【作者】 汪涛；

【导师】 侯春风；

【作者基本信息】 哈尔滨工业大学 ， 物理， 2015， 博士

【摘要】 光晶格中的超冷玻色子气体的研究近来引起了人们广泛的兴趣,因为它在固体理论和超冷量子气体系统这两个领域之间搭建起了一个桥梁。而且,由于系统的各种参数可以很容易通过实验手段进行调节,它可以被当做是一个适用范围广泛的量子模拟器。近年来,人们开始把兴趣导向更为复杂的光晶格系统,因为这些复杂的系统中往往包含更为复杂的量子行为。本论文主要研究调制光晶格中的玻色子系统,包括超光晶格系统中的玻色子系统和伴随S-波散射长度周期性调制光晶格中的的玻色子系统的量子相变和临界性质。在超光晶格中,由于人为进行的调制,相对于普通的光晶格,系统的平移对称性被破坏,从而导致了更为复杂的相图和临界性质。为了研究超光晶格系统的相图,我们把由Axel Pelster教授小组的金兹堡-朗道有效势理论从单参数推广到多参数的情况。研究表明由于平移对称性的破坏,系统出现了密度波态。我们研究了系统的莫特绝缘态和密度波态之间的竞争关系,给出了正方晶格和立方晶格的相图。得到的相图与精确地数值模拟方法的比较证明了推广的有效性。然后我们用这种推广的方法分析了阻错超光晶格的相图和临界性质。对这种更为复杂的几何形状的光晶格进行空间平移对称性的破坏调制不仅会使得系统出现密度波态,还会使系统出现新的超流现象。对于三角超光晶格和笼壁超光晶格中的玻色子系统,文中给出了系统的相图。而对笼壁超光晶格的临界行为的分析表明,系统出现了在不同的方向的超流密度不同且出现随系统参数改变而交替领先的现象。我们的研究加深了人们对超光晶格系统和超流现象的理解。对于光晶格中的玻色子系统,除了在空间范围内进行调制之外,还可以在时间周期上进行调制。本论文中我们研究的另一种调制就是使系统Feshbach共振的S-波散射长度在时间上周期性的振动。首先把这种随时间周期性变化的系统的哈密顿量等效为一个与时间无关的哈密顿量。用多种解析方法和数值模拟分析系统的相图后,发现虽然存在周期性的变化,但是系统中仍然存在从莫特绝缘态到超流态的相变,而且,这种相变与S-波散射长度的振幅相关。进一步详细的分析表明在系统的振幅幅度小于一定数值时,如果重新标度系统的跃迁幅度,系统可以用一种类似于玻色-哈伯德模型的哈密顿量来表示。该发现表明此时系统与玻色-哈伯德模型具有相同的临界性质,他们的临界行为应该属于同一类。而当S-波周期调制振幅较大时,我们发现现有的解析和数值方法都不能给出可信的结果。为了研究此时系统的量子相变和临界性质,我们将注意力转向了一种最近新出现的算法-过程链算法。我们首先在普通的光晶格系统中使用我们的算法,将得到的数值结果跟量子蒙特卡罗模拟结果进行了对比,证明了我们的方法的有效性。然后我们将这种算法运用到S-波散射长度周期性振动的二维晶格系统中,发现当系统的S-波散射振幅的长度增大时,系统的相图会发生明显的变化,而系统此时再也不能用一个类似哈伯德模型的哈密顿量来描述。更多还原

【Abstract】 Systems of ultracold bosonic gases in optical lattices represent nowadays a popularresearch topic, as they establish a versatile bridge between the field of ultracold quantummatter and solid-state systems. In particular, they can be experimentally controlled with ayet unprecedented level of precision. With this it allows for a clear theoretical analysis andwhich are even predestined as universal quantum simulators. Recent research efforts havetargeted more complex systems, because in this system the corresponding phase diagramsbecome richer and more complex. In this thesis, we study the quantum phase transitionand critical properties for Bosons on optical lattice, including the superlattice system andS-wave periodically driven system.For optical superlattice system, due to artificially tuned, the translational symmetryhas been broken, which induced more complex quantum phase diagram and critical be-havior. To study the phase diagram we generalize a recently established effective potentialLandau theory for a single component to the case of multi components. We find not onlythe characteristic incompressible solid phases with fractional filling, but also obtain theunderlying quantum phase diagram in the whole parameter region at zero temperature.The analytical of the critical points of the phase lobes shows the competition of Density-Wave phase and Mott phase. Also the comparison of the phase diagram that we got withthe high accuracy of the Quantum Monte Carlo simulation proves the e?ciency of thegeneralization.Then we use the Generalized Effective Potential Landau Theory method to studythe frustrated optical superlattice system. The tune of these more complicated systemsnot only make the Density Wave phase appear, but also shows the new phenomenon ofthe superfluid. The study of the critical behavior of Kagome optical superlattice revealsthat the bias of the anisotropy of the superfluid density is alternating between differentdirection while detuning the parameter of the system.Apart from the tune on the real space as superlattice system, another tuned opticallattice system that we study in this thesis is the Bosons on optical lattice with a periodicmodulation of the S-wave scattering length. At first we map the underlying periodicallydriven Bose- Hubbard model approximately to an effective time-independent Hamiltoni-an with a conditional hopping. Combining different analytical approaches with quantumMonte Carlo simulations then reveals that the superfluid-Mott insulator quantum phasetransition still exists despite the periodic driving and that the location of the quantumphase boundary turns out to depend quite sensitively on the driving amplitude. A moredetailed quantitative analysis shows even that the effect of driving can be described withinthe usual Bose-Hubbard model provided that the hopping is rescaled appropriately withthe driving amplitude when the driven amplitude is smaller than some certain value. Thisfinding indicates that the Bose-Hubbard model with a periodically driven s-wave scatter-ing length and the usual Bose- Hubbard model belong to the same universality class fromthe point of view of critical phenomena.For the system of Bosons on optical lattice witha periodic modulation of the s-wave scattering length, when the driven amplitude goeslarger, our analytical and numerical method will be not suitable. This made us turn ourinterest to the newly developed numerical method-process-chain method. We first checkour program by using it to calculate the strong coupling method and effective potentialtheory to high order for the Bose-Hubbard model. The result that we get comparing withthe numerical simulation result shows that we have very high accuracy. Then we use it tostudy the phase diagram of the system of Bosons on optical square lattice with a period-ic modulation of the s-wave scattering length. We found that when the driven amplitudegoes larger, the shape of phase diagram of the system will change, which indicates that wecan not use a Bose-Hubbard like effective Hamiltonian to describe the system anymore.更多还原