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arXiv:1108.4210 · Physical Review B

Relaxation and readout visibility of a singlet-triplet qubit in an Overhauser field gradient

Christian Barthel, James Medford, Hendrik Bluhm, Amir Yacoby, Charles M. Marcus, Micah P. Hanson, Arthur C. Gossard

Published Jan 11, 2012• 55 citations
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Abstract

Using single-shot charge detection in a GaAs double quantum dot, we investigate spin relaxation time (${T}_{1}$) 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 ${T}_{1}$ 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.

DOI
10.1103/physrevb.85.035306

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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.
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.
Visibility of singlet-triplet qubit readout is reduced to almost zero in large magnetic field gradients due to relaxation processes. Here we present a new readout technique that is robust against relaxation and allows for measurement when previously studied methods fail. This technique maps the qubit onto spin states that are immune to relaxation using a spin-dependent electron tunneling process between the qubit and the lead. We probe this readout's performance as a function of magnetic field gradient and applied magnetic field, and optimize the pulse applied to the qubit through experiment and simulation.
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.
We study theoretically the phonon-induced relaxation (T1{T}_{1}T1​) and decoherence times (T2{T}_{2}T2​) of singlet-triplet qubits in lateral GaAs double quantum dots (DQDs). When the DQD is biased, Pauli exclusion enables strong dephasing via two-phonon processes. This mechanism requires neither hyperfine nor spin-orbit interaction and yields ${T}_{2}\ensuremath{\ll}{T}_{1}$, in contrast to previous calculations of phonon-limited lifetimes. When the DQD is unbiased, we find ${T}_{2}\ensuremath{\simeq}2{T}_{1}$ and much longer lifetimes than in the biased DQD. For typical setups, the decoherence and relaxation rates due to one-phonon processes are proportional to the temperature TTT, whereas the rates due to two-phonon processes reveal a transition from T2{T}^{2}T2 to higher powers as TTT is decreased. Remarkably, both T1{T}_{1}T1​ and T2{T}_{2}T2​ exhibit a maximum when the external magnetic field is applied along a certain axis within the plane of the two-dimensional electron gas. We compare our results with recent experiments and analyze the dependence of T1{T}_{1}T1​ and T2{T}_{2}T2​ on system properties such as the detuning, the spin-orbit parameters, the hyperfine coupling, and the orientation of the DQD and the applied magnetic field with respect to the main crystallographic axes.
Singlet-triplet qubits typically require large magnetic field gradients on the order of militeslas to achieve high-fidelity electrically-controlled qubit operations. However, such large magnetic field gradients in quantum dot systems also increase charge noise and provide a relaxation pathway from the triplet to singlet qubit state, making high-fidelity readout challenging. Recently, shelving and latched readout have been employed in gate-defined quantum dots and donor-dot systems to achieve readout fidelities of 80% and 99.86%, respectively. In this paper, we theoretically examine shelving and latched singlet-triplet readout techniques for multidonor-based qubits in silicon where the large phosphorus hyperfine interaction of the order of 100 MHz gives rise to large effective magnetic field gradients (equivalent to tens of mT) but where it can change in time due to the presence of nuclear spin flips. Using numerical simulations, we show that shelving readout does not work giving a zero average visibility for mutidonor quantum dots, due to the time-varying nuclear spin polarization. To remedy this we propose adding a calibration step, in which we derive the nuclear spin polarization from a single shelving readout of a singlet state, before every qubit operation. The derived information can then be used via a feed-forward protocol to apply correct readout mapping, greatly improving the overall readout fidelity to >99>99%>99. We also simulate the latched readout mechanism, which is resistant to nuclear polarization changes and is thus promising for achieving high visibility readout. Here we observe a nonzero readout visibility irrespective of the nuclear spin flipping. Finally, we discuss how to optimize the readout visibility in the presence of strong hyperfine interactions and show that for both readout methods we can obtain readout fidelity >99>99%>99. These results demonstrate that singlet-triplet qubits based on multidonor quantum dots are a promising route for future electrically controlled qubits in silicon.
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.