Coherent operations and screening in multielectron spin qubits.

Multielectron spin qubits are demonstrated, and performance examined by comparing coherent exchange oscillations in coupled single-electron and multielectron quantum dots, measured in the same device. Fast (>1 GHz) exchange oscillations with a quality factor Q∼15 are found for the multielectron case, compared to Q∼2 for the single-electron case, the latter consistent with experiments in the literature. A model of dephasing that includes voltage and hyperfine noise is developed that is in good agreement with both single- and multielectron data, though in both cases additional exchange-independent dephasing is needed to obtain quantitative agreement across a broad parameter range.

Scaling of dynamical decoupling for spin qubits.

We investigate the scaling of coherence time T(2) with the number of π pulses n(π) in a singlet-triplet spin qubit using Carr-Purcell-Meiboom-Gill (CPMG) and concatenated dynamical decoupling (CDD) pulse sequences. For an even numbers of CPMG pulses, we find a power law T(2) is proportional to (n(π))(γ(e)), with γ(e)=0.72±0.01, essentially independent of the envelope function used to extract T(2). From this surprisingly robust value, a power-law model of the noise spectrum of the environment, S(ω)~ω(-ß), yields ß=γ(e)/(1-γ(e))=2.6±0.1. Model values for T(2)(n(π)) using ß=2.6 for CPMG with both even and odd n(π) up to 32 and CDD orders 3 through 6 compare very well with the experiment.

Charge-state conditional operation of a spin qubit.

We report coherent operation of a singlet-triplet qubit controlled by the spatial arrangement of two confined electrons in an adjacent double quantum dot that is electrostatically coupled to the qubit. This four-dot system is the specific device geometry needed for two-qubit operations of a two-electron spin qubit. We extract the strength of the capacitive coupling between qubit and adjacent double quantum dot and show that the present geometry allows fast conditional gate operation, opening pathways toward implementation of a universal set of gates for singlet-triplet spin qubits.

Exchange control of nuclear spin diffusion in a double quantum dot.

The influence of gate-controlled two-electron exchange on the relaxation of nuclear polarization in small ensembles (N∼10(6)) of nuclear spins is examined in a GaAs double quantum dot system. Waiting in the (2,0) charge configuration, which has large exchange splitting, reduces the nuclear diffusion rate compared to that of the (1,1) configuration. Matching exchange to Zeeman splitting significantly increases the nuclear diffusion rate.

Interlaced dynamical decoupling and coherent operation of a singlet-triplet qubit.

We experimentally demonstrate coherence recovery of singlet-triplet superpositions by interlacing qubit rotations between Carr-Purcell (CP) echo sequences. We then compare the performance of Hahn, CP, concatenated dynamical decoupling (CDD), and Uhrig dynamical decoupling for singlet recovery. In the present case, where gate noise and drift combined with spatially varying hyperfine coupling contribute significantly to dephasing, and pulses have limited bandwidth, CP and CDD yield comparable results, with T(2)∼80 µs.

Rapid single-shot measurement of a singlet-triplet qubit.

We report repeated single-shot measurements of the two-electron spin state in a GaAs double quantum dot. The readout allows measurement with a fidelity above 90% with a approximately 7 micros cycle time. Hyperfine-induced precession between singlet and triplet states of the two-electron system are directly observed, as nuclear Overhauser fields are quasistatic on the time scale of the measurement cycle. Repeated measurements on millisecond to second time scales reveal the evolution of the nuclear environment.

Measurement of temporal correlations of the overhauser field in a double quantum dot.

In quantum dots made from materials with nonzero nuclear spins, hyperfine coupling creates a fluctuating effective Zeeman field (Overhauser field) felt by electrons, which can be a dominant source of spin qubit decoherence. We characterize the spectral properties of the fluctuating Overhauser field in a GaAs double quantum dot by measuring correlation functions and power spectra of the rate of singlet-triplet mixing of two separated electrons. Away from zero field, spectral weight is concentrated below 10 Hz, with approximately 1/f2 dependence on frequency f. This is consistent with a model of nuclear spin diffusion, and indicates that decoherence can be largely suppressed by echo techniques.

Suppressing spin qubit dephasing by nuclear state preparation.

Coherent spin states in semiconductor quantum dots offer promise as electrically controllable quantum bits (qubits) with scalable fabrication. For few-electron quantum dots made from gallium arsenide (GaAs), fluctuating nuclear spins in the host lattice are the dominant source of spin decoherence. We report a method of preparing the nuclear spin environment that suppresses the relevant component of nuclear spin fluctuations below its equilibrium value by a factor of approximately 70, extending the inhomogeneous dephasing time for the two-electron spin state beyond 1 microsecond. The nuclear state can be readily prepared by electrical gate manipulation and persists for more than 10 seconds.

Electrical control of spin relaxation in a quantum dot.

We demonstrate electrical control of the spin relaxation time T1 between Zeeman-split spin states of a single electron in a lateral quantum dot. We find that relaxation is mediated by the spin-orbit interaction, and by manipulating the orbital states of the dot using gate voltages we vary the relaxation rate W identical withT1(-1) by over an order of magnitude. The dependence of W on orbital confinement agrees with theoretical predictions, and from these data we extract the spin-orbit length. We also measure the dependence of W on the magnetic field and demonstrate that spin-orbit mediated coupling to phonons is the dominant relaxation mechanism down to 1 T, where T1 exceeds 1 s.

Dynamic nuclear polarization with single electron spins.

We polarize nuclear spins in a GaAs double quantum dot by controlling two-electron spin states near the anticrossing of the singlet (S) and m(S)= +1 triplet (T+) using pulsed gates. An initialized S state is cyclically brought into resonance with the T+ state, where hyperfine fields drive rapid rotations between S and T+, "flipping" an electron spin and "flopping" a nuclear spin. The resulting Overhauser field approaches 80 mT, in agreement with a simple rate-equation model. A self-limiting pulse sequence is developed that allows the steady-state nuclear polarization to be set using a gate voltage.

Noise correlations in a Coulomb-blockaded quantum dot.

We report measurements of current noise auto- and cross correlation in a tunable quantum dot with two or three leads. As the Coulomb blockade is lifted at finite source-drain bias, the autocorrelation evolves from super- to sub-Poissonian in the two-lead case, and the cross correlation evolves from positive to negative in the three-lead case, consistent with transport through multiple levels. Cross correlations in the three-lead dot are found to be proportional to the noise in excess of the Poissonian value in the limit of weak output tunneling.

Energy-dependent tunneling in a quantum dot.

We present measurements of the rates for an electron to tunnel on and off a quantum dot, obtained using a quantum point contact charge sensor. The tunnel rates show exponential dependence on drain-source bias and plunger gate voltages. The tunneling process is shown to be elastic, and a model describing tunneling in terms of the dot energy relative to the height of the tunnel barrier quantitatively describes the measurements.

Tunable noise cross correlations in a double quantum dot.

We report measurements of the cross correlation between temporal current fluctuations in two capacitively coupled quantum dots in the Coulomb blockade regime. The sign of the cross-spectral density is found to be tunable by gate voltage and source-drain bias. We find good agreement with the data by including an interdot Coulomb interaction in a sequential-tunneling model.

Hyperfine-mediated gate-driven electron spin resonance.

An all-electrical spin resonance effect in a GaAs few-electron double quantum dot is investigated experimentally and theoretically. The magnetic field dependence and absence of associated Rabi oscillations are consistent with a novel hyperfine mechanism. The resonant frequency is sensitive to the instantaneous hyperfine effective field, and the effect can be used to detect and create sizable nuclear polarizations. A device incorporating a micromagnet exhibits a magnetic field difference between dots, allowing electrons in either dot to be addressed selectively.

Effect of exchange interaction on spin dephasing in a double quantum dot.

We measure singlet-triplet dephasing in a two-electron double quantum dot in the presence of an exchange interaction which can be electrically tuned from much smaller to much larger than the hyperfine energy. Saturation of dephasing and damped oscillations of the spin correlator as a function of time are observed when the two interaction strengths are comparable. Both features of the data are compared with predictions from a quasistatic model of the hyperfine field.

Asymmetry of nonlinear transport and electron interactions in quantum dots.

The symmetry properties of transport beyond the linear regime in chaotic quantum dots are investigated experimentally. A component of differential conductance that is antisymmetric in both applied source-drain bias V and magnetic field B, absent in linear transport, is found to exhibit mesoscopic fluctuations around a zero average. Typical values of this component allow a measurement of the electron interaction strength.

Resonant-optical-cavity photoconductive switch with 0.5% conversion efficiency and 1.0 W peak power.

We report a new photoconductive switch having an average output power of 44 microW, an instantaneous bandwidth of approximately 300 GHz, an output pulse width of approximately 2.2 ps, a peak output power of approximately 1.0 W, and an optical-to-electrical conversion efficiency of approximately 0.5% when pumped by a palm-sized mode-locked free-space laser at lambda=780.6 nm with an average power of 8.7 mW and an optical pulse width of approximately -230 fs. The switch is made from an ErAs:GaAs epitaxial layer inside a resonant optical cavity and coupled to a planar three-turn square spiral antenna.

Coherent manipulation of coupled electron spins in semiconductor quantum dots.

We demonstrated coherent control of a quantum two-level system based on two-electron spin states in a double quantum dot, allowing state preparation, coherent manipulation, and projective readout. These techniques are based on rapid electrical control of the exchange interaction. Separating and later recombining a singlet spin state provided a measurement of the spin dephasing time, T2*, of approximately 10 nanoseconds, limited by hyperfine interactions with the gallium arsenide host nuclei. Rabi oscillations of two-electron spin states were demonstrated, and spin-echo pulse sequences were used to suppress hyperfine-induced dephasing. Using these quantum control techniques, a coherence time for two-electron spin states exceeding 1 microsecond was observed.

Triplet-singlet spin relaxation via nuclei in a double quantum dot.

The spin of a confined electron, when oriented originally in some direction, will lose memory of that orientation after some time. Physical mechanisms leading to this relaxation of spin memory typically involve either coupling of the electron spin to its orbital motion or to nuclear spins. Relaxation of confined electron spin has been previously measured only for Zeeman or exchange split spin states, where spin-orbit effects dominate relaxation; spin flips due to nuclei have been observed in optical spectroscopy studies. Using an isolated GaAs double quantum dot defined by electrostatic gates and direct time domain measurements, we investigate in detail spin relaxation for arbitrary splitting of spin states. Here we show that electron spin flips are dominated by nuclear interactions and are slowed by several orders of magnitude when a magnetic field of a few millitesla is applied. These results have significant implications for spin-based information processing.

Manipulation of a single charge in a double quantum dot.

We manipulate a single electron in a fully tunable double quantum dot using microwave excitation. Under resonant conditions, microwaves drive transitions between the (1,0) and (0,1) charge states of the double dot. Local quantum point contact charge detectors enable a direct measurement of the photon-induced change in occupancy of the charge states. From charge sensing measurements, we find T1 approximately 16 ns and a lower bound estimate for T*(2) of 400 ps for the charge two-level system.