Atomic Simulator Reveals Universal Behaviour Across Dimensions and Temperature.

The behaviour of physical systems changes markedly with dimensionality, a principle central to diverse fields from particle physics to materials science. Understanding how systems transition between dimensionalities, and the resulting emergent properties, remains a significant challenge. Researchers at Peking University and the University of Geneva now present findings concerning the universal phase diagram governing this dimensional crossover, utilising a novel atomic quantum simulator. Jinyuan Tian, Zhongcheng Yu, Jing Liu, Chi-Kin Lai, Lorenzo Pizzino, Chengyang Wu, Hongmian Shui, Thierry Giamarchi, Hepeng Yao, and Xiaoji Zhou detail their work in the article, “Probing universal phase diagram of dimensional crossover with an atomic quantum simulator”, demonstrating a tunable system capable of revealing regimes from three to zero dimensions and, crucially, identifying a thermal regime existing between integer dimensional states. Their results offer fundamental insights into the behaviour of complex systems in unconventional dimensions and provide a basis for exploring novel condensed matter phenomena.

Research details an investigation into the behaviour of interacting atoms within precisely controlled, low-dimensional environments, establishing a comprehensive diagram charting dimensional crossover. Researchers utilise a novel atomic simulator, allowing continuous adjustment of both anisotropy and temperature, to explore the transition from three-dimensional to zero-dimensional behaviour. This confirms that reducing dimensionality amplifies fluctuations and induces emergent properties, a principle central to condensed matter physics and other fields. The study meticulously examines how interactions between atoms change as they are confined to lower dimensions, providing valuable insights into the fundamental physics governing these systems.

The experiment centres on manipulating ultracold atoms trapped within optical lattices, created by interfering laser beams. Scientists effectively control the dimensionality of the lattice by altering laser intensities, transitioning the atomic gas from a three-dimensional configuration through two and one-dimensional states, ultimately reaching a quasi-condensate or thermal state. Measurements focus on the zero-momentum fraction ($f_c$), a key indicator of superfluidity and phase transitions, representing the proportion of atoms occupying the lowest momentum state. Consistent demonstration of identical phase transition points across the x and y planes simplifies analysis and confirms the reliability of the experimental setup. The team carefully controls the temperature and interaction strength, allowing them to map out the phase diagram and identify the different quantum phases.

Analysis reveals a clear progression through distinct regimes as temperature increases. At low temperatures, the system exhibits behaviour characteristic of three, two, and zero dimensions. Crucially, the research identifies a non-trivial thermal regime existing between these integer and zero-dimensional states, challenging conventional expectations and opening new avenues for exploration. The team meticulously investigates this new regime, characterizing its properties and identifying the underlying mechanisms responsible for its occurrence.

Analysis of the momentum distribution, utilising time-of-flight imaging – a technique where the expansion of the atomic cloud after release from the trap is observed – and measurements of the zero-momentum fraction, provides a robust method for determining the critical points at which dimensional crossover occurs. The consistency of measurements along different lattice directions validates the chosen experimental approach and confirms the symmetry of the system. Piecewise fitting of the data, alongside comparison with harmonic oscillator models, further strengthens the accuracy of the determined critical points.

The study identifies four distinct universality classes governing the transition from the zero-dimensional to the thermal regime, categorizing behaviours based on dimensionality and interaction strength. A universality class describes the collective behaviour of a system near a critical point, where the system exhibits scale invariance. Notably, the research also uncovers a fifth, unexpected universality class where the system accesses the thermal regime via a transition through a lower-dimensional phase, challenging conventional expectations. This suggests a more complex interplay between dimensionality and thermalisation than previously understood.

These findings have significant implications for understanding the behaviour of strongly correlated systems in condensed matter physics, where interactions between electrons play a crucial role. The ability to control and manipulate dimensionality opens up new possibilities for designing novel quantum materials. The research also provides valuable insights into the fundamental physics governing low-dimensional systems, and the team plans to extend this work to explore other types of interactions and geometries. This research represents a significant step forward in our understanding of quantum many-body systems.