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arXiv:0902.0227 · Physical Review Letters

Rapid Single-Shot Measurement of a Singlet-Triplet Qubit

Christian Barthel, D. J. Reilly, Charles M. Marcus, Micah P. Hanson, Arthur C. Gossard

Published Oct 14, 2009• 304 citations
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Abstract

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.

DOI
10.1103/physrevlett.103.160503

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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.
We have evaluated hyperfine-induced electron spin dynamics for two electrons confined to a double quantum dot. Our quantum solution accounts for decay of a singlet-triplet correlator even in the presence of a fully static nuclear spin system, with no ensemble averaging over initial conditions. In contrast to an earlier semiclassical calculation, which neglects the exchange interaction, we find that the singlet-triplet correlator shows a long-time saturation value that differs from 12\frac{1}{2}21​, even in the presence of a strong magnetic field. Furthermore, we find that the form of the long-time decay undergoes a transition from a rapid Gaussian to a slow power law $(\ensuremath{\sim}1∕{t}^{3∕2})$ when the exchange interaction becomes nonzero and the singlet-triplet correlator acquires a phase shift given by a universal (parameter independent) value of $3\ensuremath{\pi}∕4$ at long times. The oscillation frequency and time-dependent phase shift of the singlet-triplet correlator can be used to perform a precision measurement of the exchange interaction and Overhauser field fluctuations in an experimentally accessible system. We also address the effect of orbital dephasing on singlet-triplet decoherence and find that there is an optimal operating point where orbital dephasing becomes negligible.
Using single-shot charge detection in a GaAs double quantum dot, we investigate spin relaxation time (T1{T}_{1}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{T}_{1}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.
Two-electron charged self-assembled quantum dot molecules exhibit a decoherence-avoiding singlet-triplet qubit subspace and an efficient spin-photon interface. Here, we demonstrate that the cycling transitions originating from auxiliary ground states in the same system allow for an efficient optical read-out of a singlet-triplet qubit. By implementing a spin-selective state transfer to the auxiliary state using a resonant laser field, we observe an improvement approaching two orders of magnitude in fidelity as compared to spin measurement by light scattering directly from the qubit states. Embedding the quantum dot molecule inside a low quality-factor micro-cavity structure should enable single-shot qubit read-out.
Decoherence of a quantum system arising from its interaction with an environment is a key concept for understanding the transition between the quantum and classical world as well as performance limitations in quantum technology applications. The effects of large, weakly coupled environments are often described as a classical, fluctuating field whose dynamics is unaffected by the qubit, whereas a fully quantum description still implies some backaction from the qubit on the environment. Here we show direct experimental evidence for such a backaction for an electron-spin qubit in a GaAs quantum dot coupled to a mesoscopic environment of order 10^{6} nuclear spins. By means of a correlation measurement technique, we detect the backaction of a single qubit-environment interaction whose duration is comparable to the qubit's coherence time, even in such a large system. We repeatedly let the qubit interact with the spin bath and measure its state. Between such cycles, the qubit is reinitialized to different states. The correlations of the measurement outcomes are strongly affected by the intermediate qubit state, which reveals the action of a single electron spin on the nuclear spins.
We report a single-shot-based projective readout of a semiconductor hybrid qubit formed by three electrons in a GaAs double quantum dot. Voltage-controlled adiabatic transitions between the qubit operations and readout conditions allow high-fidelity mapping of quantum states. We show that a large ratio both in relaxation time vs tunneling time (≈50) and singlet-triplet splitting vs thermal energy (≈20) allows energy-selective tunneling-based spin-to-charge conversion with a readout visibility of ≈92.6%. Combined with ac driving, we demonstrate high visibility coherent Rabi and Ramsey oscillations of a hybrid qubit in GaAs. Further, we discuss the generality of the method for use in other materials, including silicon.
A pulsed-gate technique with charge sensing is used to measure the singlet-triplet relaxation time for nearly degenerate spin states in a two-electron double quantum dot. Transitions from the (1,1) charge occupancy state to the (0,2) state, measured as a function of pulse cycle duration and magnetic field, allow the (1,1) singlet-triplet relaxation time $(\ensuremath{\geqslant}70\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s})$ and the (0,2) singlet-triplet splitting to be measured. This technique can be readily applied to read out a spin-qubit operating in a singlet-triplet basis.