门控量子点反铁磁海森堡链的量子模拟
Quantum simulation of antiferromagnetic Heisenberg chain with gate-defined quantum dots
摘要：
相互作用的费米子的量子力学关联导致奇异相的出现。在费米-哈伯德模型的莫特绝缘体区域中，磁相自然出现，其中电荷被局域化，自旋自由度保持不变。在这一制度下，发生的现象，如共振价键，受挫的磁性，和自旋液体的预测。具有工程化哈密顿量的量子系统可以用作这种自旋物理的模拟器，以提供超越分析方法和经典计算机能力的见解。为了有用，需要准备复杂的多体自旋态和获得相关观测值的方法。在这里，我们展示了磁性的量子模拟在莫特绝缘体制度与线性量子点阵列。我们描述了海森堡自旋链的能谱，从中我们可以确定何时满足均匀交换耦合的条件。接下来，我们研究了海森堡哈密顿量的单重态和三重态子空间中具有全局交换振荡的多自旋相干性。最后，我们用化学方法制备了均匀自旋链的低能整体单重态，并利用每个最近邻对的双自旋单重态三重态测量及其相关性对其进行了探测。这里提出的方法和控制打开了新的机会，受益于灵活性的调整和布局的门定义的量子点阵列的量子磁性的模拟。
英文摘要：
Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases. Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains. In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted. Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers. To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required. Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array. We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met. Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian. Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlettriplet measurements on each nearest-neighbor pair and the correlations therein. The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.
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