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Physical Review A

Effect of electron spin-spin interaction on level crossings and spin flips in a spin-triplet system

Wei Jia, Fang-Qi Hu, Ning Wu, Qing Bo Zhao

Published Dec 15, 2017• 3 citations
Publisher

Abstract

We study level crossings and spin flips in a system consisting of a spin-1 (an electron spin triplet) coupled to a nuclear spin of arbitrary size $K$, in the presence of a uniform magnetic field and the electron spin-spin interaction within the triplet. Through an analytical diagonalization based on the $\mathrm{SU}(3)$ Lie algebra, we find that the electron spin-spin interaction not only removes the curious degeneracy which appears in the absence of the interaction, but also produces some level anticrossings (LACs) for strong interactions. The real-time dynamics of the system shows that periodic spin flips occur at the LACs for arbitrary $K$, which might provide an option for nuclear or electron spin polarization.

DOI
10.1103/physreva.96.062507

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We study level crossings and spin flips in a system consisting of a spin-1 (an electron spin triplet) coupled to a nuclear spin of arbitrary size KKK, in the presence of a uniform magnetic field and the electron spin-spin interaction within the triplet. Through an analytical diagonalization based on the SU(3)\mathrm{SU}(3)SU(3) Lie algebra, we find that the electron spin-spin interaction not only removes the curious degeneracy which appears in the absence of the interaction, but also produces some level anticrossings (LACs) for strong interactions. The real-time dynamics of the system shows that periodic spin flips occur at the LACs for arbitrary KKK, which might provide an option for nuclear or electron spin polarization.
We theoretically study the interplay of spin-orbit and hyperfine interactions in dynamical nuclear polarization in two-electron semiconductor double quantum dots near the singlet-triplet ($S\ensuremath{-}{T}_{+}$) anticrossing. The goal of the scheme under study is to extend the singlet-triplet ($S\ensuremath{-}{T}_{0}$) qubit decoherence time T2∗{T}_{2}^{*}T2∗​ by dynamically transferring the polarization from the electron spins to the nuclear spins. This polarization transfer is achieved by cycling the electron spins over the $S\ensuremath{-}{T}_{+}$ anticrossing. Here, we investigate, both quantitatively and qualitatively, how this hyperfine-mediated dynamical polarization transfer is influenced by the Rashba and Dresselhaus spin-orbit interaction. In addition to T2∗{T}_{2}^{*}T2∗​, we determine the singlet return probability Ps{P}_{s}Ps​, a quantity that can be measured in experiments. Our results suggest that the spin-orbit interaction establishes a mechanism that can polarize the nuclear spins in the direction opposite to that of hyperfine-mediated nuclear spin polarization. In materials with relatively strong spin-orbit coupling, this interplay of spin-orbit and hyperfine-mediated nuclear spin polarizations prevents any notable increase in the $S\ensuremath{-}{T}_{0}$ qubit decoherence time T2∗{T}_{2}^{*}T2∗​.
The role of a uniform magnetic field in the collision of two one-electron atoms is analyzed using previously developed density-matrix techniques. During the collision, all magnetic-moment interactions are small compared to the usual singlet and triplet potentials, and the only effect of the magnetic field is to alter the asymptotic states. This effect may be described in terms of the unitary transformation which diagonalizes the Breit-Rabi Hamiltonian. The properties of this transformation are given in detail for electronic spin \textonehalf{} and arbitrary nuclear spin. In addition to presenting a general formulation for this scattering problem, explicit formulas are given for spin exchange in the scattering of polarized beams from unpolarized targets.
Two independent anticrossings have been observed between singlet and triplet levels in the He atom, one between the 71D7^{1}D71D and 73D7^{3}D73D states, the other between the 81D8^{1}D81D and 83D8^{3}D83D states. The states are excited by electron bombardment. Compensatory changes in the luminosity of the singlet and triplet states are detected as the levels are tuned through the anticrossing points by a magnetic field. The positions of the anticrossings have been analyzed to provide new values for these singlet-triplet separations accurate to \ensuremath{\sim}0.03 GHz. These results show the previous best optical determinations for the separations to be in error by over a GHz. The widths of the anticrossings are analyzed to provide the most direct measures of the spin-orbit coupling constant between a singlet and a triplet state yet obtained for any system. The measured values of these coupling constants are found to be several times larger than their corresponding diagonal value in the 73D7^{3}D73D and 83D8^{3}D83D states.
We simulate the control of the spin states in a two-electron double quantum dot when an external detuning potential is used to pass the system through an anticrossing. The hyperfine coupling of the electron spins with the surrounding nuclei causes not only anticrossing of the spin states but also decoherence of the spin states. We calculate numerically the singlet–triplet decoherence for different detuning values and find good agreement with the experimental measurement results for a similar setup. We predict an interference effect due to the coupling of the T 0 and T + states.
We consider electron spin-exchange collisions between an atom with an electron spin of \textonehalf{} and a target atom with an arbitrary electron spin. The cross sections that describe the collision are expressed in terms of generalized direct and exchange amplitudes and are shown to depend only on the electron spin, polarization, and alignment of the target atom. We include the effects of an external magnetic field and the nuclear spin of the spin-\textonehalf{} atom on the collision. We calculate the cross sections connecting the initial and final states of the free Hamiltonian describing the spin-\textonehalf{} atom, with analytic results being displayed for the two limiting cases of the external magnetic field. For the general case, graphical results are presented for several common values of nuclear spin that allow the cross sections to be evaluated for arbitrary magnetic fields. The results are applied to several situations of current interest.
Energies of the coupled system of a spin-1/2 atom in a static magnetic field and an oscillating rf field are analyzed with the resolvent formalism and numerically calculated by quantizing the rf field, for the general case that the strong rf field is oriented in an arbitrary direction to the static magnetic field. It is shown that, if the component of the static field along the direction of the rf field has particular values, level crossings take place and multiphoton transitions by even or odd numbers of rf photons become forbidden, even when the polarization of the rf field satisfies the parity condition for the multiphoton transitions. Particular attention is given to the direction and amount of the shifts of the level crossings by the rf field, together with the shifts of the anticrossings or of the multiphoton transitions. Theoretical results are verified by the optical-pumping experiments with cesium vapor.