Final Report Summary - LIBEC (Light scattering in Bose Einstein Condensates)
In this project, we proposed to study the interplay between light and ultracold atoms, for which nor Doppler broadening nor collisions are important effects. In particular, we aimed to employ an experimental setup which combines a machine for the production of ultracold atomic samples with the tiny electron beam derived from a custom made electron scanning microscope. The objective was to have an insight on the emission process of the photons that should be released after electron-atom impact and on the basic mechanisms that can trap light in a dense vapour. The collision between high energy electrons and atoms can indeed lead to the excitation of dipole transitions. The excited atoms would emit photons by spontaneous emission and hence one resonant photon would be released to the surrounding cloud after each excitation. Some important features of the experiment at the University of Kaiserslautern are represented by the possibility to tune the temperature of the sample up and down the condensation critical temperature, to load the atoms in optical lattices with the possibility of independently changing the periodicity along each direction and the dimensionality of the sample, and finally to introduce point and line defects by means of the electron beam.
During the preliminary studies of the planned experiments, we discovered that the electron microscope could be an ideal tool to measure in situ the correlation properties of the atomic trapped clouds above and below the critical temperature and in different dimensionalities. Such experiments are not complicated by the time of flight expansion and directly manifest the properties of the many-body system. Moreover, if the detection method is only locally probing the system, even time-resolved correlation measurements are possible. In our first work, we reported on the first observation of temporal thermal bunching of ultracold bosonic atoms in a trap. The measurement of temporal local pair correlation functions in an ultracold quantum gas was a major breakthrough in the field of ultracold Bose gases. In subsequent experiments, we studied one-dimensional (1D) Bose gases in the crossover between the weakly (quasicondensate) and the strongly interacting (Tonks-Girardeau) regime. We measured the temporal two-particle correlation function and compared it with calculations performed using the time evolving block decimation algorithm. More pronounced antibunching is observed when entering the more strongly interacting regime. Even though this mimics the onset of a fermionic behaviour, we highlight that the exact and simple duality between 1D bosons and fermions does not hold when such dynamical response is probed. The onset of fermionisation is also reflected in the density distribution, which we measured in situ to extract the relevant parameters and to identify the different regimes. We have further investigated one-dimensional Bose gases by studying the thermodynamics in the strongly correlated regime. Thermodynamic studies of strongly interacting 1D gases would open new possibilities to investigate the interplay between non-equilibrium dynamics, thermalisation, and strong correlations in a quantum many-body system. We performed high-resolution in situ imaging of the column-integrated density distribution by means of the electron microscope. Using an inverse Abel transformation we derived effective 1D line-density profiles and compared them to exact theoretical models. The high resolution allowed for a direct thermometry of the trapped ensembles. The knowledge about the temperature enabled us to extract thermodynamic equations of state such as the phase-space density, the entropy per particle and the local pair correlation function.
The electron microscopy technique, which we have extensively characterized in this project, represents a powerful, fast, and efficient way to measure correlations, with the possibility to probe the system in space and time and particularly suited for systems of reduced dimensionality. Indeed this work paves the way to the study of complex dynamics as those resulting from quenches and to the investigation of thermalisation processes in 1D. Notably, pair correlations in time can give access to the dynamical structure factor and reveal, in contrast to static pair correlations, the dynamical properties of the quantum system.
During the preliminary studies of the planned experiments, we discovered that the electron microscope could be an ideal tool to measure in situ the correlation properties of the atomic trapped clouds above and below the critical temperature and in different dimensionalities. Such experiments are not complicated by the time of flight expansion and directly manifest the properties of the many-body system. Moreover, if the detection method is only locally probing the system, even time-resolved correlation measurements are possible. In our first work, we reported on the first observation of temporal thermal bunching of ultracold bosonic atoms in a trap. The measurement of temporal local pair correlation functions in an ultracold quantum gas was a major breakthrough in the field of ultracold Bose gases. In subsequent experiments, we studied one-dimensional (1D) Bose gases in the crossover between the weakly (quasicondensate) and the strongly interacting (Tonks-Girardeau) regime. We measured the temporal two-particle correlation function and compared it with calculations performed using the time evolving block decimation algorithm. More pronounced antibunching is observed when entering the more strongly interacting regime. Even though this mimics the onset of a fermionic behaviour, we highlight that the exact and simple duality between 1D bosons and fermions does not hold when such dynamical response is probed. The onset of fermionisation is also reflected in the density distribution, which we measured in situ to extract the relevant parameters and to identify the different regimes. We have further investigated one-dimensional Bose gases by studying the thermodynamics in the strongly correlated regime. Thermodynamic studies of strongly interacting 1D gases would open new possibilities to investigate the interplay between non-equilibrium dynamics, thermalisation, and strong correlations in a quantum many-body system. We performed high-resolution in situ imaging of the column-integrated density distribution by means of the electron microscope. Using an inverse Abel transformation we derived effective 1D line-density profiles and compared them to exact theoretical models. The high resolution allowed for a direct thermometry of the trapped ensembles. The knowledge about the temperature enabled us to extract thermodynamic equations of state such as the phase-space density, the entropy per particle and the local pair correlation function.
The electron microscopy technique, which we have extensively characterized in this project, represents a powerful, fast, and efficient way to measure correlations, with the possibility to probe the system in space and time and particularly suited for systems of reduced dimensionality. Indeed this work paves the way to the study of complex dynamics as those resulting from quenches and to the investigation of thermalisation processes in 1D. Notably, pair correlations in time can give access to the dynamical structure factor and reveal, in contrast to static pair correlations, the dynamical properties of the quantum system.