Periodic Reporting for period 1 - CriticalBoseBox (Critical behaviour of Bose gases with tuneable interactions in uniform box traps) Reporting period: 2019-04-01 to 2021-03-31 Summary of the context and overall objectives of the project The theory of quantum mechanics is fundamental for the description of the microscopic. Its understanding is vital for the details of chemical reactions, the development of novel materials, the accuracy of atomic clocks and the upcoming technological quantum revolution. But even after almost a century of research, many questions remain open, especially about the quantum mechanical behaviour of many interacting particles. For example, how exactly does a gas of classical colliding atoms turn into a quantum gas dominated by wave behaviour?In this project, we experimentally study this question with one of the most simple and best-controlled materials: A quantum gas; which is a gas of atoms less than a millionth of a degree above absolute zero, which is trapped in ultra-high vacuum by laser beams (see Figure). These artificial gases show almost unperturbed quantum behaviour and are thus an ideal platform to both study fundamental questions about quantum mechanics and to test potential quantum technologies. More precisely, we use ultracold potassium-39 atoms with tuneable interactions in a box trap to investigate the effect of interactions on the phase transition from a classical gas to a Bose-Einstein condensate; a phase, where a hundred thousand atoms form a macroscopic quantum wave. Of particular interest is the dynamical behaviour of our gas. In all ordinary materials, the microscopic processes (collisions between atoms) are much fast than macroscopic processes (e.g. sound waves, temperature changes). Thus, these systems are always close to an equilibrium. In dilute quantum gases, the situation is typically reversed because collisions are rare. But in our homogeneous trap, we can change the collision rate almost arbitrarily and thus connect both limits. Due to our geometry, we avoid loss processes that plague comparable experiments. This allows, on the one hand, to study the unexplored interplay of classical and quantum sound waves and, on the other hand, to generate exotic far-from-equilibrium states of matter. The overall objective of this experimental project is to study dynamics in interacting quantum gases related to the phase transition from a classical to a quantum system. Quantitative results are to serve as confirmations of established theories or as benchmarks for novel theoretical descriptions. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far During the project, we observed, for the first time, two speeds of sound in a quantum gas with moderate interactions. The measurement confirms that Lev Landau's theory of superfluidity (1941) not only applies to strongly interacting fluids but also to gases with large compressibility. This effect was experimentally confirmed in 1944 with superfluid Helium and now we found that the same is true for weakly interacting quantum gases at densities a trillion times lower.The surprising fact that there can be two speeds of sound in a single fluid is best understood by considering that a quantum fluid shows sound-like behaviour due to the wave nature of quantum mechanics. But any gas with sufficient interactions shows classical, hydrodynamic, sound waves. So interacting quantum gases have two types of sound waves: the classical plus the quantum sound. Those two sound waves travel at different speeds, thus one would hear a distant source twice. We measured the sound by exciting standing waves of our gas in a cylindrical container made from light. A crucial difference to earlier experiments with ultracold gases is that our system has a homogeneous density and thus the speed of sound does not vary in space. The second major result of the project is the observation of so-called spatio-temporal scaling far from equilibrium. By turning off all interactions in a classical gas of particles, we can create an initial state with many particles at intermediate momenta. Switching interactions back on, the system relaxes and redistributes the particles towards low and high momentum scales (long and short wavelength in the quantum description). Interestingly this relaxation is not exponential but the time-evolution instead shows self-similar behaviour, so after some time the system looks the same as before just on a different length scale. Finally, this self-similarity breaks down and the gas reaches an equilibrium state deep inside the quantum phase. Analysing this scaling, we found however experimentally that wave-like effects play a dominant role even long before the final quantum state is reached.In total, the project results in 5 scientific papers. One is published in Physical Review Letters, two are in the peer-review stage (Nature Physics and Physical Review Letters) and two are currently being written (October 2020). Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) The observation of the first sound (classical sound) in a Bose-Einstein-Condensate is a breakthrough as it allows to use quantum gases to study hydrodynamics. With our systems, we are in the unique situation that we can tune the collision rate between particles from zero to as high as quantum mechanics allows. It is thus possible to smoothly tune the ratio of internal to external timescales, which is described by the Knudsen number in classical fluid mechanics. This controls the viscosity and gives us a knob analogue to one that turns water into honey. In a first study, we showed that a description in terms of viscosity holds far beyond the classical range of Stokes-Kirchhoff damping. Future studies can thus test fundamental predictions also because ultracold gases can be probed very differently from traditional gases and fluids. For example, we are able to separate the quantum part of our gas from the classical one to observe their motion independently. The understanding of far-from-equilibrium systems is a large, open research front. As we have shown in our strong-quench study, isolated quantum gases are ideally suited to study such situations in a textbook setting. The fact that we see the self-similar behaviour supports the recent theory of non-thermal fix points, which found common principles in dynamics as different as cosmic inflation, experiments in colliders, and quantum gases. It gives hope that future research will be able to find so-called universality classes for such complex dynamics. If this holds, our lab-based experiments can provide quantitative support to the understanding of systems otherwise impossible to experiment on for example in astrophysics. To put it in an analogy to every-day systems: It is like finding common patterns in the dynamics of the weather and the evolution of the stock market. With these results, this project contributed to the deeper understanding of the quantum world and helped to pave the way for the quantum revolution in the next decades. The experiements are performed with ultracold atoms in a box-like potential
