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arXiv:2203.16138 · Advanced Quantum Technologies

Theory on Electron–Phonon Spin Dephasing in GaAs Multi‐Electron Double Quantum Dots

Guanjie He, Guo Xuan Chan, Xin Wang

Published Jan 11, 2023• 3 citations

Abstract

Abstract Recent studies reveal that a double‐quantum‐dot system hosting more than two electrons may be superior in certain aspects as compared to the traditional case in which only two electrons are confined (a singlet–triplet qubit). The electron–phonon dephasing occurring in a GaAs multi‐electron double‐quantum‐dot system is studied, in a biased case in which the singlet state is hybridized, as well as in an unbiased case in which the hybridization is absent. It is found that while the electron–phonon dephasing rate increases with the number of electrons confined in the unbiased case, this does not hold in the biased case. A merit figure is defined as a ratio between the exchange energy and the dephasing rate, and have shown that in experimentally relevant range of the exchange energy, the merit figure actually increases with the number of electrons in the biased case. The results show that the multi‐electron quantum‐dot system has another advantage in mitigating the effect of electron–phonon dephasing, which is previously under‐appreciated in the literature.

DOI: 10.1002/qute.202200074

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Abstract Recent studies reveal that a double‐quantum‐dot system hosting more than two electrons may be superior in certain aspects as compared to the traditional case in which only two electrons are confined (a singlet–triplet qubit). The electron–phonon dephasing occurring in a GaAs multi‐electron double‐quantum‐dot system is studied, in a biased case in which the singlet state is hybridized, as well as in an unbiased case in which the hybridization is absent. It is found that while the electron–phonon dephasing rate increases with the number of electrons confined in the unbiased case, this does not hold in the biased case. A merit figure is defined as a ratio between the exchange energy and the dephasing rate, and have shown that in experimentally relevant range of the exchange energy, the merit figure actually increases with the number of electrons in the biased case. The results show that the multi‐electron quantum‐dot system has another advantage in mitigating the effect of electron–phonon dephasing, which is previously under‐appreciated in the literature.

We study electron-phonon interaction induced decoherence between two-electron singlet and triplet states in a semiconductor double quantum dot using a spin-boson model. We investigate the onset and time evolution of this dephasing, and study its dependence on quantum dot parameters such as dot size and double dot separations, as well as the host materials (GaAs and Si). At the short time limit, electron-phonon interaction only causes an incomplete initial Gaussian decay of the off-diagonal density matrix element in the singlet-triplet Hilbert space; a complete long-time exponential decay due to phonon relaxation would eventually dominate over two-spin decoherence. We analyze two-spin decoherence in both symmetric and biased double quantum dots, identifying their difference in electron-phonon coupling and the relevant consequences.

We show that singlet-triplet superpositions of two-electron spin states in a double quantum dot undergo a phonon-induced pure dephasing which relies only on the tunnel coupling between the dots and on the Pauli-exclusion principle. As such, this dephasing process is independent of spin-orbit coupling or hyperfine interactions. The physical mechanism behind the dephasing is elastic phonon scattering, which persists to much lower temperatures than real phonon-induced transitions. Quantitative calculations performed for a lateral GaAs/AlGaAs gate-defined double quantum dot yield microsecond dephasing times at sub-Kelvin temperatures, which is consistent with experimental observations.

We study theoretically the phonon-induced relaxation (

{T}_{1}

) and decoherence times (

{T}_{2}

) 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

T

, whereas the rates due to two-phonon processes reveal a transition from

{T}^{2}

to higher powers as

T

is decreased. Remarkably, both

{T}_{1}

and

{T}_{2}

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

{T}_{1}

and

{T}_{2}

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.

We study electron-phonon interaction induced decoherence between two-electron singlet and triplet states in a semiconductor double quantum dot using a spin-boson model. We investigate the onset and time evolution of this dephasing, and study its dependence on quantum dot parameters such as dot size and double dot separations, as well as the host materials (GaAs and Si). We find that electron-phonon interaction causes an initial Gaussian decay of the off-diagonal density matrix element in the singlet-triplet Hilbert space, and a long-time exponential decay originating from phonon relaxation.