Few-body physics of quasi-one dimensional atomic gases

Jingkun, Wang, Wei Wei +2 more

A. N. Wenz

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.

Shimpei Endo

Javier von Stecher

Jingkun Wang, Wei Yi, Wei Zhang

One of the most dynamic directions in ultracold atomic gas research is the study of low-dimensional physics in quasi-low-dimensional geometries, where atoms are confined in strongly anisotropic traps. Recently, interest has significantly intensified with the realization of synthetic spin–orbit coupling (SOC). As a first step toward understanding the SOC effect in quasi-low-dimensional systems, the solution of two-body problems in different trapping geometries and different types of SOC has attracted great attention in the past few years. In this review, we discuss both the scattering-state and the bound-state solutions of two-body problems in quasi-one and quasi-two dimensions. We show that the degrees of freedom in tightly confined dimensions, in particular with the presence of SOC, may significantly affect system properties. Specifically, in a quasi-one-dimensional atomic gas, a one-dimensional SOC can shift the positions of confinement-induced resonances whereas, in quasitwo- dimensional gases, a Rashba-type SOC tends to increase the two-body binding energy, such that more excited states in the tightly confined direction are occupied and the system is driven further away from a purely two-dimensional gas. The effects of the excited states can be incorporated by adopting an effective low-dimensional Hamiltonian having the form of a two-channel model. With the bare parameters fixed by two-body solutions, this effective Hamiltonian leads to qualitatively different many-body properties compared to a purely low-dimensional model.

Mingyuan He, Qi Zhou

In quasi-one- or quasi-two-dimensional traps with strong transverse confinements, quantum gases behave like strictly one- or two-dimensional systems at large length scales. However, at short distance, the two-body scattering intrinsically has three-dimensional characteristics such that an exact description of any universal thermodynamic relation requires three-dimensional contacts since the range of interaction (a few nm) is orders of magnitude smaller than the harmonic-oscillator length of the transverse confinement ($\ensuremath{\sim}{10}^{2}\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$ for a 100 kHz trap). A fundamental question arises as to whether one- or two-dimensional contacts, which were originally defined for strictly one or two dimensions, are capable of describing quantum gases in quasi-one- or quasi-two-dimensional traps. Here, we point out an exact relation between the three- and low-dimensional contacts in these highly anisotropic traps. Such relation allows us to directly connect physical quantities at different length scales and to characterize the quasi-one- or quasi-two-dimensional traps using universal thermodynamic relations that were derived for strict one or two dimensions.