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arXiv:0903.0783 · Physical Review B

Phonon-induced dephasing of singlet-triplet superpositions in double quantum dots without spin-orbit coupling

Katarzyna Roszak, Paweł Machnikowski

Published Nov 17, 2009• 27 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.80.195315

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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.
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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.
We investigate theoretically the hyperfine-induced dephasing of two-electron-spin states in a double quantum dot with a finite singlet-triplet splitting JJJ. In particular, we derive an effective pure dephasing Hamiltonian, which is valid when the hyperfine-induced mixing is suppressed due to the relatively large JJJ and the external magnetic field. Using both a quantum theory based on resummation of ring diagrams and semiclassical methods, we identify the dominant dephasing processes in regimes defined by values of the external magnetic field, the singlet-triplet splitting, and inhomogeneity in the total effective magnetic field. We address both free induction and Hahn echo decay of superposition of singlet and unpolarized triplet states (both cases are relevant for singlet-triplet qubits realized in double quantum dots). We also study hyperfine-induced exchange gate errors for two single-spin qubits. Results for III-V semiconductors as well as silicon-based quantum dots are presented.
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.