Michelle A Moreno Armijos

Understanding the relaxation dynamics of isolated quantum systems remains a central challenge in nonequilibrium physics. In this short review, we discuss recent experimental and theoretical advances in universal dynamics of turbulent Bose gases, with particular emphasis on nonthermal fixed points and wave turbulence in our experimental system at the São Carlos Institute of Physics of the University of São Paulo. We highlight the emergence of self-similar scaling behavior and its connection to particle and energy transport across momentum scales. In addition, we discuss an approach in which a differential equation has a universal scaling solution, providing a practical framework for extracting universal exponents from limited regions of the momentum distribution. Furthermore, we recap experimental observations of direct and inverse cascades in a three–dimensional trapped Bose–Einstein condensate, revealing distinct relaxation stages governed by universal scaling laws. These results demonstrate that turbulence plays a key role in far–from–equilibrium dynamics, offering a unified perspective on transport processes and thermalization in quantum many–body systems.

The dynamics of nonequilibrium closed quantum systems and their route to thermalization are of fundamental interest to several fields, from cosmology to particle physics. However, a comprehensive description of nonequilibrium phenomena still presents a significant challenge. In this work, we report the observation of distinct stages during the relaxation of the decaying turbulence in trapped Bose-Einstein condensates. Our findings show a direct particle cascade from low to high momenta, a consequence of the energy injection in the system, exhibiting a characteristic universal scaling. This stage is followed by an inverse particle cascade responsible for repopulating the previously depleted condensate. Both cascades can be explained through self-similar solutions provided by wave turbulence theory. These findings provide important insights into the relaxation stages of out-of-equilibrium quantum many-body systems.

Recent progress in out-of-equilibrium closed quantum systems has significantly advanced the understanding of mechanisms behind their evolution toward thermalization. Notably, the concept of nonthermal fixed points (NTFPs)—responsible for the emergence of spatiotemporal universal scaling in far-from-equilibrium systems—has played a crucial role in both theoretical and experimental investigations. In this work, we introduce a differential equation that has the universal scaling associated with NTFPs as a solution. The advantage of working with a differential equation, rather than only with its solution, is that we can extract several insightful properties not necessarily present in the solution alone. How the differential equation is derived allows physical interpretation of the universal exponents in terms of the time dependence of the amplitude of the distributions and their momentum scaling. Employing two limiting cases of the equation, we determined the universal exponents related to the scaling using the distributions near just two momentum values. We established a solid agreement with previous investigations by validating this approach with three distinct physical systems. This consistency highlights the universal nature of scaling due to NTFPs and emphasizes the predictive capabilities of the proposed differential equation. Moreover, under specific conditions, the equation predicts a power-law related to the ratio of the two universal exponents, leading to implications concerning particle and energy transport. This suggests that the observed power-laws in far-from-equilibrium turbulent fluids could be related to the universal scaling due to NTFPs, potentially offering insights into the study of turbulence.

We study the emergence of universal scaling in the time-evolving momentum distribution of a harmonically trapped three-dimensional Bose-Einstein condensate, parametrically driven to a turbulent state. We demonstrate that the out-of-equilibrium dynamics post excitation is described by a single function due to nearby nonthermal fixed points. The observed behavior connects the dynamics of a quantum turbulent state to several far-from-equilibrium phenomena. We present a controllable protocol to explore universality in such systems, obtaining the associated scaling exponents. Our experimental results thus offer a promising route to investigate the complex dynamics of the quantum turbulent regime.

Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and in time. In this work, we investigate the decaying regime of quantum turbulence in a trapped Bose-Einstein condensate. We present an alternative way of exploring this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. We reconstruct the three-dimensional momentum distributions with the inverse Abel transform, as we have done successfully in other works. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to intuitively visualize the time evolution of the turbulent state.

Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and time. The advances in trapping, cooling, and tuning the interparticle interactions in atomic Bose-Einstein condensates (BECs) make them excellent candidates for studying quantum turbulence. In this work, we investigate the decaying regime of quantum turbulence in a trapped BEC. Although much progress has been made in understanding quantum turbulence, other strategies are needed to overcome some intrinsic difficulties. We present an alternative way of investigating this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. One intrinsic difficulty related to these systems is that absorption images of BECs are projected to a plane, thus eliminating some of the information present in the original momentum distribution. We overcome this difficulty by exploring the symmetry of the cloud, which allows us to reconstruct the three-dimensional momentum distributions with the inverse Abel transform. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to visualize the time evolution of the turbulent state intuitively.