Bose-Einstein Condensates (BEC) are excellent macroscopic samples quantum behavior of matter study.Since it was experimentally observed in dilute atomic gases, there are important properties related to these systems that were intensely explored, as thermodynamic properties and BEC dynamics both in stationary and turbulent regime.In this work we present and discuss the results and properties determined from Bose-Einstein Condensed time-of-flight images processed using algorithms capable of extract relevant information from atomic density fluctuations observed in this kind of sample.Based on advanced data process we can go beyond the standard results, already presented, and obtain linear momentum maps, density fluctuations and correlations, vortices properties, as well as develop other analysis types to characterization and understanding improve results obtained in turbulent regime, besides other related properties.In this way, we developed specialized data processing library to be used in the general analyses and also to the determination of non-trivial properties, which are essential for the future study of quantum degenerate turbulent gases, with a three-dimensional atomic cloud reconstruction method from three non-orthogonal absorption images obtained from experimentally acquired time-of-flight images.In order to accomplish this we have used "three-dimensional inverse Radon Transform", analogous to tomography in the two-dimensional case, however, unlike the indetermination theorem requirement, that the number of images be large enough, we have just a few of them.This issue is lessened, but not solved, using an iterative correction method.
Bose-Einstein Condensates (BEC) are excellent macroscopic samples quantum behavior of matter study.Since it was experimentally observed in dilute atomic gases, there are important properties related to these systems that were intensely explored, as thermodynamic properties and BEC dynamics both in stationary and turbulent regime.In this work we present and discuss the results and properties determined from Bose-Einstein Condensed time-of-flight images processed using algorithms capable of extract relevant information from atomic density fluctuations observed in this kind of sample.Based on advanced data process we can go beyond the standard results, already presented, and obtain linear momentum maps, density fluctuations and correlations, vortices properties, as well as develop other analysis types to characterization and understanding improve results obtained in turbulent regime, besides other related properties.In this way, we developed specialized data processing library to be used in the general analyses and also to the determination of non-trivial properties, which are essential for the future study of quantum degenerate turbulent gases, with a three-dimensional atomic cloud reconstruction method from three non-orthogonal absorption images obtained from experimentally acquired time-of-flight images.In order to accomplish this we have used "three-dimensional inverse Radon Transform", analogous to tomography in the two-dimensional case, however, unlike the indetermination theorem requirement, that the number of images be large enough, we have just a few of them.This issue is lessened, but not solved, using an iterative correction method.
Bose-Einstein Condensates (BEC) are excellent macroscopic samples quantum behavior of matter study. Since it was experimentally observed in dilute atomic gases, there are important properties related to these systems that were intensely explored, as thermodynamic properties and BEC dynamics both in stationary and turbulent regime. In this work we present and discuss the results and properties determined from Bose-Einstein Condensed time-of-flight images processed using algorithms capable of extract relevant information from atomic density fluctuations observed in this kind of sample. Based on advanced data process we can go beyond the standard results, already presented, and obtain linear momentum maps, density fluctuations and correlations, vortices properties, as well as develop other analysis types to characterization and understanding improve results obtained in turbulent regime, besides other related properties. In this way, we developed specialized data processing library to be used in the general analyses and also to the determination of non-trivial properties, which are essential for the future study of quantum degenerate turbulent gases, with a three-dimensional atomic cloud reconstruction method from three non-orthogonal absorption images obtained from experimentally acquired time-of-flight images. In order to accomplish this we have used \"three-dimensional inverse Radon Transform\", analogous to tomography in the two-dimensional case, however, unlike the indetermination theorem requirement, that the number of images be large enough, we have just a few of them. This issue is lessened, but not solved, using an iterative correction method.
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.
In this thesis I present two different research topics investigated during the course of my PhD, regarding the analysis of spatial structures in a Bose Einstein condensate. Ultracold atomic gases offer a privileged platform for such kind of experiments, thanks to the fine control that can be achieved on the system’s parameters and to the availability of advanced imaging schemes allowing for a great measurement accuracy. \nThe first topic is about the shape of quantized vortices in an elongated condensate, with the goal of providing a quantitative analysis of the density structure of a quantized vortex filament hosted in a bulk 3D superfluid. We analyzed the shape of the vortex and studied its dynamics during a free expansion, or time of flight (TOF), of the hosting BEC, with the goal of making a quantitative comparison between theory and experiment for the structure of the core of a quantized vortex in three-dimensional (3D) condensates. Simultaneously imaging the sample along orthogonal directions after a long TOF allowed to map the complete 3D shape of the vortex at the end of the free flight, while the full expansion dynamics has been simulated with numerical solutions of the Gross-Pitaevskii equation. The same data analysis procedure has been applied to both the experimental images and to the density profiles computed with the simulations to ensure a faithful comparison. \nWe were able to detail the evolution of the vortex parameters at all times combining a simple analytic scaling-law model valid at early times, experimental data for the width and the depth of the core at long expansion times, and the numerics that were used to bridge between the two. Additionally, we could check the validity of the predictions on the scaling of vortex parameters with the size of the BEC using the experimental data to interpolate between theoretical limiting models. We concluded that quantized vortex filaments can be optically imaged with standard techniques in 3D atomic BECs, at a level of accuracy which indeed is enough to show good quantitative agreement with the predictions of the GP theory for the width, depth, and overall shape of the vortex core. \nThe second topic is a measurement of the equation of state of a single component BEC. The goal of this project is to verify the non-monotonic behaviour of the chemical potential of a homogeneous Bose gas of weakly interacting particles as a function of temperature, where one expects to find a maximum across the critical point of transition to the superfluid phase. This effect is believed to be a general feature of the normal-to-superfluid phase transition: it has been already experimentally demonstrated in unitary Fermi gases, and although the same is predicted to happen also in a gas of weakly interacting bosons, no experimental evidence has been reported so far. The measurement relies on the local density approximation, which allows to extract information about the thermodynamics of a homogeneous system from accurate measurements of the local properties of a trapped one. My work has focused on developing a series of imaging and data analysis techniques to measure the 3D density profile of a harmonically trapped gas, even in regimes of extreme density such as inside a Bose condensate. With a new high-dynamic-range method we were able to image the 3D density distribution of a trapped sample, leading to a low-noise measurement of the density distribution. \nWe confirmed the existence of the non-monotonic behaviour of the chemicial potential across, and set the basis for further measurements of the thermodynamics of the system across the transition.In this thesis I present two different research topics investigated during the course of my PhD, regarding the analysis of spatial structures in a Bose Einstein condensate. Ultracold atomic gases offer a privileged platform for such kind of experiments, thanks to the fine control that can be achieved on the system’s parameters and to the availability of advanced imaging schemes allowing for a great measurement accuracy. \nThe first topic is about the shape of quantized vortices in an elongated condensate, with the goal of providing a quantitative analysis of the density structure of a quantized vortex filament hosted in a bulk 3D superfluid. We analyzed the shape of the vortex and studied its dynamics during a free expansion, or time of flight (TOF), of the hosting BEC, with the goal of making a quantitative comparison between theory and experiment for the structure of the core of a quantized vortex in three-dimensional (3D) condensates. \nSimultaneously imaging the sample along orthogonal directions after a long TOF allowed to map the complete 3D shape of the vortex at the end of the free flight, while the full expansion dynamics has been simulated with numerical solutions of the Gross-Pitaevskii equation. The same data analysis procedure has been applied to both the experimental images and to the density profiles computed with the simulations to ensure a faithful comparison. \nWe were able to detail the evolution of the vortex parameters at all times combining a simple analytic scaling-law model valid at early times, experimental data for the width and the depth of the core at long expansion times, and the numerics that were used to bridge between the two. Additionally, we could check the validity of the predictions on the scaling of vortex parameters with the size of the BEC using the experimental data to interpolate between theoretical limiting models. We concluded that quantized vortex filaments can be optically imaged with standard techniques in 3D atomic BECs, at a level of accuracy which indeed is enough to show good quantitative agreement with the predictions of the GP theory for the width, depth, and overall shape of the vortex core. \nThe second topic is a measurement of the equation of state of a single component BEC. The goal of this project is to verify the non-monotonic behaviour of the chemical potential of a homogeneous Bose gas of weakly interacting particles as a function of temperature, where one expects to find a maximum across the critical point of transition to the superfluid phase. This effect is believed to be a general feature of the normal-to-superfluid phase transition: it has been already experimentally demonstrated in unitary Fermi gases, and although the same is predicted to happen also in a gas of weakly interacting bosons, no experimental evidence has been reported so far. The measurement relies on the local density approximation, which allows to extract information about the thermodynamics of a homogeneous system from accurate measurements of the local properties of a trapped one. My work has focused on developing a series of imaging and data analysis techniques to measure the 3D density profile of a harmonically trapped gas, even in regimes of extreme density such as inside a Bose condensate. With a new high-dynamic-range method we were able to image the 3D density distribution of a trapped sample, leading to a low-noise measurement of the density distribution. \nWe confirmed the existence of the non-monotonic behaviour of the chemicial potential across, and set the basis for further measurements of the thermodynamics of the system across the transition.
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.
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.
Dilute gas Bose-Einstein condensates (BECs) provide unique and powerful experimental platforms to study fluid turbulence. Some aspects of BEC hydrodynamics are specific to atomic quantum fluids such as quantized vortices and flexible trapping geometries. However, there are features of turbulence that are universal and simpler to understand in such systems. BECs are also of interest in fundamental physics in their own right and a rich synthesis of theory and experiment has yielded powerful numerical methods to simulate and study BEC dynamics. In this dissertation I present two experiments, one conducted and one proposed, describing novel aspects of the generation and detection of vorticity in Bose-Einstein condensates. Models of BEC dynamics at zero temperature are provided by the Gross-Pitaevskii equation. Simple and fast numerical solutions of this equation have yielded a wealth of literature. However, in experimental reality the atomic ensemble exists at a finite temperature and consists of a BEC coexisting with a thermal cloud of non-condensed atoms. The interaction between the condensate and the thermal fraction yields rich and complex physics that require more advanced models. We present an experiment demonstrating the relaxation dynamics of a BEC in a rotating trap perturbed by a repulsive laser barrier. The data provided by this experiment are valuable to further development of theoretical models that incorporate interactions between the BEC and noncondensed atoms. In the field of quantum fluid dynamics, an experimental method to determine the position and circulation of vortices is a highly sought-after capability. Onsager's point-vortex model of turbulence completely determines the kinetic energy spectrum of an incompressible fluid by these degrees of freedom. We present proof-of-principle simulations that describe a new method of spatially sampling the velocity field of a two-dimensional BEC by using an optical lattice analogously to a Shack-Hartmann Wavefront Sensor. Extracting vortex information from the appropriately sampled velocity field can be accomplished either qualitatively or with detection algorithms. This method requires minimal experimental infrastructure and is generally applicable across atomic species. The implications of measuring a condensate velocity field are broad and these initial results provide the first step towards realizing a valuable tool in BEC physics.