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arXiv:2403.09952 · Physical Review A

Anomalous external-magnetic-field dependence of dephasing in a spin bath

Rui Li

Published Sep 24, 2012• 1 citation
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Abstract

We theoretically investigate the dephasing of a central spin-1 model. An interesting mechanism of spin decoherence is found with this model, namely, hyperfine mediated spectral diffusion. This mechanism contains the features of both the dipolar-interactions-induced spectral diffusion and the hyperfine mediated interactions. We also find an anomalous magnetic field dependence of decoherence, which is caused by the competition between crystal field splitting and Zeeman splitting of the central spin. As the external magnetic field increases, in the V type level structure regime, the decoherence rate becomes much stronger; while in the cascade type level structure regime, just like localized electron spin in quantum dots, the decoherence rate becomes much weaker.

DOI
10.1103/physreva.86.032333

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We theoretically investigate the dephasing of a central spin-1 model. An interesting mechanism of spin decoherence is found with this model, namely, hyperfine mediated spectral diffusion. This mechanism contains the features of both the dipolar-interactions-induced spectral diffusion and the hyperfine mediated interactions. We also find an anomalous magnetic field dependence of decoherence, which is caused by the competition between crystal field splitting and Zeeman splitting of the central spin. As the external magnetic field increases, in the V type level structure regime, the decoherence rate becomes much stronger; while in the cascade type level structure regime, just like localized electron spin in quantum dots, the decoherence rate becomes much weaker.
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.
In this contribution we study carrier tunneling in a system consisting of a pair of coupled quantum dots.We predict the presence of a spin dephasing channel in such a system, which is associated with a "welcher-weg" type of decoherence process occurring during carrier tunneling.In our model such a process is caused by a mismatch of g-factor values in two quantum dots in the presence of external magnetic field.This leads to a mismatch in spin Zeeman splitting between the dots and, in consequence, to the distinguishability of phonons emitted during the tunneling of carriers with opposite spins.Thus we demonstrate a process of spin dephasing without any direct spin-environment coupling present in the model.
We investigate in detail, using both analytical and numerical tools, the decoherence of electron spins in quantum dots (QDs) coupled to a bath of nuclear spins in magnetic fields or with various initial bath polarizations, focusing on the longitudinal relaxation in low and moderate field and polarization regimes. An increase of the initial polarization of nuclear-spin bath has the same effect on the decoherence process as an increase of the external magnetic field, namely, the decoherence dynamics changes from smooth decay to damped oscillations. This change can be observed experimentally for a single QD and for a double-QD setup. Our results indicate that substantial increase of the decoherence time requires very large bath polarizations, and the use of other methods (dynamical decoupling or control of the nuclear spins distribution) may be more practical for suppressing decoherence of QD-based qubits.
We study the decay of entanglement of quantum-dot electron-spin qubits under hyperfine-interaction-mediated decoherence. We show that two-qubit entanglement of a single entangled initial state may exhibit decay characteristic of two disentanglement regimes in a single sample, when the external magnetic field is changed. The transition is manifested by the suppression of time-dependent entanglement oscillations which are superimposed on the slowly varying entanglement decay related to phase decoherence which results in oscillatory behavior of entanglement sudden death time as a function of the magnetic field. This unique behavior allows us to propose the double-quantum-dot two-electron spin Bell state as a promising candidate for precise measurements of the magnetic field.
We predict a spin pure dephasing channel in electron relaxation between states with unequal Zeeman splittings, exemplified by a spin-preserving electron tunneling between quantum dots in a magnetic field. The dephasing is caused by a mismatch in electron ggg factors in the dots leading to distinguishability of phonons emitted during tunneling with opposite spins. Combining multiband $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ modeling and dynamical simulations via a master equation, we show that this fundamental effect of spin measurement effected by the phonon bath may be widely controlled by the size and composition of the dots or on demand via tuning of external fields. By comparing the numerically simulated degree of dephasing with the predictions of general theory based on distinguishability of environment states, we show that the proposed mechanism is the dominant phonon-related spin dephasing channel and may limit spin coherence time in tunnel-coupled structures at cryogenic temperatures.
The many-body dynamics of an electron spin−1/2 qubit coupled to a bath of nuclear spins by hyperfine interactions, as described by the central spin model in two kinds of external field, are studied in this paper. In a completely polarized bath, we use the state recurrence method to obtain the exact solution of the X X Z central spin model in a constant magnetic field and numerically analyze the influence of the disorder strength of the magnetic field on fidelity and entanglement entropy. For a constant magnetic field, the fidelity presents non-attenuating oscillations. The anisotropic parameter λ and the magnetic field strength B significantly affect the dynamic behaviour of the central spin. Unlike the periodic oscillation in the constant magnetic field, the decoherence dynamics of the central spin act like a damping oscillation in a disordered field, where the central spin undergoes a relaxation process and eventually reaches a stable state. The relaxation time of this process is affected by the disorder strength and the anisotropic parameter, where a larger anisotropic parameter or disorder strength can speed up the relaxation process. Compared with the constant magnetic field, the disordered field can regulate the decoherence over a large range, independent of the anisotropic parameter.