Session T36: Focus Session: Semiconductor Qubits: Magnetic Control & Nuclear Dynamics

Spin measurement in an undoped Si/SiGe double quantum dot incorporating a micromagnet

We present measurements on a double dot formed in an accumulation-mode undoped Si/SiGe heterostructure. The double dot incorporates a proximal micromagnet to generate a stable magnetic field difference between the quantum dots. The gate design incorporates two layers of gates, and the upper layer of gates is split into five different sections to decrease crosstalk between different gates. A novel pattern of the lower layer gates enhances the tunability of tunnel rates. We will describe our attempts to create a singlet-triplet qubit in this device. This work was supported in part by ARO(W911NF-12-0607), NSF(DMR-1206915), and the United States Department of Defense. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressly or implied, of the US Government.   

Single-spin manipulation via exchange interaction in a double quantum dot with micromagnet

The manipulation of single spins in double quantum dots by making use of the exchange interaction and a highly inhomogenous magnetic field was discussed in W. A. Coish and D. Loss, Phys. Rev. B 75, 161302 (2007). Given that such large inhomogeneity of the magnetic field is difficult to achieve, we examine an analogous scheme applicable to current double quantum dot setups in the presence of the stray field of a neighboring micromagnet. We estimate typical gate times realized at the singlet-triplet anticrossing induced by the micromagnet field, and discuss the optimization of the single-spin gates through suitable pulse shapes and orientation of the micromagnet magnetization. We also examine the effect of several decoherence sources, as in particular the Overhauser field induced by nuclear spins and charge noise from the electric gates, and characterize the corresponding decay of the Rabi oscillations. Our results suggest that this scheme is a promising approach for the realization of fast single-spin operations.   

Strongly excited electric dipole spin resonance with field gradient

Coherent manipulation of the qubit is the essential part of the quantum information processing. Traditionally, spin manipulation is realized by electron spin resonance, where time-dependent transverse magnetic field of frequency close to the Zeeman energy by the external static magnetic field. The idea of electric dipole spin resonance, which uses oscillating electric field, instead of magnetic field, had been proposed. Electron spin dipole itself is independent of the electric field, while the charge (orbital) degree of freedom in a quantum dot (QD) is efficiently coupled to it. With the gradient of the static magnetic field coupling the orbital degree with the spin, the spin can be manipulated. Rabi frequency characterizes the driving speed of the spin, which is usually regarded as linearly proportional to the electric field amplitude. We had studied the Rabi frequency in two models. One is that the orbital state is also two-level system [1], which may be corresponding to the lowest levels in the coupled QDs. The other is that the electron is in anharmonic potential. In both cases, we predict a clear deviation of the Rabi frequency from the linear dependence for large electric field.\\[4pt] [1] Y. Tokura T. Kubo, and W. J. Munro, to appear in J. Phys. Soc. Jpn. (arXiv: 1308.0071).   

Control and coherence of Loss-DiVincenzo qubits in Si/SiGe quantum dots

Electron spins in Si/SiGe quantum dots are one of the most promising candidates for a quantum~bit~for their potential to scale up and their long dephasing time. We report for the first time the experimental realization of single electron spin rotations in a single quantum dot (QD) defined in a Si/SiGe 2D electron gas. The electron spin is read out in single-shot mode by a QD charge sensor. Spin rotations are achieved by applying microwave excitation to one of the gates, which oscillates the electron wave function back and forth in the gradient field produced by cobalt micro-magnets fabricated near the dot. By measuring the electron spin resonance frequency as a function of the external magnetic field, the electron g-factor of 1.994 $\pm$ 0.007 is determined. A dephasing time of T2*$=$850 ns, about 20 times longer than that in GaAs quantum dots, is extracted from the linewidth of the electron spin resonance peak. We observe spin Rabi oscillations with Rabi frequencies up to 5 MHz. Because the coherence time can be longer than the spin manipulation time, we are able to rotate the electron spin even when detuned in frequency, giving the typical chevron pattern when sweeping detuning and microwave burst time. We also realized Ramsey interference experiments, giving a free induction decay T2* $=$ 800 ns. Looking closely, all these data exhibit interference patterns resulting from the contribution of two resonances separated by a frequency difference $\Delta $f $=$2-4 MHz. We tentatively interpret these two resonances as intra-valley spin resonance for two different valley states. Due to the valley-orbit mixing, the orbital wavefunction of each valley state is slightly different, which yields a different Zeeman splitting for each valley state. Finally, we perform Hahn-echo measurement and deduce, for the first time in Si/SiGe, a single spin T2$=$37$\mu $s.\\[4pt] This work has been done in collaboration with E. Kawakami, Kavli Institute of Nanoscience, TU Delft, Lorentzweg 1, 2628 CJ Delft, The Netherlands; D. Ward, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA; F.R. Braakman, Kavli Institute of Nanoscience, TU Delft; D. E. Savage, M. G. Lagally, S.N. Coppersmith, M. A. Eriksson, University of Wisconsin-Madison; and L. M. K. Vandersypen, Kavli Institute of Nanoscience, TU Delft.   

Spin-orbit effects on nuclear state preparation at the $S-T_{+}$ anti-crossing in double quantum dots

We explore the interplay of spin-orbit and hyperfine effects on the nuclear preparation schemes in two-electron double quantum dots, e.g. in GaAs. The quantity of utmost interest is the electron spin decoherence time $T_{2}^{*}$ in dependence of the number of sweeps through the electron spin singlet $S$ triplet $T_{+}$ anti-crossing. Decoherence of the electron spin is caused by the difference field induced by the nuclear spins. We study the case where a singlet $S(2,0)$ is initialized, in which both electrons are in the left dot. Subsequently, the system is driven repeatedly through the anti-crossing and back using linear electrical bias sweeps. Our model describes the passage through the anti-crossing with a large number of equally spaced, step-like parameter increments. We develop a numerical method describing the nuclear spins fully quantum mechanically, which allows us to track their dynamics. Both Rashba and Dresselhaus spin-orbit terms do depend on the angle $\theta$ between the $[110]$ crystallographic and the inter-dot axis. Our results show that the suppression of decoherence (and therefore the enhancement of $T_{2}^{*}$) is inversely proportional to the strength of the spin-orbit interaction, which is tuned by varying the angle $\theta$.   

Nuclear spin dynamics and spin orbit effects in Landau-Zener sweep correlations at the S-$\mathrm{T_+}$ Transition

In GaAs-based double quantum dot spin qubits, nuclear spins have been used for qubit control, but are also an important source of decoherence. The S and $\mathrm{T_+}$ levels exhibit a small avoided crossing as a function of detuning. It has been used for S-$\mathrm{T_+}$ qubit control and for dynamic nuclear polarization (DNP). The transition matrix element contains the nuclear Overhauser fields perpendicular to the external B-field and spin-orbit coupling. We show, both theoretically and experimentally, that nuclear spin dynamics can be seen in the temporal correlation of single-shot measurements after Landau-Zener sweeps across this transition. A semi-classical model of the nuclear spins is sufficient. The dynamics consist of the relative Larmor precession of the three GaAs nuclear spin species in the external B-field and dephasing of the oscillations due to local field fluctuations. Theoretically, it is expected that the absolute Larmor precessions also become visible in the presence of spin-orbit coupling. This can be used to qualitatively and quantitatively observe spin-orbit coupling and to distinguish it from the nuclear spin contribution. Understanding these dynamics is relevant for the fidelity of S-$\mathrm{T_+}$ qubit operations and the effectiveness of DNP.   

Mechanisms of $S-T_+$ coupling in singlet-triplet qubits

Semiconductor quantum dots provide a unique environment for studying a variety of problems, from few-particle systems to the central spin problem. Investigating these systems furthers our understanding of fundamental physics and advances efforts to achieve semiconductor spin-based quantum information processing. We study two electron spins in a semiconducting double quantum dot and measure the spin singlet to $m_s=1$ triplet ($S-T_+$) avoided crossing. Our results suggest that several processes, including the hyperfine interaction between the electrons and the host nuclei and spin-orbit coupling in the quantum dots, compete to drive the $S-T_+$ transition. This work gives insight into the poorly understood nuclear dynamics in these systems and provides a path forward for improving nuclear pumping efficiency and therefore coherence times in semiconducting spin qubits.   

Precise Measurement of Nuclear Magnetic Fields with Gallium Arsenide Spin Qubits

Qubits that can be easily initialized and read out hold promise both for metrology and for quantum information processing. In particular, spin qubits in semiconductor quantum dots are able probe their rich magnetic and electric environment and study spin and charge dynamics in semiconductors. In this talk, we present measurements using a singlet-triplet (S-T$_{\mathrm{0}})$ qubit in a gallium arsenide double quantum dot to measure the nuclear magnetic field gradient surrounding it. This nuclear bath has slow dynamics compared to the timescale of qubit operations and measurement, so precise sensing of nuclear fields can be done with repeated projective measurement. We compare three techniques for rapidly estimating the nuclear gradient, and verify it to within 1 MHz in 800 us of real time for the best performing scheme. This level of precision offers the prospect of performing real-time monitoring of the nuclear gradient, which could both yield insight into quantum many-body problems such as nuclear spin diffusion and be used to drive the qubit adaptively in a way that is insensitive to nuclear noise.   

Suppression of Dephasing using Real Time Environmental Monitoring

Electron spins in semiconductor quantum dots are promising candidates for the building blocks of a quantum information processor due to their potential for scalability and miniaturization. However, interactions between the electrons and a fluctuating nuclear bath cause these qubits to dephase in tens of nanoseconds. These ill effects can be partially mitigated by nuclear programming or dynamical decoupling; however, these techniques are limited by nuclear pumping efficiency and the complexity of decoupled sequences. Here we present a new scheme that stabilizes the qubit by exploiting the slow nuclear dynamics. The qubit measures the size of the nuclear splitting, which is used in real time to feed back on the control of the qubit. We employ this technique on a singlet-triplet qubit operated in the rotating frame in a regime where it is sensitive to fluctuating nuclear magnetic fields, and we show that this feedback increases qubit coherence times. This feedback is distinct from schemes that constantly monitor a qubit through weak measurement and can improve arbitrary qubit operations in all qubits that suffer dephasing from slow environmental fluctuations, including all spin qubits.   

Quantum limit for nuclear spin polarization in semiconductor quantum dots

One of main sources of decoherence for spin qubits confined in semiconductor quantum dots comes from hyperfine interaction of the electron spin with the nuclear spins. By polarizing the nuclear spins to 100\% it is possible to extend coherence times. A recent experiment [E. A. Chekhovich \emph{et al.}, Phys. Rev. Lett. \textbf{104}, 066804 (2010)] has demonstrated that high nuclear spin polarization can be achieved in self-assembled quantum dots by exploiting an optically forbidden transition between a heavy hole and a trion state. However, a fully polarized state is not obtained as expected from a classical rate equation. We theoretically investigate this problem with the help of a quantum master equation and we demonstrate that a fully polarized state cannot be reached due to formation of a nuclear dark state. We also show that the maximal degree of polarization depends on the form of the electron envelope wave function inside of the quantum dot.   

Feedback control of nuclear spin bath for a single hole spin in a quantum dot

In a semiconductor quantum dot, the nuclear spin bath plays an important role as the ultimate environment of an electron or hole spin at low temperature. Through dynamic nuclear spin polarization driven by an oscillating electric field, we show that feedback controls can be implemented on the nuclear spin bath of a single hole spin. The feedback controls utilize the anisotropic hyperfine interaction between the hole spin and the nuclear spins. The negative feedback can suppress the statistical fluctuations of the nuclear hyperfine field and lead to longer coherence time of the hole spin. Positive feedback can possibly lead to cat like state of nuclear spin bath. The efficiency of the controls schemes is investigated under different parameters and control strategies.   

Optical nuclear spin polarization in the presence of heavy hole hyperfine interactions

In self-assembled quantum dots, the form of the effective hyperfine Hamiltonian for heavy holes states is still under debate. The first theories suggested an Ising-like type of interaction with a strength on the order of 10\% of the one of the electron and with opposite sign. Consequently, flip-flop terms similar to those of the electronic hyperfine Hamiltonian are very weak and do not provide an efficient mechanism for exchange of angular momentum. However, due to band mixing, matrix elements of the hyperfine Hamiltonian taken with the same effective heavy hole state are non-zero and can lead to transitions in the nuclear spin state. Here, we propose an experiment aiming at detecting and simultaneously cancel the effective hyperfine heavy hole non-collinear interaction. Although its relative strength is in average three orders of magnitude smaller than the electronic hyperfine coupling constant, the effective non-collinear interaction is efficient at polarizing nuclear spins. Our results force a complete reinterpretation of experiments dealing with nuclear spins in optically active quantum dots.