Lattice Bose-Einstein Condensate Exhibits Anomalous Particle Number Fluctuations Near Phase Transition

Fluctuations are a fundamental aspect of physics, crucial for understanding how systems change and transition between states, and the formation of a Bose-Einstein condensate (BEC) is no exception. Zahra Jalali-Mola, from ICFO, The Barcelona Institute of Science and Technology, and Niklas Käming, from the University of Hamburg, lead a team that investigates these fluctuations in BECs created within optical lattices, a setting where previous experimental and theoretical work has been lacking. Combining experimental data from ultracold rubidium atoms with advanced numerical simulations, the researchers demonstrate unexpectedly strong fluctuations in the number of atoms within the condensate, scaling in a manner that differs from predictions for standard systems. This discovery, also involving contributions from Luca Asteria and colleagues at Kyoto University and ETH Zurich, reveals the significant influence of the trap geometry and atomic interactions on the mechanical properties of the condensate, offering new insights into the behaviour of matter at extremely low temperatures.

Combining theoretical techniques, including the Bogoliubov method and a master equation approach, with numerical simulations, the study models these complex quantum systems. Understanding these fluctuations is crucial for characterizing the stability and properties of BECs. A BEC isn’t composed entirely of atoms in the lowest energy state; some occupy excited states. The research focuses on variations in the number of atoms within the condensate itself and discovered that stronger interactions between atoms lead to larger fluctuations in the number of condensed atoms.

The master equation method, which accounts for atoms entering and leaving the condensate, provides a more accurate description of these fluctuations than simpler models. The temperature at which fluctuations peak shifts to lower temperatures as interactions strengthen, consistent with interactions reducing the number of condensed atoms at a given temperature. This research contributes to a deeper understanding of BECs and has implications for developing quantum technologies, such as quantum sensors and computers, where understanding and controlling fluctuations is essential. The findings also provide insights into the behavior of many-body systems, where interactions between particles are dominant.

Hybrid Theory Models Bose-Einstein Condensate Fluctuations

Researchers developed a novel theoretical approach to model fluctuations within a Bose-Einstein condensate held within a lattice structure. Combining experimental observations of rubidium atoms with sophisticated numerical simulations, the team addressed the challenge of accurately modelling particle number fluctuations, particularly during phase transitions. The approach combines the Bogoliubov quasiparticle framework, which describes the condensate as a classical field with quantum fluctuations, with a master equation analysis, treating non-condensed particles as a thermal reservoir. The Bogoliubov method alone struggles to capture the thermal behaviour of the system, especially near the critical temperature. Incorporating the master equation allows for a more realistic depiction of energy exchange and fluctuation evolution, providing a more accurate description of the condensate’s behaviour across a wide range of temperatures. This hybrid method proves particularly valuable in understanding anomalous fluctuations observed in experiments and offers a powerful new tool for studying the fundamental properties of BECs in lattice structures and exploring the interplay between quantum mechanics and thermal effects.

BEC Fluctuations in Triangular Optical Lattices

Researchers have uncovered unusual behaviour in the fluctuations of Bose-Einstein condensates created within triangular optical lattices, systems combining lattice structures with the quantum phenomena of BECs. These fluctuations, describing the variability in the number of particles within the condensate, deviate significantly from predictions for standard continuous systems. The study combines precise experimental measurements using ultracold rubidium atoms with advanced numerical simulations to provide a comprehensive understanding of this complex phenomenon. The research focused on a unique geometry where the BEC forms within a triangular array of tubes created by the optical lattice, confined by a weaker harmonic trap.

Surprisingly, the team discovered that the fluctuations in the condensate number do not scale as expected for purely two- or three-dimensional systems. Instead, the variance scales with an exponent of approximately 0. 62 experimentally and 0. 74 in simulations, falling between the predictions for 2D and 3D systems, suggesting the geometry of the lattice and resulting confinement significantly influence the fluctuations. Researchers employed a matter-wave microscope to precisely measure the density and temperature of the ultracold atoms, allowing them to extract the condensate fraction from each image. Simulations utilized a hybrid approach, combining the Bogoliubov quasiparticle framework with a master equation analysis. The close agreement between experimental and theoretical results validates the approach and reinforces the understanding of these unusual fluctuations, opening new avenues for exploring the fundamental properties of quantum matter in tailored lattice environments.

Anomalous Scaling in Triangular Lattice BECs

This research presents a combined experimental and theoretical investigation into fluctuations of the condensate particle number in a Bose-Einstein condensate held within a triangular lattice of tubes. The team discovered that these fluctuations exhibit anomalous scaling with the total atom number, meaning the variance does not change as predicted by simpler models. Specifically, the variance scales with an exponent of approximately 0. 74 from numerical simulations and 0. 62 from experimental data, differing from the values expected for non-interacting systems in either purely two- or three-dimensional lattices.

These findings are significant because they contribute to the ongoing debate regarding anomalous scaling behaviour in the thermodynamic limit, essentially, how these properties behave in large systems. The study demonstrates these anomalous fluctuations in a relatively large system of 30,000 atoms, strengthening the evidence for this behaviour. Future research directions include exploring BEC fluctuations in systems that exchange energy with a heat source, or where atom loss occurs, as well as extending the study to investigate local fluctuations or higher-order statistical properties. A deeper understanding of these fluctuations could also have implications for quantum metrology, potentially aiding the creation of entangled atom pairs for use in atom interferometers.