Indian Institute of Technology Mandi: Researchers Model Vortex Formation in Bose-Einstein Condensation with Stochastic Processes

Scientists Subhadeep Patra and colleagues at the Indian Institute of Technology Mandi, in collaboration with the Institute of Nanotechnology, have demonstrated universality in the spatial arrangement of topological defects formed during the nonequilibrium condensation of coherently coupled Bose gases. The team employed the stochastic projected Gross-Pitaevskii equation, a powerful theoretical framework, to model the behaviour of these defects, demonstrating that their positions conform to a Poisson point process and exhibit predictable Voronoi tessellation statistics. These findings extend beyond the conventional Kibble-Zurek mechanism, identifying a universal stochastic geometry as a key characteristic of nonequilibrium condensation and offering new insights into the behaviour of these quantum systems, potentially impacting future quantum technologies.

Kibble-Zurek scaling predicts defect density and reveals Poisson point process geometry in Bose

Defect densities now reach a predicted value of ρKZM ∝τ^−1/2 Q, representing a significant improvement over previous limitations that struggled to accurately characterise defect formation in two-dimensional systems. The Gross-Pitaevskii equation, a cornerstone of Bose-Einstein condensate (BEC) theory, was adapted to include stochastic noise, accurately representing the inherent randomness of the quench process. This stochastic projected version allows for the modelling of vortex nucleation, the creation of topological defects, during the symmetry-breaking transition induced by the rapid change in chemical potential. The Kibble-Zurek mechanism (KZM) posits that the density of these defects is inversely proportional to the square root of the quench time (τ), with ‘Q’ representing a system-specific parameter. Previous studies often relied on mean-field approximations, which failed to capture the crucial fluctuations influencing defect formation. This research demonstrates a clear link between quench time and the density of topological defects, validating the KZM with increased precision.

The researchers from the Indian Institute of Technology Mandi and CNR NANOTEC demonstrated that both elementary and composite defects within coherently coupled Bose gases follow a Poisson point process, revealing a previously unknown universal stochastic geometry. A Poisson point process describes a random distribution of points where the probability of finding a point in a given area is proportional to the area itself, implying that defects are distributed independently and randomly, yet with a consistent average density. This contrasts with ordered or correlated defect arrangements. The team also introduced a spatial form factor, a mathematical tool used to map vortex configurations, identifying a characteristic dip-ramp-plateau structure indicative of consistent spatial organisation despite the underlying randomness. Analysis of Voronoi tessellation, a computational geometry method of dividing space into areas around each defect (Voronoi cells), revealed predictable statistical patterns in the size of these areas, providing further evidence for this consistent arrangement. Specifically, the distribution of Voronoi cell areas exhibited characteristics consistent with a Poisson-tessellated random field, reinforcing the observed universality.

However, the current analysis does not yet bridge the gap between these fundamental observations and the creation of practical, controllable quantum devices. While understanding defect formation is crucial for manipulating quantum states, translating this knowledge into functional devices requires further research into controlling the quench parameters and defect interactions. This work provides a valuable baseline for understanding how topological defects, or flaws in a material’s structure, arrange themselves during phase transitions. The researchers explored a limited range of conditions and focused on Bose gases, but the established Kibble-Zurek mechanism does not fully explain defect formation, particularly concerning the observed stochastic geometry. Further investigation is needed to determine if this observed stochastic geometry extends to other systems undergoing similar phase transitions, such as those found in condensed matter physics or cosmology, and to explore a wider range of parameters, including different inter-component coupling strengths and dimensionality.

Random defect placement challenges established phase transition theory

A predictable arrangement of topological defects is vital for manipulating quantum systems and potentially building future technologies, such as robust quantum memories or topological quantum computation platforms. Observing a universal randomness in defect placement, characterised by the Poisson point process, extends beyond the established Kibble-Zurek mechanism, although this work focused on coherently coupled Bose gases. The KZM primarily predicts defect density, not their precise spatial arrangement. This raises whether these findings extend to other systems undergoing similar phase transitions, and the abstract acknowledges a limited exploration of parameter ranges, potentially restricting the broad applicability of this newly identified stochastic geometry. Investigating systems with different symmetry groups or dimensionality could reveal deviations from the observed universality.

The spatial positioning of both individual and combined defects adheres to a Poisson point process, establishing a universal stochastic geometry previously unrecognised in these systems. These defects, imperfections at the quantum level, do not simply appear randomly but follow a distinct, predictable pattern in terms of their statistical distribution, as the team identified a key principle governing their arrangement within Bose gases undergoing condensation. This finding details how these defects organise themselves in space, extending beyond the conventional theory previously used to predict defect density. The implications of this work are significant because it suggests that the spatial correlations between defects are weaker than previously assumed, potentially simplifying the modelling of complex quantum systems. Understanding the statistical properties of these defects is crucial for predicting the overall behaviour of the condensate and for designing experiments to control and manipulate these quantum states. This research provides a foundation for exploring the interplay between topological defects and quantum coherence, potentially leading to novel quantum phenomena and applications.

The research demonstrated that the spatial arrangement of topological defects in coherently coupled Bose gases follows a Poisson point process, revealing a universal stochastic geometry. This means the positioning of these defects, imperfections within the quantum system, is statistically random but adheres to a predictable pattern, extending beyond existing theories that only predicted defect density. Researchers analysed the arrangement of both individual and combined defects, identifying a principle governing their spatial organisation during the condensation process. The findings suggest weaker spatial correlations between defects than previously thought, which may simplify the modelling of complex quantum systems.