Single-Qubit Operations for Singlet-Triplet Qubits in an Isolated Double-Well with Fixed Tunneling
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Abstract:
We propose a scheme to implement single-qubit operations for singlet-triplet qubits located in an isolated double-well potential with fixed inter-site tunneling when superexchange interactions predominate. Arbitrary single-qubit gates can be realized by a sequence composed of two elementary operations which can be switched between different parameter regimes by adjusting slightly the relative energy bias of trapped atoms in each sub-well site. The experimental feasibility of the strategy and the fidelity of basic rotation operations are also analyzed.Keywords:
Superexchange
Sequence (biology)
초교환 상호작용은 MnO, $MnF_2$ 와 같은 전이금속 화합물에서 나타나는 반강자성을 설명하기 위해서 도입된 상호작용이다. 이 초교환 상호작용에 스핀-궤도 결합 효과를 포함시키면 비등방성 초교환(Dzyaloshinskii-Moriya: DM) 상호작용이 된다. 이 비등방성 초교환 DM 상호작용으로 ${\alpha}-Fe_2O_3$ , $MnCO_3$ , $CrF_3$ 등에서 나타나는 약강자성을 설명할 수 있다. The superexchange interaction is introduced to explain antiferromagnetic ordering in transition metal compounds such as MnO and $MnF_2$ . The anisotropic superexchange (Dzyaloshinskii-Moriya: DM) interaction can be derived by incorporating the spin-orbit interaction into the superexchange interaction. The anisotropic superexchange DM can account for the weak ferromagnetism observed in transition metal compounds such as ${\alpha}-Fe_2O_3$ , $MnCO_3$ , $CrF_3$ .
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Magnetic susceptibility, heat capacity, and EPR studies reported here show that close to 50% of the high-spin ${\mathrm{Fe}}^{3+}$ ions in this compound form isolated spin pairs each of which shows a highly anisotropic superexchange coupling. Direct EPR transitions between the superexchange-split energy levels have been observed.
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Tetraphenylporphyrin
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The values and signs of the contributions to the superexchange interaction of Co3+ ions in LaCoO3 in different spin states, namely, the superexchange of a pair of ions in the intermediate (IS) state and the superexchange of a pair of ions, one of which is in the intermediate state and the other in the high-spin (HS) state, are studied. For this purpose, virtual electron-hole pairs produced in the course of superexchange (the so-called exchange loops) have been studied within the framework of a multiband generalization of the Hubbard model. It is shown that the cobalt ions in the intermediate state are ordered ferromagnetically, while a pair of ions in different HS and IS states makes an AFM contribution to the superexchange.
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The magnitude of superexchange interaction of the MnO crystal is calculated according to the methods proposed previously. Various mechanisms of superexchange interaction are taken into consideration. Overlaps between neighbouring ions are assumed to be small and the energy of the crystal is developed in powers of S, the overlap integral between manganese and oxygen ions. The superexchange interaction of all mechanisms appears from S4 terms and it is concluded from calculation that the Slater mechanism may play a dominant role in MnO. The numerical value of magnitude of interaction agrees with experiment in the order of magnitude. Several discussions about superexchange interactions of other substances, particularly of MnF3 and LaMnO3, are given.
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Abstract Studies are made of superexchange interaction in ionic crystals using the Heitler‐London theory and with particular reference to KNiF 3 . The generalized Heitler‐London quantitative theory of covalency allows a detailed study to be made of the transfer of an electron from cation to cation and the transfer of two electrons from an anion to the cations. No further assumptions are made and the calculations are performed numerically. The antiferromagnetic superexchange constant given by this calculations is in good agreement with the experimental superexchange constant.
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Constant (computer programming)
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Starting with the Anderson periodic Hamiltonian for a system of the narrow- and wide-band electrons, an explicit expression for the superexchange coupling between spins of localized electrons is derived and analyzed. The superexchange coupling is based on the fourth-order p-d hybridization. One special aspect of the problem is systematically discussed at T=0 K. It is shown that the presence of compensating holes produced in Ca2+:YIG by the valence-uncompensated doping, can result in a decrease in the strength of the superexchange coupling and, depending on the concentration of the doping Ca2+ ions, a change of the sign of the coupling constant is obtained. Numerical results are calculated both for the charge-transfer and Mott–Hubbard models for insulators
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Coupling constant
Hamiltonian (control theory)
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Magnetic properties of silver(II) compounds have been of interest in recent years. In covalent compounds, the main mechanism of interaction between paramagnetic sites is the superexchange via the connecting ligand. To date, little is known of magnetic interactions between Ag(II) cations and other paramagnetic centres. It is because only a few compounds bearing Ag(II) cation and other paramagnetic transition metal cation are known experimentally. Recently the high-pressure synthesis of ternary silver(II) fluorides with 3d metal cations AgMF4 (M = Co, Ni, Cu) was predicted to be feasible. Here, we investigate the magnetic properties of these compounds in their diverse polymorphic forms. Using well established computational methods we predict superexchange pathways in AgMF4, evaluate coupling constants and calculate the impact of Ag(II) presence on superexchange between the other cations. The results indicate that the low-pressure form of AgCuF4, the only composed of stacked layers as the parent AgF2, would hold mainly Ag-Ag and Cu-Cu superexchange interactions. Upon compression, or with the nickel(II) cation, the Ag-M interactions in AgMF4 intensify, which is emphasized by an increase of Ag-M superexchange coupling constants and Ag-F-M angles. All the strongest Ag-M superexchange pathways are quasi-linear, leading to the formation of antiferromagnetic chains along the crystallographic directions. The impact of Ag(II) on M-M superexchange turns out to be moderate, due to factors connected to the crystal structure.
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New superexchange four-particle mechanisms are suggested for dielectrics containing magnetic ions linked through several bridge ligands. These mechanisms may suppress as well as amplify Anderson's superexchange which is additive over the ligands.
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Bridge (graph theory)
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The negative thermal expansion (NTE) in CuO is explained via electron-transfer-driven superexchange interaction. The elusive connection between the spin-lattice coupling and NTE of CuO is investigated by neutron scattering and principal strain axes analysis. The density functional theory calculations show as the temperature decreases, the continuously increasing electron transfer accounts for enhancing the superexchange interaction along [101̅], the principal NTE direction. It is further rationalized that only when the interaction along [101̅] is preferably enhanced to a certain level compared to the other competing antiferromagnetic exchange pathways can the corresponding NTE occur. Outcomes from this work have implications for controlling the thermal expansion through superexchange interaction, via, for example, optical manipulation, electron or hole doping, etc.
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Negative Thermal Expansion
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The values and signs of the contributions to the superexchange interaction of Co 3+ ions in LaCoO 3 in different spin states, namely, the superexchange of a pair of ions in the intermediate (IS) state and the superexchange of a pair of ions, one of which is in the intermediate state and the other in the high-spin (HS) state, are studied. For this purpose, virtual electron-hole pairs produced in the course of superexchange (the so-called exchange loops) have been studied within the framework of a multiband generalization of the Hubbard model. It is shown that the cobalt ions in the intermediate state are ordered ferromagnetically, while a pair of ions in different HS and IS states makes an AFM contribution to the superexchange. Keywords: superexchange interaction, magnetic structure, Hubbard model, projection operator method, exchange loop.
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Spin states
Exchange interaction
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