One-Dimensional Quantum Systems - From Few to Many Particles
arXiv:1801.04993
Abstract
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical models and numerical methods both for the few- and many-body systems. One-dimensional systems are very interesting in a sense that particles aligned on a line can only change seats by going through each other. This property can be exploited in the strongly interacting regime, where particles are forced to sit in a specific configuration, which can be easily manipulated. The knowledge of how and where the particles are can be exploited in future quantum applications. In short, the thesis is about establishing a solid knowledge about everything that one needs to know about the one-dimensional few- and many-component interacting quantum systems trapped in harmonic oscillator potentials.
162 pages, PhD Thesis, July 2017
References in corpus (52)
- Many-Body Physics with Ultracold Gases
- Feshbach Resonances in Ultracold Gases
- The density-matrix renormalization group
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
- One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
- Transition from a strongly interacting 1D superfluid to a Mott insulator
- Realization of an Excited, Strongly-Correlated Quantum Gas Phase
- Fermi gases in one dimension: From Bethe Ansatz to experiments
- Exciting Collective Oscillations in a Trapped 1D Gas
- Deterministic Preparation of a Tunable Few-Fermion System
- Metastability and Coherence of Repulsive Polarons in a Strongly Interacting Fermi Mixture
- Attractive and repulsive Fermi polarons in two dimensions
- A one-dimensional liquid of fermions with tunable spin
- The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
- Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance
- From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time
- Fermionization of two distinguishable fermions
- Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
- Confinement-Induced Resonances in Low-Dimensional Quantum Systems
- Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
- Quantum transport through a Tonks-Girardeau gas
- Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
- Strongly interacting confined quantum systems in one dimension
- Pairing in few-fermion systems with attractive interactions
- Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases
- Spin-charge separation in ultra-cold quantum gases
- A Single Atom Transistor in a 1D Optical Lattice
- Mixing property of triangular billiards
- Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
- Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
- Theory of spinor Fermi and Bose gases in tight atom waveguides
- Polarons and Molecules in a Two-Dimensional Fermi Gas
- Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture
- Symmetries of Three Harmonically-Trapped Particles in One Dimension
- Quantum Impurity in a One-dimensional Trapped Bose Gas
- A bosonic Josephson junction controlled by a single trapped ion
- Non-ergodicity and localization of invariant measure for two colliding masses
- Quantum dynamics of an atomic double-well system interacting with a trapped ion
- A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap
- DMRG study of the spin gap in a one dimensional Hubbard model: effect of the distant transfer and exchange coupling
- Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions
- Quantum Simulation of Abelian Lattice Gauge Theories via State-Dependent Hopping
- CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension
- Impact of Many-Body Correlations on the Dynamics of an Ion-Controlled Bosonic Josephson Junction
- Four fermions in a one-dimensional harmonic trap: Accuracy of a variational-ansatz approach
- Generalised Kronig-Penney model for ultracold atomic quantum systems
- Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap
- Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps
- Inserting single Cs atoms into an ultracold Rb gas
- Parity effect in a mesoscopic Fermi gas
- Exactly solvable quantum few-body systems associated with the symmetries of the three-dimensional and four-dimensional icosahedra