SciPost Physics: Pauli crystal melting

Pauli crystals are ordered geometric structures that appear when noninteracting fermionic gases – such as ⁸Li – are cooled to extremely low temperatures and confined by optical traps. Under these conditions, the quantum nature of the atoms in the gas dominate, and the crystal structure emerges because each atom in the gas repels its neighbors due to the Pauli exclusion principle. Pauli crystals are notoriously difficult to realize because of the very high degree of control needed in the experiments, and were definitively observed for the first time only in 2020 (see the original Physical Review Letter article or this Physics outreach article). When the conditions are not perfect, the Pauli crystal gets deformed – a phenomenon called melting. Pauli crystal melting has been observed in experiments, too, but the mechanism that leads to it remains unclear.

We have addressed this question by studying the melting dynamics of a few-particle fermionic system as a function of periodic driving and experimental imperfections in the optical trap (anisotropy and anharmonicity). To do so, we employed a combination of numerical simulations with MCTDH-X and Floquet theory. Surprisingly, we revealed that the melting of Pauli crystals is not simply a direct consequence of heating up the system, but is instead more related to the trap geometry, and to the population and behaviour of the time-periodic quantum states (Floquet states). We showed that the melting is absent in traps without imperfections and triggered only by a sufficiently large shaking amplitude in traps with imperfections.

Our study sheds light into the geometric and dynamical mechanisms that lead to melting and should help devise experimental protocols that prolong the lifetime of Pauli crystals. Reducing geometric distortions of the trap will substantially increase the stability and duration of the Pauli crystal phase. Our results also highlight that many-body correlations offer a very rich phenomenology to explore and that dynamical excitations play a crucial role for the stability of crystalline phases of matter of quantum gases.

The evolution of a Pauli crystal (star-like structure in panels a) as a function of time in a shaken optical trap. In a perfect harmonic trap, shown in the top panels, the Pauli crystal remains stable for a long time. In a trap with imperfections (such as anharmonicities), shown in the bottom panels, the crystals becomes progressively deformed and eventually loses its geometric structure – a phenomenon called melting.

PRL: Dipolar Bosonic Crystal Orders via Full Distribution Functions

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.093602

Quantum Simulation of Crystal Formation with Ultracol Dipolar Bosons

The quantum properties underlying crystal formation can be replicated and investigated with the help of ultracold atoms. Our recent paper in Physical Review Letters shows how the use of dipolar atoms enables even the realization and precise measurement of structures that have not yet been observed in any material.

Crystals are ubiquitous in nature. They are formed by many different materials – from mineral salts to heavy metals like bismuth. Their structures emerge because a particular regular ordering of atoms or molecules is favorable, because it requires the smallest amount of energy. A cube with one constituent on each of its eight corners, for instance, is a crystal structure that is very common in nature. A crystal’s structure determines many of its physical properties, such as how well it conducts a current or heat or how it cracks and behaves when it is illuminated by light. But what determines these crystal structures? They emerge as a consequence of the quantum properties of and the interactions between their constituents, which, however, are often scientifically hard to understand and also hard measure.

To nevertheless get to the bottom of the quantum properties of the formation of crystal structures, scientists can simulate the process using Bose-Einstein condensates – trapped ultracold atoms cooled down to temperatures close to absolute zero or minus 273.15 degrees Celsius. The atoms in these highly artificial and highly fragile systems are extremely well under control. With careful tuning, the ultracold atoms behave exactly as if they were the constituents forming a crystal. Although building and running such a quantum simulator is a more demanding task than just growing a crystal from a certain material, the method offers two main advantages: First, scientists can tune the properties for the quantum simulator almost at will, which is not possible for conventional crystals. Second, the standard readout of cold-atom quantum simulators are images containing information about all crystal particles. For a conventional crystal, by contrast, only the exterior is visible, while the interior – and in particular its quantum properties – is difficult to observe.

Our paper demonstrates that a quantum simulator for crystal formation is much more flexible when it is built using ultracold dipolar quantum particles. Dipolar quantum particles make it possible to realize and investigate not just conventional crystal structures, but also arrangements that were hitherto not seen for any material. The study explains how these crystal orders emerge from an intriguing competition between kinetic, potential, and interaction energy and how the structures and properties of the resulting crystals can be gauged in unprecedented detail.

Quantum Science and Technology: MCTDH-X software tutorial paper published

https://doi.org/10.1088/2058-9565/ab788b

We introduce and describe the multiconfigurational time-depenent Hartree for indistinguishable particles (MCTDH-X) software, which is hosted, documented, and distributed at http://ultracold.org.

We give an introduction to the MCTDH-X software via an easy-to-follow tutorial with a focus on accessibility. The illustrated exemplary
problems are hosted at http://ultracold.org/tutorial and consider the physics of a few interacting bosons or
fermions in a double-well potential.

A complete set of input files and scripts to redo all computations in this paper is provided at http://ultracold.org/data/tutorial_input_files.zip, accompanied by tutorial videos at https://tinyurl.com/tjx35sq

Read more at Quantum Science and Technology and arXiv.

RMP Colloquium on MCTDH-X et al.

https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.92.011001

In this Colloquium, the wavefunction-based Multiconfigurational Time-Dependent Hartree approaches to the dynamics of indistinguishable particles (MCTDH-F for Fermions and MCTDH-B for Bosons) are reviewed. MCTDH-B and MCTDH-F or, together, MCTDH-X are methods for describing correlated quantum systems of identical particles by solving the time-dependent Schrödinger equation from first principles.

We highlight some applications to instructive and experimentally-realized quantum many-body systems: the dynamics of atoms in Bose-Einstein condensates in magneto-optical and optical traps and of electrons in atoms and molecules.

We discuss the current development and frontiers in the field of MCTDH-X: theories and numerical methods for indistinguishable particles, for mixtures of multiple species of indistinguishable particles, the inclusion of nuclear motion for the nonadiabatic dynamics of atomic and molecular systems, as well as the multilayer and second-quantized-representation approaches, and the orbital-adaptive time-dependent coupled-cluster theory are discussed.