We report repeated single-shot measurements of the two-electron spin state in a GaAs double quantum dot. The readout scheme allows measurement with fidelity above 90% with a ∼ 7 µs cycle time. Hyperfine-induced precession between singlet and triplet states of the two-electron system are directly observed, as nuclear Overhauser fields are quasi-static on the time scale of the measurement cycle. Repeated measurements on millisecond to second time scales reveal evolution of the nuclear environment.Qubits constructed from spin states of confined electrons are of interest for quantum information processing [1], for investigating decoherence and controlled entanglement, and as probes of mesoscopic nuclear spin environments. For logical qubits formed from pairs of electron spins in quantum dots [2], several requirements for quantum computing [3] have been realized [4,5,6,7]. To date, however, measurements of these systems have constituted ensemble averages over time, while protocols for quantum control, including quantum error correction, typically require high-fidelity single-shot readout. Coherent evolution conditional on individual measurement outcomes can give rise to interesting non-classical states [8,9]. Rapidly repeated single-shot measurements can also give access to the dynamics of the environment, allowing, for instance, feedback-controlled manipulation of the nuclear state. Single-shot measurements of solidstate quantum systems have been reported for superconducting qubits [10], the charge state of a single quantum dot [11], the spin of a single electron in a quantum dot in large magnetic fields [12,13], and the two-electron spin state in a single quantum dot [14].In this Letter, we demonstrate rapidly repeated highfidelity single-shot measurements of a two-electron spin (singlet-triplet) qubit in a double quantum dot. Singlet and triplet spin states are mapped to charge states [4], which are measured by a radio-frequency quantum point contact (rf-QPC) that is energized only during readout. The measurement integration time required for > 90% readout fidelity is a few microseconds. On that time scale, nuclear Overhauser fields are quasi-static, leading to observed periodic precession of the qubit. By measuring over longer times, the evolution of the Overhauser fields from milliseconds to several seconds can be seen as well. We apply a model of single-shot readout statistics that accounts for T 1 relaxation, and find good agreement with experiment. Finally, we examine the evolution of the two-electron spin state at the resonance between the singlet (S) and the m = +1 triplet (T + ) via repeated single-shot measurement, and show that the transverse component of the Overhauser field difference is not quasistatic on the time scale of data acquisition, as expected theoretically.The double quantum dot is formed by Ti/Au depletion gates on a GaAs/Al 0.3 Ga 0.7 As heterostructure with a two-dimensional electron gas (density 2 × 10 15 m −2 , mobility 20 m 2 /Vs) 100 nm below the surface. In order to split the three t...

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.

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(-β), yields β=γ(e)/(1-γ(e))=2.6±0.1. Model values for T(2)(n(π)) using β=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.

Single-shot measurement of the charge arrangement and spin state of a double quantum dot are reported, with times down to 100 ns. Sensing uses radio-frequency reflectometry of a proximal quantum dot in the Coulomb blockade regime. The sensor quantum dot is up to 30 times more sensitive than a comparable quantum point contact sensor, and yields three times greater signal to noise in rf single-shot measurements. Numerical modeling is qualitatively consistent with experiment and shows that the improved sensitivity of the sensor quantum dot results from reduced screening and smaller characteristic energy needed to change transmission. PACS numbers:Experiments on few-electron quantum dots [1], including spin qubits, have benefitted in recent years from the use of proximal charge sensing, a technique that allows the number and arrangement of charges confined in nanostructures to be measured via changes in conductance of a nearby sensor to which the device of interest is capacitively coupled [2,3]. Quantum point contacts (QPCs) have been widely used as charge sensors, allowing, for instance, high-fidelity single-shot readout of spin qubits via spin-to-charge conversion [4,5]. Single electron transistors (SETs) based on metallic tunnel junctions, and gate defined sensor quantum dots (SQD), conceptually equivalent to SETs, have also been widely used as proximal sensors, and provide similar sensitivity and bandwidth [6][7][8][9]. As a typical application, measuring the state of a spin qubit via spin-to-charge conversion involves determining whether two electrons in a double quantum dot are in the (1, 1) or the (0, 2) charge configuration, where (left, right) denotes occupancies in the double dot [ Fig. 1(a)], on time scales faster than the spin relaxation time [5].In this Communication, we demonstrate the use of a sensor quantum dot for fast charge and two-electron spinstate measurement in a GaAs double quantum dot, biased near the (1,1)-(0,2) charge transition. We compare the performance of the SQD to conventional quantum point contact (QPC) sensors for dc and radio-frequency (rf) measurement. We find experimentally that the SQD is up to 30 times more sensitive, and provides roughly three times the signal to noise ratio (SNR) of a comparable QPC sensor for detecting the charge arrangement and spin state of a double quantum dot. Numerical simulations, also presented, give results consistent with experiment and elucidate the role of screening in determining the sensitivity of these proximal charge sensors.Double quantum dots with integrated sensors are defined by Ti/Au depletion gates on a GaAs/Al 0.3 Ga 0.7 As heterostructure with a two-dimensional electron gas (density 2 × 10 15 m −2 , mobility 20 m 2 /Vs) 100 nm be-low the surface. The charge state of the double quantum dot is controlled by gate voltages V L , V R [see Fig. 1(a)]. Three gates next to the right dot form the SQD, which is operated in the multi-electron Coulomb blockade (CB) regime, with center gate voltage V D setting the SQD energy. A single gate next to ...

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.

A recently discovered mechanism of electric dipole spin resonance, mediated by the hyperfine interaction, is investigated experimentally and theoretically. The effect is studied using a spin-selective transition in a GaAs double quantum dot. The resonant frequency is sensitive to the instantaneous hyperfine effective field, revealing a nuclear polarization created by driving the resonance. A device incorporating a micromagnet exhibits a magnetic field difference between dots, allowing electrons in either dot to be addressed selectively. An unexplained additional signal at half the resonant frequency is presented.

Using single-shot charge detection in a GaAs double quantum dot, we investigate spin relaxation time (T1) and readout visibility of a two-electron singlet-triplet qubit following single-electron dynamic nuclear polarization (DNP). For magnetic fields up to 2 T, the DNP cycle is in all cases found to increase Overhauser field gradients, which in turn decrease T1 and consequently reduce readout visibility. This effect was previously attributed to a suppression of singlet-triplet dephasing under a similar DNP cycle. A model describing relaxation after singlet-triplet mixing agrees well with experiment. Effects of pulse bandwidth on visibility are also investigated.

A technique for creation of well-defined preselected coherent superpositions of multiple quantum states is proposed. It is based on an extension of the technique of stimulated Raman adiabatic passage ͑STIRAP͒ to degenerate levels. As an example, the nine-state system composed of the magnetic sublevels of three levels with angular momenta J g =0, J e = 1, and J f = 2 is studied in detail. Starting from the ͉J g =0, M g =0͘ state, STIRAP can create an arbitrary preselected coherent superposition between the five M f sublevels ͑M f =−2,−1,0, +1, +2͒ of the J f = 2 level with 100% efficiency in the adiabatic limit. The populations and the phases of the M f states in this superposition are determined entirely by the polarizations of the two laser fields. It is shown that this technique allows one to create any superposition of the five M f states, that is, to reach any point in the Hilbert space of the J f = 2 manifold, and the corresponding recipes for choosing the laser polarizations are presented.