing diamond nanocrystals. Such materials may be useful for surface transfer of polarization to target molecules for enhanced NMR sensitivity. Additionally, we investigate the dynamics and decoherence of the hyperpolarized nuclear spin ensemble and its interaction with electronic defect spins. Such phenomena are of fundamental interest to the use of diamond for quantum information applications.