Relaxation of an out-of-equilibrium closed quantum systems: experimental observations of decay of turbulence and the stages to reach equilibrium
Vanderlei Salvador Bagnato, Michelle M. Amijos, A. R. Fritsch, Arnol Daniel Garcia Orozco, Sarah Sab, Leandro S. Machado, Lucas Madeira, M. A. Caracanhas
Starting with a Bose-Einstein Condensate of Rb atoms in equilibrium, the System is brought to turbulence and left to relax under the occurrence of reactions from the introduced excitations. The typical phenomena of the evolution to establishment of the turbulence states are observed. After excitation is removed, the system begins to relax, giving way to diverse phenomena such as the presence of non-thermal fixed points, pre-thermalization and finally equilibrium with or without the reconstitution of the condensate depending of the quantity of injected energy. The work paves the way for the study of the thermalization of an out-of-equilibrium many-body quantum system.
Starting with a Bose-Einstein Condensate of Rb atoms in equilibrium, the System is brought to turbulence and left to relax under the occurrence of reactions from the introduced excitations. The typical phenomena of the evolution to establishment of the turbulence states are observed. After excitation is removed, the system begins to relax, giving way to diverse phenomena such as the presence of non-thermal fixed points, pre-thermalization and finally equilibrium with or without the reconstitution of the condensate depending of the quantity of injected energy. The work paves the way for the study of the thermalization of an out-of-equilibrium many-body quantum system.
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.
Investigating the initial conditions that lead many-body quantum systems to an out-of-equilibrium state is fundamental for understanding their thermalization dynamics. In this work we observe the relaxation for two regimes of excitation that can drive the turbulent Bose-Einstein condensate into two distinct final states, and are defined by the amount of energy injected into the system. The subcritical regime is characterized by a lower injection of energy, which can lead to an inverse particle cascade and, consequently, to the BEC mode repopulation during the relaxation process. The supercritical regime is marked by a higher energy injection, that may lead to the BEC dissolution and a final thermal state. In both cases we observe relaxation stages that exhibit the same key features: a direct cascade, a non-thermal fixed point with the same exponents, a prethermalization region and, finally, the thermalization of the system. In the final thermalization stage, universal scaling is observed for both regimes, even though their final states are completely different. By analyzing the coherence length of our turbulent cloud, we clearly visualize the recovery and the loss of the coherence for the subcritical and supercritical regimes after relaxation. These results indicate that the evolution of turbulence occurs independent of its initial conditions and of the final state achieved.
Abstract 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 study of quantum systems out of thermal equilibrium is currently a topic of great interest and constitutes one of the frontiers of knowledge. Bose-Einstein condensate is considered a fundamental quantum system in this context. In this thesis, the Bose-Einstein condensate of 87Rb is used to study an out-of-equilibrium system that is reached using mechanics excitations. The turbulent state is achieved through these excitations in the magnetic trap that confines the cloud. The characterization of the system is made through the momentum distribution obtained by absorption image technique in time of flight. Physical quantities such as energy flux, entropy, and length scale were calculated to help characterize the turbulence state, which is generally characterized by the appearance of a power-law in momentum distribution. The energy flux is constant within the inertial region, where the power-law appears, which is the initial indication of turbulence in the system. The entropy per particle increases rapidly when the system achieves the turbulence state, and the scale length shows the evolution of the establishment of the quantum turbulence regimen. Another topic investigated is the so-called non-thermal fixed points. In these points, where the system remains out of equilibrium but evolves according to certain special laws of scale, the system can be said to belong to a particular universality class. A single function describes the dynamics post excitation due to nearby non-thermal fixed points characterized by two exponents, which allows predicting the temporal evolution of the momentum distribution. This class of phenomena opens up new research possibilities in the quantum world out of thermal equilibrium.
We investigate the emergence and evolution of turbulence in Bose-Einstein condensates driven far from equilibrium through a controlled energy injection. By applying a timeperiodic modulation for a fixed duration, we trigger nonequilibrium dynamics that lead to the formation of a turbulent state characterized by a complex distribution of excitations and density fluctuations. Our study focuses on the post-excitation relaxation process, where we observe a transient broadening of the momentum distribution: a signature of a direct energy cascade followed by an inverse particle cascade due to the nonlinear intra-scales energy transfer. Through systematic analysis based on the nonthermal fixed points and weak wave turbulence theories, we identify universal scaling laws governing the repopulation dynamics of the condensate. These findings advance our understanding of turbulent relaxation pathways in superfluids while enhancing the understanding of driven-dissipative quantum systems.
Quantum turbulence deals with the phenomenon of turbulence in quantum fluids, such as superfluid helium and trapped Bose-Einstein condensates (BECs). Although much progress has been made in understanding quantum turbulence, several fundamental questions remain to be answered. In this work, we investigated the entropy of a trapped BEC in several regimes, including equilibrium, small excitations, the onset of turbulence, and a turbulent state. We considered the time evolution when the system is perturbed and let to evolve after the external excitation is turned off. We derived an expression for the entropy consistent with the accessible experimental data, which is, using the assumption that the momentum distribution is well-known. We related the excitation amplitude to different stages of the perturbed system, and we found distinct features of the entropy in each of them. In particular, we observed a sudden increase in the entropy following the establishment of a particle cascade. We argue that entropy and related quantities can be used to investigate and characterize quantum turbulence.