Session X29: Focus Session: Semiconductor Qubits - Managing or Eliminating Nuclei

Ultrafast optical coherent control of individual electron and hole spins in a semiconductor quantum dot

We report on the complete optical coherent control of individual electron and hole spin qubits in InAs quantum dots. With a magnetic field in Voigt geometry, broadband, detuned optical pulses couple the spin-split ground states, resulting in Rabi flopping. In combination with the Larmor precession around the external magnetic field, this allows an arbitrary single-qubit operation to be realized in less than 20 picoseconds [1,2]. Slow fluctuations in the spin's environment lead to shot-to-shot variations in the Larmor precession frequency. In a time-ensemble measurement, these would prevent a measurement of the true decoherence of the qubit, and instead give rise to ensemble dephasing. This effect was overcome by implementing a spin echo measurement scheme for both electron and hole spins, where an optical $\pi $-pulse refocuses the spin coherence and filters out the slow variations in Larmor precession frequency. We measured coherence times up to 3 microseconds [2,3]. Finally, our optical pulse manipulation scheme allows us to probe the hyperfine interaction between the single spin and the nuclei in the quantum dot. Interesting non-Markovian dynamics could be observed in the free-induction decay of a single electron spin, whereas the complete absence of such effects illustrates the reduction of the hyperfine interaction for hole spin qubits. We measured and modeled these effects, and explain the non-Markovian electron spin dynamics as involving a feedback effect resulting from both the strong Overhauser shift of the electron spin and spin dependent nuclear relaxation [2,4]. \\[4pt] [1] D. Press, T. D. Ladd, B. Zhang and Y. Yamamoto, Nature \textbf{456}, 218 (2008)\\[0pt] [2] K. De Greve, P. McMahon, D. Press \textit{et al.}, Nat. Phys. \textbf{7}, 872 (2011)\\[0pt] [3] D. Press, K. De Greve, P. McMahon \textit{et al.}, Nat. Phot. \textbf{4}, 367 (2010)\\[0pt] [4] T. D. Ladd, D. Press, K. De Greve \textit{et al.}, Phys. Rev. Lett. 105, 107401 (2010)   

Ultrafast optical control of interacting hole spins in coupled quantum dots

Recently, hole spins in quantum dots (QDs) have shown great promise as quantum bits due to a reduced hyperfine interaction with nuclear spins, the primary source of decoherence for electron spins. We have developed a system of two vertically stacked InAs QDs that can be charged with a number of holes. In this way, an isolated hole in one QD or two interacting holes in separate dots can be studied. We demonstrate ultrafast optical control of both systems and find a number of differences compared to electron spins. Complete control of the single hole qubit is obtained through optical initialization and single qubit rotations. These control measurements give a hole spin T$_{2}^{\ast }$ of 20ns, an order of magnitude longer than electrons in similar QDs. Spin echo experiments extend the coherence time but are complicated by oscillations in the echo amplitude. For the case of two hole spins, we can observe and tune the coherent exchange interaction that acts as a two qubit gate. We also initialize and perform gates on an entangled spin state, taking a significant step toward a scalable platform for quantum information processing. [1] ``Optical control of one and two hole spins in interacting quantum dots,'' A. Greilich, S. G. Carter, D. Kim, A. S. Bracker and D. Gammon. \textit{Nature Photon.}\textbf{5}, 702 (2011).   

Electrical control of single hole spins in InSb nanowire quantum dots

The spin-orbit interaction provides an efficient handle for all-electric control of individual spins in quantum dots. Recently, III-V semiconductor nanowires, which have a strong spin-orbit coupling, have emerged as a promising platform for spin-based qubits. Previous work has been focused on the electrical control of electron spins in InAs nanowires. In contrast, spin-dependent quantum transport with holes has so far remained largely unexplored. Here, we demonstrate gate tuning from the few-electron double dot to the few-hole double-dot regimes in InSb nanowires and observe Pauli spin-blockade for both electrons and holes. We use electric-dipole spin resonance (EDSR) to determine the effective g-factors of the two types of carriers. EDSR control over the hole spins is promising for driving coherent rotations of hole-spin qubits. These hole qubits are expected to be less sensitive to hyperfine-mediated decoherence effects than electron-spin qubits as a result of the p-wave symmetry of the hole wavefunction.   

Theory of heavy-hole spin-echo decay

Heavy-hole spin states have emerged as a robust new candidate for realizing a qubit. Nevertheless, the coupling of the hole spin to nuclei in the surrounding medium likely limits hole-spin coherence and has, until very recently, been overlooked. We describe the real-time spin decoherence of a heavy-hole in a semiconductor quantum dot, subject to spin echo pulses. We obtain an analytical expression which we compute numerically for an experimentally realistic number ($\sim 10^4$) of nuclear spins. Including the (previously neglected) nuclear Zeeman term in the Hamiltonian, we observe novel effects uniquely characterizing the decoherence mechanisms under study. In particular, we find a nontrivial dependence of the decay on the applied magnetic field, as well as novel predictions for motional narrowing and envelope modulation, which could significantly extend the hole-spin memory time in near-future experiments.   

High Quality Two-Dimensional Electron Gases (2DEGs) in Isotopically-Enriched Strained Silicon

Silicon quantum dots (QDs) formed in a Si/SiGe two-dimensional electron gas (2DEG) are a promising candidate for quantum computation. To capture a single electron in a QD, the dot must be very small, which requires a short distance from the surface to Si 2DEG layer for fine gating. Here we demonstrate a high quality modulation-doped Si 2DEG grown by chemical vapor deposition (CVD), with a distance of 65 nm from the surface to 2DEG layer. The electron mobility at 0.3K of 504,000 cm$^{2}$/V-s (density 4.3 x 10$^{11}$ cm$^{-2})$ is the highest yet reported by CVD for ungated Si 2DEGs. Further, a Si 2DEG layer consists of isotopically-enriched $^{28}$Si to minimize spin decoherence due to $^{29}$Si. SIMS results show that in the Si 2DEG layer, $^{28}$Si is enriched from natural abundance of 92.2{\%} to 99.8{\%} with $^{29}$Si reduced from 4.7{\%} to an upper limit of $\sim $ 0.24{\%} and $^{30}$Si reduced from 3.1{\%} to $\sim $ 63ppm. Finally, effective Schottky gating requires a sharp turn-off slope in phosphorus from the doped layer to the surface for low electric fields near the surface. We have achieved ultra-sharp turn-off slope of $\sim $16 nm/dec, and demonstrate Schottky gating to fully deplete the 2DEG with extremely low leakage current.   

Implanted bismuth donors in 28-Si: Process development and electron spin resonance measurements

Spins of donor atoms in silicon are excellent qubit candidates. Isotope engineered substrates provide a nuclear spin free host environment, resulting in long spin coherence times [1,2]. The capability of swapping quantum information between electron and nuclear spins can enable quantum communication and gate operation via the electron spin and quantum memory via the nuclear spin [2]. Spin properties of donor qubit candidates in silicon have been studied mostly for phosphorous and antimony [1-3]. Bismuth donors in silicon exhibit a zero field splitting of 7.4 GHz and have attracted attention as potential nuclear spin memory and spin qubit candidates [4,5] that could be coupled to superconducting resonators [4,6]. We report on progress in the formation of bismuth doped 28-Si epi layers by ion implantation, electrical dopant activation and their study via pulsed electron spin resonance measurements showing narrow linewidths and good coherence times. \\[4pt] [1] A. M. Tyryshkin, et al. arXiv: 1105.3772 [2] J. J. L. Morton, et al. Nature (2008) [3] T. Schenkel, et al APL 2006; F. R. Bradbury, et al. PRL (2006) [4] R. E. George, et al. PRL (2010) [5] G. W. Morley, et al. Nat Mat (2010) [6] M. Hatridge, et al. PRB (2011), R. Vijay, et al. APL (2010) This work was supported by NSA (100000080295) and DOE (DE-AC02-05CH11231).   

Isotopic enrichment and growth of material for quantum coherent devices

We demonstrate isotopic enrichment and growth of highly pure materials in support of quantum coherent devices. Efforts to produce devices capable of quantum computation rely on long coherence times of the electron or nuclear spin being used. Impurities with nuclear spin are a major cause of decoherence in such systems, and their elimination is essential towards longer T$_{2}$ realization. The produced material must be isotopically enriched as well as chemically pure and defect free, and we present an alternative method for achieving these goals. Unenriched material is ionized and filtered using a mass selecting magnet and then epitaxially deposited. As an initial check on enrichment, $^{22}$Ne is implanted into Si demonstrating an isotopic selectivity over 1800:1 which extrapolates to a $^{28}$Si enrichment better than 99.994{\%}. In progression towards Si deposition from a silane precursor, methane is used as an analog to grow enriched $^{13}$C on semiconductor grade silicon. Analysis of this material by SIMS and ESR as a check on estimated levels of isotopic and chemical purity is presented.   

Realization of a double quantum dot in an isotopically purified $^{28}$Si 2DES

The Si/SiGe material system shows great promise for the realization of electron spin qubits due to the weak hyperfine interaction in natural silicon [2]. The electron spin coherence time is expected to further increase for spins embedded in a nuclear spin-refined $^{28}$Si host crystal. In this contribution, we report on the realization and characterization of a 2DES in a MBE grown hybrid $^{28}$Si/SiGe heterostructure with a record mobility of $5.5\cdot10^4 cm^2/Vs$ at an electron density of $3\cdot10^{11}/cm^2$ in which the electron-nuclear spin overlap is greatly suppressed [1]. Based on this heterostructure, we present the first double quantum dot device in isotopically purified silicon. Our device can be operated down to the few electron regime and by using an additional global topgate above the quantum dot gates, the overall charge noise performance can be optimized significantly. This recent progress is fundamental for further experiments towards e.g. measurements of spin relaxation times in $^{28}$Si. \\[4pt] [1] J. Sailer et al., Phys. status solidi RRL 3, 61 (2009)\\[0pt] [2] A. Wild et al., New J. Phys. 12, 113019 (2010)   

Deterministic preparation of Dicke states of donor nuclear spins in silicon

We present a scheme to deterministically prepare various symmetric and asymmetric Dicke states for donor nuclear spins in silicon. The state preparation is realized by cooperative pumping of nuclear spins by coupled donor electrons, and the required controls are in situ to the prototype Kane's architecture for quantum computation. This scheme only requires a sub-gigahertz donor exchange coupling which can be achieved without atomically precise donor placement, hence it could be a practical way to prepare multipartite entanglement of spins in silicon with current technology. All desired Dicke states appear as the steady state under various pumping scenarios and therefore the preparation is robust and does not require accurate temporal controls. Numerical simulations with realistic parameters show that Dicke states of 10 - 20 qubits can be prepared with high fidelity in the presence of decoherence and undesired dynamics.   

Optical Patterning of Nuclear Polarization in Gallium Arsenide

Large enhancements of nuclear spin polarization can quench weak electron-nuclear fluctuations, mitigate electron spin decoherence, and provide control of electron spins in devices for quantum information processing. Such enhancements might include spatially patterned regions of polarized nuclei so as to prepare a spatially-dependent effective Zeeman field acting on electron spins as well as coherently manipulate the spin state of drifting electrons. By exploiting two competing mechanisms for optical nuclear polarization in semi-insulating GaAs, we use high field stray-field NMR imaging to demonstrate all-optical creation of three-dimensional patterns of positive and negative nuclear polarization without the need for ferromagnets or lithographic patterning techniques. These patterns may be controlled on the micron length scale.   

Integrating MREV and XYXY Pulse Sequences to Decouple Dipolar Interactions in ESR Experiments

Dynamical decoupling (DD) techniques employ a series of strong refocusing pulses to combat decoherence in quantum systems. A great number of the new improved DD sequences have been designed recently aiming to decouple from a specific kind of decohering noise, arising in the direction of an externally applied quantizing field. MREV-type pulse sequences have long been used in NMR community to decouple spins from another source of decoherence - the dipolar interactions between like spins. Here, we report on our experience while using MREV sequences in ESR experiments on donors in silicon. We find MREV sequences to be very sensitive to even small instrumental errors in the applied pulses. The errors accumulate upon repeating the MREV pulse sequence, destroying the coherenence instead of protecting it. A possible solution to this pulse error problem is found by integrating an MREV pulse sequence with a self-correcting XYXY sequence. The new MREV-XYXY sequence appears to satisfy all the requirements of a ``good'' DD sequence: (1) providing a protection to an arbitrary coherent state with good fidelity (at least 95\% after more than 17,000 pulses), (2) decoupling from dipolar interactions of like spins, and (3) cancelling the phase noise arising from fluctuations in the magnetic field.   

Master equation approach to the central spin decoherence problem

The electron-nuclear hyperfine interaction is the leading source of decoherence for electron spin qubits in III-V semiconductor quantum dots. For sufficiently low external B-field, the dynamics is purely hyperfine-induced. Generalized master equations embody an attractive approach to this problem due to strong analytical control, but so far they have only been applied in the case of high magnetic fields where a standard perturbative treatment is reliable. In the low field regime where pure hyperfine effects are measurable, this standard treatment breaks down. We show how to overcome this problem by first arguing that the detailed shape of the electron wavefunction is irrelevant for the electron spin decoherence at low B-fields. We then employ a powerful technique involving so-called correlated projection operators to vastly improve the convergence of the perturbative master equation approach by taking advantage of the symmetries that arise when the electron wavefunction is coarse-grained. This brings the low B-field regime into the scope of the master equation description, paving the way for the development of a well-controlled theory of pure hyperfine decoherence that is relevant for current experiments. [E. Barnes, L. Cywinski, S. Das Sarma, Phys. Rev. B 84, 155315 (2011)]   

Two-electron-spin dephasing due to hyperfine interaction in a GaAs double dot

We study hyperfine interaction induced pure dephasing of two electron spin states in a GaAs double quantum dot. We construct the effective pure dephasing Hamiltonian for the two electron spins, and apply the ring-diagram theory [1] to calculate the decoherence function of the double dot two-spin system. With a finite exchange coupling, singlet and triplet states are the electron spin eigenstates, and we focus on the dephasing between the singlet state S and the unpolarized triplet state T$_{0}$. We find that the effective Overhauser fields for these two states are suppressed because of their state symmetries, leading to weaker effective coupling between the nuclear spins. On the other hand, the weaker Overhauser field also allows more nuclear spins to flip-flop with each other. We show that these competing effects lead to interesting two-spin decoherence dynamics. We calculate the coherence decay as functions of the external field, the exchange splitting, and the quantum dot size, and compare our results with those for a single spin and for two uncorrelated spins. [1] L. Cywinski, W. Witzel, and S. Das Sarma, Phys. Rev. B 79, 245314 (2009).