Quantum fluctuations in dipolar gases: Quantum droplets, vortices and impurities

多体系统中的关联和涨落是物理学的起源，超出了系统平均场的描述。如果相互作用比动能强，这是很自然的。在量子系统中，有时会出现强烈的--甚至是微观上难以处理的--量子关联，并导致宏观尺度上出现的新物理学。然而，最近的研究表明，如果两个弱相互作用在平均场水平上几乎相互补偿，而它们引起的涨落累积起来，那么弱微扰关联也可以主导物理。这种关联主导的物理学的第一个例子是令人惊讶地发现了极稀薄量子液体的自束束态--也就是所谓的量子液滴。在这个系统中，长程和短程相互作用相互补偿，而它们的涨落稳定了在平均场水平上不稳定的多体状态。在这里，我们打算研究这种液滴的基本性质以及这些新的孤立量子对象的应用。为此，我们将研究强偶极镝原子的多体系统，重点是偶极超流、低维和费米子杂质中的量子涨落效应。首先，我们将通过系统的维度戏剧性地改变偶极量子涨落的行为。有趣的是，在两个维度中，存在偶极-偶极相互作用时量子涨落的理论描述到目前为止还不为人所知，需要通过实验来澄清它们的影响。在一个维度上，有关于偶极量子涨落的第一个理论工作，然而，由于对该理论的有效性存在争议的观点，这一工作需要检验。第二，我们将研究涨落对系统超流体性质的影响。在从三维到准二维的交叉中，我们将研究偶极涨落的各向异性以及由此产生的朗道临界速度的各向异性。此外，还将研究从Abrikosov涡旋晶格到涡带排列的转变。如果这些现象被观测到接近平均场不稳定性，它们就会变得最容易受到波动的影响。第三，研究热和量子涨落的一个重要工具是研究溶解的杂质。在量子液滴的情况下，我们计划使用测量的液滴中费米子杂质的数量来进行测温，并确定热力学性质，如比热。这些对杂质的研究将试图回答有关液滴蒸发过程的问题。最后，我们将使用这个工具来研究从气态到液态的转变的性质。

Correlations and fluctuations in a many-body system are the origin of physics beyond mean-field description of the system. This appears naturally if interactions are strong compared to the kinetic energy. In quantum systems, sometimes strong - and microscopically even intractable - quantum correlations can appear and lead to new physics that emerges on the macroscopic scale. However recently it was shown that weak perturbative correlations can also dominate the physics if two weak interactions almost compensate each other on the mean-field level while the fluctuations they induce add up. One first example of this kind of correlation-dominated physics was the surprising discovery of self-bound states of extremely dilute quantum liquids - so called quantum droplets. In this system long and short range interactions compensate each other while their fluctuations stabilize a many-body state that would be unstable on the mean-field level.Here we propose to investigate the fundamental properties of such droplets as well as the applications of these novel isolated quantum objects. We will do so by investigating many-body systems of strongly dipolar dysprosium atoms with a focus on quantum fluctuation effects in dipolar superfluidity, in low dimensions and on fermionic impurities. First, we will dramatically modify the behavior of dipolar quantum fluctuations via the dimensionality of the system. Interestingly, in two dimensions the theoretical description of quantum fluctuations in the presence of dipole-dipole interactions is not known to date calling for experiments to clarify their effect. In one dimension there is first theoretical work on dipolar quantum fluctuations, which however needs to be tested as there are controversial views on the validity of that theory. Again there is clear need for experimental clarification.Second we will investigate the effect of the fluctuations on the superfluid properties of the system. In the crossover from three to quasi-two dimensions we will study the anisotropy of dipolar fluctuations as well as the resulting anisotropy in the Landau critical velocity. Also the transition from Abrikosov vortex lattices to stripe arrangements of vortices will be studied. If those phenomena are observed close to mean-field instabilities they become most susceptible to the effects of fluctuations. Third, an important tool to study thermal and quantum fluctuations is to study dissolved impurities. In the case of a quantum droplet we plan to use the measured number of fermionic impurities in a droplet to do thermometry and determine thermodynamic properties like specific heat. These studies of impurities will try to answer questions on the evaporation process of the droplets. Finally we will investigate the nature of the transition from a gaseous to a liquid state using this tool.