Ultra-cold atoms in optical lattices: simulating quantum spin systems
Ultra-cold atoms in optical lattices: simulating quantum spin systems
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光学晶格中的超冷原子：模拟量子自旋系统
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发表时间：
2012
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通讯作者：
R. Walters
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作者：
R. Walters
光学晶格为模拟各种物理系统提供了理想的实验工具。它们具有优异的相干性，微观动力学被很好地理解，并且可以以很高的精度进行动态控制。在冷却和捕获偶极分子和里德伯原子气体方面的最新进展进一步增加了光学晶格作为量子模拟器的多功能性，特别是对于具有远程相互作用的固态系统。在本论文中，我们进一步研究了被困在光学晶格中的冷原子的微观性质，超越了晶格轴正交的情况。我们提出了将单粒子能量特征态转换为一个完整的标准正交基的所谓的“广义万尼尔函数”，该函数定位于每个晶格点。与普通的万尼尔函数相反，广义万尼尔函数是由带之间的混合状态形成的，当带简并时需要它。我们修改了由Marzari和Vanderbilt（物理学家）设计的算法。Rev. B 56(20) 12847)用于计算最大局部化广义万尼尔函数，特别是用于确定任意几何光学晶格系统的这些函数，包括具有退化下带的光学晶格系统。此外，我们克服了原始算法初始化的一个问题，可以无故障地找到最大局部集。然后，我们提出了各种光学晶格系统在一维和二维，包括六边形和Kagome几何的结果。在每种情况下，我们都使用广义万尼尔函数来计算跳跃和相互作用参数，从而确定只包含局部相互作用的系统哈密顿量的简化形式。我们还研究了两个具有远程相互作用的自旋-1/2系统，作为可以用负载偶极分子的光学晶格模拟的模型范例。我们首先研究了一维自旋1/2伊辛链随着相互作用范围的增加而呈指数衰减的相互作用的临界性质。利用无限密度矩阵重整化群方法，我们计算了临界点的位置，并观察到在无限范围相互作用的极限下，经典平均场的光滑逼近结果。我们继续考虑单个自旋1/2耦合到一组相互作用自旋的量子动力学，作为固态量子记忆中的退相干模型。由无限范围Lipkin-Meshkov-Glick模型描述的大程度对称性，使我们能够找到在量子位准备后在定义好的时间内恢复初始量子位状态的参数体系。我们观察到，对于大型槽，这些时间可能与槽的大小无关，因此即使在与槽存在强耦合的情况下，也可以实现忠实的量子位存储。
Optical lattices provide ideal experimental tools for simulating a wide variety of physical systems. They exhibit excellent coherence properties, their microscopic dynamics are well-understood, and they can be dynamically controlled with great precision. Recent advances in cooling and trapping gases of dipolar molecules and Rydberg atoms have further increased the versatility of optical lattices as quantum simulators, particularly for solid state systems possessing long-range interactions. In this thesis we further examine the microscopic properties of cold atoms trapped in an optical lattice, going beyond the case where the lattice axes are orthogonal. We present a transformation of the single-particle energy eigenstates to a complete, orthonormal basis of so-called 'generalised Wannier functions' that are localised to each lattice site. Generalised Wannier functions, as opposed to ordinary Wannier functions, are formed by mixing states between bands and are required when the bands are degenerate. We modify an algorithm devised by Marzari and Vanderbilt (Phys. Rev. B 56(20) 12847) for calculating maximally localised generalised Wannier functions, specifically to determine these functions for optical lattice systems of arbitrary geometry, including those with degenerate lower bands. Moreover, we overcome an issue with the initialisation of the original algorithm to find the maximally localised set without fail. We then present results for a variety of optical lattice systems in one- and two-dimensions, including hexagonal and Kagome geometries. In each case we use the generalised Wannier functions to calculate the hopping and interaction parameters, and thus determine a reduced form of the system's Hamiltonian that contains only local interactions. We also study two spin-1/2 systems with long-range interactions as paradigm examples of the models that can be simulated using optical lattices loaded with dipolar molecules. We first examine the critical properties of a 1D spin-1/2 Ising chain possessing exponentially decaying interactions as the range of the interactions is increased. Using the infinite density matrix renormalisation group method, we calculate the location of the critical point and observe a smooth approach to the classical mean-field result in the limit of infinite-ranged interactions. We go on to consider the quantum dynamics of a single spin-1/2 coupled to a bath of interacting spins as a model for decoherence in solid state quantum memories. The large degree of symmetry of the bath, described by the infinite-ranged Lipkin-Meshkov-Glick model, allows us to find parameter regimes where the initial qubit state is revived at well-defined times after the qubit preparation. We observe that these times may become independent of the bath size for large baths and thus enable faithful qubit storage even in the presence of strong coupling to the bath.