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.
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.
From almost one century, Bose-Einstein condensation has become progressively more important especially due to its connection with superfluidity, superconductivity and manybody physics. Nowadays quantum gases are powerful experimental tools to discover new physics and to emulate systems in condensed matter due to their versatility and very high control. Despite the increasing use of quantum gases as platforms for studying many problems in physics, their comprehension is very limited if we consider systems that are out-of-equilibrium due to the lack of experimental controllability of all the parameters involved in these systems. Another limitation in the understanding of this kind of systems comes from the limitation of the theoretical frameworks used to understand non-equilibrium dynamics, although many efforts have been made in this direction. Hence, many interesting phenomena in non-equilibrium quantum systems have not yet been discovered or well understood from a theoretical and experimental point of view, and thus its physics have not been the focus of much attention, although this situation has recently changed due to the rapid development of experimental techniques which enables a better control of parameters of these systems. Motivated by this progress, we study non-equilibrium Bose gases in the search of turbulence using an oscillatory excitation performed in a Bose-Einstein condensate of 87Rb atoms. In this thesis, we describe these experiments and characterize our non-equilibrium quantum system through some quantifiers. One of these quantifiers is a dimensionless value that represent the exponent γ obtained from the cascade of the transverse momentum distribution ñ(k). ñ(k) is obtained from absorption images of atoms in expansion using the time-of-flight technique in a well defined range of momenta. We analyze the dependence of γ with the amount of the pumped energy, and we found a steady-value which describe a well-established non-equilibrium regime. Also, it is analyzed the viability of using the fluctuations statistics in order to extract some quantifier from the power-spectrum of the fluctuations assuming that it represents an analog to the energy spectrum, due to the consideration of the time-of-flight technique. From the powerspectrum it is extracted an exponent, in the same range as for ñ(k), and compared with γ 2, that will be the exponent for the pseudo-energy spectrum in the kinetic dominated regime. Finally, we consider, again with the time-of-flight technique, the continuous Shannon entropy as quantifier that measure the disorder of the excited clouds and study their dependence with the pumped energy. These studies show us that there is an out-ofequilibrium regime that takes place when we inject a fixed quantity of energy into the system.
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.
From almost one century, Bose-Einstein condensation has become progressively more important especially due to its connection with superfluidity, superconductivity and manybody physics. Nowadays quantum gases are powerful experimental tools to discover new physics and to emulate systems in condensed matter due to their versatility and very high control. Despite the increasing use of quantum gases as platforms for studying many problems in physics, their comprehension is very limited if we consider systems that are out-of-equilibrium due to the lack of experimental controllability of all the parameters involved in these systems. Another limitation in the understanding of this kind of systems comes from the limitation of the theoretical frameworks used to understand non-equilibrium dynamics, although many efforts have been made in this direction. Hence, many interesting phenomena in non-equilibrium quantum systems have not yet been discovered or well understood from a theoretical and experimental point of view, and thus its physics have not been the focus of much attention, although this situation has recently changed due to the rapid development of experimental techniques which enables a better control of parameters of these systems. Motivated by this progress, we study non-equilibrium Bose gases in the search of turbulence using an oscillatory excitation performed in a Bose-Einstein condensate of 87 Rb atoms. In this thesis, we describe these experiments and characterize our non-equilibrium quantum system through some quantifiers. One of these quantifiers is a dimensionless value that represent the exponent obtained from the cascade of the transverse momentum distribution ( ). ( ) is obtained from absorption images of atoms in expansion using the time-of-flight technique in a well defined range of momenta. We analyze the dependence of with the amount of the pumped energy, and we found a steady-value which describe a well-established non-equilibrium regime. Also, it is analyzed the viability of using the fluctuations statistics in order to extract some quantifier from the power-spectrum of the fluctuations assuming that it represents an analog to the energy spectrum, due to the consideration of the time-of-flight technique. From the powerspectrum it is extracted an exponent, in the same range as for ( ), and compared with -2, that will be the exponent for the pseudo-energy spectrum in the kinetic dominated regime. Finally, we consider, again with the time-of-flight technique, the continuous Shannon entropy as quantifier that measure the disorder of the excited clouds and study their dependence with the pumped energy. These studies show us that there is an out-ofequilibrium regime that takes place when we inject a fixed quantity of energy into the system.
Turbulence is a young field of research which is characterized by chaotic spinning flow regimes which appears in many important processes in nature. Vorticity, in superfluid systems, may present the simplest form of turbulence, and be a gateway to the study of this phenomenon in quantum gases. A 87Rb Bose condensate was used to observe and investigate the emergence of quantum turbulence, a few years back in our group. The vortices are created on the condensed-thermal interface and propagate across the cloud, setting up the experimental conditions favorable to the emergence of turbulence. Once the turbulent regime is set, the condensate is released and expands under free fall. Then, the atomic density profile is acquired, after some time-of-flight, and used to determine the in situ momentum distribution of the BEC. In this work, we have observed that, the perturbed density profiles are characteristic and different from the standard, non-perturbed ones. We have seen evidences of power law in the studied momentum and energy distributions and also coupling of quadrupolar mode to the momentum distribution of the excited condensate which is the main part of our findings. Additional features of the system, such as the condensates excited collective modes which plays a very important role on the roadmap to the turbulence regime, are discussed. We are currently setting up an experiment to be able to further investigate such features, and also to unfold the effects of interactions on the energy and momentum spectra associated to the density profiles. In doing so, we will further develop the tools and techniques needed to acquire more accurate and reliable results.
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.
Turbulence is a young field of research which is characterized by chaotic spinning flow regimes which appears in many important processes in nature. Vorticity, in superfluid systems, may present the simplest form of turbulence, and be a gateway to the study of this phenomenon in quantum gases. A 87Rb Bose condensate was used to observe and investigate the emergence of quantum turbulence, a few years back in our group. The vortices are created on the condensed-thermal interface and propagate across the cloud, setting up the experimental conditions favorable to the emergence of turbulence. Once the turbulent regime is set, the condensate is released and expands under free fall. Then, the atomic density profile is acquired, after some time-of-flight, and used to determine the in situ momentum distribution of the BEC. In this work, we have observed that, the perturbed density profiles are characteristic and different from the standard, non-perturbed ones. We have seen evidences of power law in the studied momentum and energy distributions and also coupling of quadrupolar mode to the momentum distribution of the excited condensate which is the main part of our findings. Additional features of the system, such as the condensates excited collective modes which plays a very important role on the roadmap to the turbulence regime, are discussed. We are currently setting up an experiment to be able to further investigate such features, and also to unfold the effects of interactions on the energy and momentum spectra associated to the density profiles. In doing so, we will further develop the tools and techniques needed to acquire more accurate and reliable results.