Limitations on the maximal level of entanglement of two singlet-triplet qubits in GaAs quantum dots

• URL: http://arxiv.org/abs/2312.16583v1
• Date: Wed, 27 Dec 2023 14:19:22 GMT
• Title: Limitations on the maximal level of entanglement of two singlet-triplet qubits in GaAs quantum dots
• Authors: Igor Bragar, {\L}ukasz Cywi\'nski
• Abstract summary: We analyze in detail a procedure of entangling of two singlet-triplet ($S$-$T_0$) qubits operated in a regime when energy associated with the magnetic field gradient, $Delta B_z$, is an order of magnitude smaller than the exchange energy, $J$, between singlet and triplet states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We analyze in detail a procedure of entangling of two singlet-triplet ($S$-$T_{0}$) qubits operated in a regime when energy associated with the magnetic field gradient, $\Delta B_{z}$, is an order of magnitude smaller than the exchange energy, $J$, between singlet and triplet states [Shulman M. et al., Science 336, 202 (2012)]. We have studied theoretically a single $S$-$T_{0}$ qubit in free induction decay and spin echo experiments. We have obtained analytical expressions for time dependence of components of its Bloch vector for quasistatical fluctuations of $\Delta B_{z}$ and quasistatical or dynamical $1/f^{\beta}$-type fluctuations of $J$. We have then considered the impact of fluctuations of these parameters on the efficiency of the entangling procedure which uses an Ising-type coupling between two $S$-$T_{0}$ qubits. Particularly, we have obtained an analytical expression for evolution of two qubits affected by $1/f^{\beta}$-type fluctuations of $J$. This expression indicates the maximal level of entanglement that can be generated by performing the entangling procedure. Our results deliver also an evidence that in the above-mentioned experiment, the $S$-$T_{0}$ qubits were affected by uncorrelated $1/f^{\beta}$ charge noises.

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