This thesis reports on experiments with few-fermion systems in quasi one dimensional confining potentials with tunable interaction. \nUsing ultracold atoms we prepare these systems in a well defined quantum state with fidelities of 90% for up to 8 particles. The interparticle interaction in the 1D environment can be effectively described by a 1D contact interaction where the coupling strength can be tuned with a confinement induced resonance (CIR). \nWe investigate a system of two repulsively interacting distinguishable fermions and compare it to a system of two identical noninteracting fermions. For diverging coupling strength we show the fermionization of two distinguishable fermions, i.e. we observe the energy and the square modulus of the wavefunction of both system to be identical. We also perform radio frequency spectroscopy to measure the energy of a single minority particle interacting repulsively with a defined number of majority particles of different spin. We study the crossover from a few-particle system to a many-particle system by adding majority particles one by one. \nWe observe that already four majority particles are enough to describe the properties of the minority by that of a polaron-like particle, i.e. by a single impurity dressed by a 1D Fermi sea. \nInvestigating attractively interacting systems we observe that for increasing interaction strength the pair correlations in the system increases. This correlation leads to a strong odd-even effect of the single particle dissociation energy similar to the one observed for nuclei.
This thesis reports on experiments with few-fermion systems in quasi one dimensional confining potentials with tunable interaction. \nUsing ultracold atoms we prepare these systems in a well defined quantum state with fidelities of 90% for up to 8 particles. The interparticle interaction in the 1D environment can be effectively described by a 1D contact interaction where the coupling strength can be tuned with a confinement induced resonance (CIR). \nWe investigate a system of two repulsively interacting distinguishable fermions and compare it to a system of two identical noninteracting fermions. For diverging coupling strength we show the fermionization of two distinguishable fermions, i.e. we observe the energy and the square modulus of the wavefunction of both system to be identical. We also perform radio frequency spectroscopy to measure the energy of a single minority particle interacting repulsively with a defined number of majority particles of different spin. We study the crossover from a few-particle system to a many-particle system by adding majority particles one by one. \nWe observe that already four majority particles are enough to describe the properties of the minority by that of a polaron-like particle, i.e. by a single impurity dressed by a 1D Fermi sea. \nInvestigating attractively interacting systems we observe that for increasing interaction strength the pair correlations in the system increases. This correlation leads to a strong odd-even effect of the single particle dissociation energy similar to the one observed for nuclei.
This thesis reports on experimental studies exploring few and many-body physics of ultracold \nBose and Fermi gases with reduced dimensionality. These experiments illustrate the versatility \nand great amount of control over the particle number, the interaction and other degrees of \nfreedom, like the spin, that these generic quantum systems offer. In the first part of this \nthesis, we use quasi one-dimensional few-particle systems of one to ten fermionic atoms to \ninvestigate the crossover from few to many-body physics. This is achieved by measuring the \ninteraction energy between a single impurity atom in a state |down> which repulsively interacts \nwith an increasing number of majority atoms in a state |up>. We find that the system quickly \napproaches the results from the many-body theory, which describes the behavior of a single \nimpurity immersed in a Fermi sea of an infinite number of majority particles. The second \npart of this thesis presents studies of the time evolution of a bosonic F=1 spinor BEC of 87Rb \natoms. In this system, we investigate the emergence and coarsening of ferromagnetic spin \ntextures from initially unmagnetized samples. While the ferromagnetic domains grow, we \nobserve the development of a spin space anisotropy which is in agreement with the predicted \nphase-diagram. The last part of this thesis presents our first steps towards the investigation \nof phase coherence of quasi two-dimensional quantum gases in the crossover from bosonic \nmolecules to fermionic atoms.
Knowing when a physical system has reached sufficient size for its macroscopic properties to be well described by many-body theory is difficult. We investigated the crossover from few- to many-body physics by studying quasi-one-dimensional systems of ultracold atoms consisting of a single impurity interacting with an increasing number of identical fermions. We measured the interaction energy of such a system as a function of the number of majority atoms for different strengths of the interparticle interaction. As we increased the number of majority atoms one by one, we observed fast convergence of the normalized interaction energy toward a many-body limit calculated for a single impurity immersed in a Fermi sea of majority particles.
In this thesis, I report on the deterministic preparation and the observation of strongly correlated few-fermion systems in single and double-well potentials. In a first experiment, we studied a system of one impurity interacting with a number of majority atoms which we prepared in a single potential well in the one-dimensional limit. With increasing number of majority particles, we observed a decrease in the quasi-particle residue which is in agreement with expectations from the Anderson orthogonality catastrophe. In a second experiment, we prepared two fermions in a double-well potential which represents the fundamental building block of the Fermi-Hubbard model. By increasing the repulsion between the two fermions, we observed the crossover into the antiferromagnetic Mott-insulator regime. Furthermore, I describe a new imaging technique, which allows spin-resolved single-atom detection both in in-situ and in time-of-flight. We use this technique to investigate the emergence of momentum correlations of two repulsive fermions in the ground state of the double well. With the methods developed in this thesis, we have established a framework for quantum simulation of strongly correlated many-body systems in tunable potentials.
We study quasi-one-dimensional few-particle systems consisting of one to six ultracold fermionic atoms in two different spin states with attractive interactions. We probe the system by deforming the trapping potential and by observing the tunneling of particles out of the trap. For even particle numbers, we observe a tunneling behavior that deviates from uncorrelated single-particle tunneling indicating the existence of pair correlations in the system. From the tunneling time scales, we infer the differences in interaction energies of systems with different number of particles, which show a strong odd-even effect, similar to the one observed for neutron separation experiments in nuclei.
In this thesis, we study the physical properties of several ultracold few-boson systems depending on the interactions between their constituents. Nowadays, experimentally, it is possible to have great control with high precision over the geometry and the interactions between the particles, making them an excellent setup to test directly the principles of quantum mechanics. A very interesting point is to study the evolution of their properties with the number of particles. The theoretical study of these systems pretends to microscopically understand the current experimental results and give support to new experimental developments.\n\n\t\t\t\t The method that will be used is the exact diagonalization of the Hamiltonian of the system. As we will see, in spite of the attempts to improve it, the method is limited by the fact that, in practice, it is only useful to study few-particle systems. The method has several advantages. First of all, one has access to both the ground and the excited states. In second place, the method is variational and converges to the exact solution as long as the Hilbert space in which we diagonalize is enlarged.\n\t\t\t\t Moreover, since we have access to the states of the system, it is possible to calculate any observable quantity of interest.\n\n\t\t\t\t First, we will study a system of spinless bosons trapped in a two-dimensional harmonic potential. The effect of the trap is to keep the system bound. It will be seen how the presence of a repulsive interaction changes the energy spectrum and other properties of the system. For instance, the density profile, which is usually measurable, and also the two-body distribution function, which is intimately related to the existence of correlations.\n\n\t\t\t\t Afterwards, the focus will be on the particular case of having only two bosons in the system interacting through a strong repulsive force. Inspired by the one-dimensional case where the fermionization phenomenon takes place in the strongly-interacting limit, we will study whether in two dimensions there is a resembling reminiscent effect. In other words, we will analyze if there are properties of the two strongly-interacting bosons in two dimensions that are like the ones of two noninteracting fermions.\n\n\t\t\t\t After that, we will tackle the localization phenomenon in a one-dimensional system that is caused by an external speckle potential that introduces disorder in the system. We will show that the localization is a robust phenomenon against repulsive contact interactions.\n\n\t\t\t\t Finally, we will study the influence of the spin-orbit coupling in a system of bosons with two possible pseudospin components, associated, for instance, to two hyperfine levels, confined in a two-dimensional harmonic trap. We will present an exhaustive analysis of the combined effects of the interaction and the spin-orbit coupling in the spectrum and the properties of the system. In particular we show the existence of a crossover in the ground state of the system susceptible to be experimentally identified.
This dissertation presents the first experiments on radio frequency (rf) spectroscopy of a quasi-two dimensional strongly interacting ultracold atomic Fermi gas. A 50-50 mixture of spin-up and spin-down atoms is confined in a series of pancake-shaped traps produced using an optical standing-wave. To make the system quasi-two dimensional, I adjust the Fermi energy in the weakly confined direction to be comparable to the harmonic oscillator energy level spacing in the tightly confined direction. For a perfectly two dimensional system, at low enough temperature, spin-up and spin-down atoms should form dimers in the ground state of the tightly confined direction. However, in our quasi-two dimensional system I find that the simple dimer theory does not agree with the measured radio-frequency spectra. Instead, the data can be explained by polaron to polaron transitions, which is a many-body effect. Here, a polaron is a spin-down impurity surrounded by a cloud of particle-hole pairs in a spin-up Fermi sea. With this unique strongly interacting quasi-two dimensional system, I am able to study the interplay between confinement induced two-body pairing and many-body physics in confined mesoscopic systems of several hundred atoms, which has not been previously explored and offers new challenges for predictions.