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

多体系统中的关联和涨落是系统的平均场描述之外的物理学的起源。如果与动能相比，相互作用很强，这很自然地出现。在量子系统中，有时会出现强烈的--微观上甚至难以处理的--量子关联，并导致宏观尺度上出现的新物理。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，而它们引起的涨落加起来，那么弱微扰相关也可以主导物理学。 这种相关性主导的物理学的第一个例子是令人惊讶地发现了极度稀释的量子液体（所谓的量子液滴）的自束缚态。 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一个在平均场水平上不稳定的多体态。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物体的应用。我们将通过研究强偶极镝原子的多体系统来做到这一点，重点是偶极超流性、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极大地修改偶极量子涨落的行为。有趣的是，在两个维度中，在偶极-偶极相互作用存在下的量子涨落的理论描述迄今为止还不为人所知，需要实验来阐明它们的影响。在一维中，有关于偶极量子涨落的第一个理论工作，但是需要进行测试，因为该理论的有效性存在争议。这显然需要实验来澄清。其次，我们将研究涨落对系统超流性质的影响。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，从Abrikosov涡格的条纹安排的涡的过渡将进行研究。如果这些现象是在接近平均场不稳定性的地方观察到的，它们就变得最容易受到波动的影响。第三，研究热涨落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温度测量并确定热力学性质，如比热。这些对杂质的研究将试图回答关于液滴蒸发过程的问题。最后，我们将调查的性质，从气态到液态的过渡使用这个工具。

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.