Project ABC: Origins of collectivity in few-body systems

Project Leaders: Tilman Enss, Selim Jochim, Silvia Masciocchi, Aleksas Mazeliauskas

Summary: Experiments with just ten interacting ultracold atoms released from an elliptic potential show the inversion of its aspect ratio, or elliptic flow — a key signature of collective behaviour. Within this project we would like to understand the physical mechanism of emerging collective dynamics in a few-atom system and relate this knowledge to similar collectivity observed in high-energy hadron collisions. For the first time in our CRC, we will bring experimentalists from two different fields to work on a common project. To underline the unifying character of this project, it was named ABC* — connecting all three project areas of CRC ISOQUANT. From far-from-equilibrium dynamics (A) initiated by the sudden release of a cold atom gas or the collisions of heavy ions emerges surprising collective behaviour normally associated to a hydrodynamic phase of matter (C). However, the observed buildup of correlations might also indicate the presence of an order parameter (B). Therefore, in order to understand the origins of collectivity in few-body fermion systems, we will need to combine the knowledge of isolated quantum systems in extreme conditions from different areas of the CRC. The ABC* program, linking theory and experiment, in cold quantum gases and in heavy-ion physics, is organised into four pillars:

ABC*-1 Experimental studies of collective phenomena with few ultracold fermions.

Measurements of two- particle correlations [ABC*.1] show that an initially almost unpaired strongly interacting sample becomes fully paired as the density drops. This indicates that the particle correlations and entanglement play an important role in the observed collective behaviour. In the first set of experiments, we will study multi-particle correlations for different fermion number and interaction strength using analysis techniques developed in collaboration with heavy-ion experimentalists (ABC*-2). Together with theorists in (ABC*-3) we will work towards an understanding of the pair formation process. We will also perform measurements of collective excitations in a trap as a precision tool to gain insight into the hydrodynamic behaviour of mesoscopic systems. Near equilibrium, they reveal essential parameters of hydrodynamics, such as shear and bulk viscosity [ABC*.2], which will be compared to theory (ABC*-3). Far from equilibrium, emerging macroscopic dynamics might be interpreted in different hydrodynamic frameworks, such as the hydrodynamic attractor (ABC*-4). In a quark-gluon plasma (QGP) produced in heavy-ion collisions, Hanbury Brown and Twiss correlations point to the freeze-out radius of the system. We aim to get a deeper understanding of freeze-out mechanisms from such measurements in ultracold atoms.d heavy-quark diffusion (A02-2) for pinning down the fundamental QCD transport properties.

ABC*-2 Multi-particle correlations in heavy-ion and cold-atom experiments.

Multi-particle azimuthal correla- tions are a powerful tool to study the evolution of hadron-hadron and heavy-ion collisions and to separate various sources of correlations, from few- to many-body, among the produced hadrons [ABC*.3]. We will bring the expertise of studying collectivity in hadron collisions [ABC*.4] to the analysis of cold-atom experiments (ABC*-1). The systematic comparison of experimental data to theory predictions (ABC*-3 and ABC*-4) will al- low us to constrain model parameters. Cold-atom experiments performed in (ABC*-1) have control over initial conditions and access to the time evolution, in a way which is not available in heavy-ion collisions. This will allow us to develop new observables and techniques, which could be later applied in heavy-ion experiments.

ABC*-3 Emergent bulk physics in few-to-many-atom systems.

The bulk properties in equilibrium are well characterised by the equation of state and dynamical response [ABC*.2, 5]. An important question is how well they describe the observed dynamics of strongly correlated few-particle systems (ABC*-1). Because these are already beyond the reach of exact diagonalisation, we will seek efficient theoretical descriptions in terms of fermions and pairs and explore whether slow decay of order parameter correlations can lead to robust collectivity even for small systems. We will compute how the equation of state and transport properties depend on short-range correlations and system size. Our results are the basis for hydrodynamic and kinetic simulations of observed collective behaviour (ABC*-2 and ABC*-4).

ABC*-4 Hydrodynamic attractors and transport in small systems.

The emergence of a hydrodynamic attractor — a universal far-from-equilibrium fluid behaviour — is one of the dominant explanations of the success of hydrodynamic models in heavy-ion collisions [ABC*.6]. Ultracold quantum gas experiments (ABC*-1) provide unique access to precisely investigate the applicability of different hydrodynamic frameworks in mesoscopic systems. Drawing on our experience in heavy-ion collisions [ABC*.7–9] and in collaboration with cold atom theory (ABC*-3) we will build kinetic and hydrodynamic descriptions of a few-fermion system. We aim to identify which features of collective behaviour (ABC*-2) can be effectively described by hydrodynamic attractor and transport even in small cold atom systems.