We study a strongly interacting array of Bose-Einstein condensates trapped in a one-dimensional (1D) optical lattice. The system is described by a nonstandard 1D Bose-Hubbard model in which both the tunneling matrix element and the on-site atomic interaction depend on the lattice site due to the interaction broadening of the local wave function and the system inhomogeneity. We quantitatively compare theoretical analyses based on the Gutzwiller approximation with experimental observations obtained using ytterbium atoms. We show that atomic states are highly number squeezed owing to strong interatomic interactions as the lattice potential becomes deeper. Furthermore, the calculated inhomogeneous collisional broadening of spectroscopic line shapes agrees well with high-resolution spectra measured by using the ultranarrow magnetic quadrupole ${}^{1}{S}_{0}{\ensuremath{-}}^{3}{P}_{2}$ transition.
We study a strongly interacting array of Bose-Einstein condensates trapped in a one-dimensional (1D) optical lattice. The system is described by a nonstandard 1D Bose-Hubbard model in which both the tunneling matrix element and the on-site atomic interaction depend on the lattice site due to the interaction broadening of the local wave function and the system inhomogeneity. We quantitatively compare theoretical analyses based on the Gutzwiller approximation with experimental observations obtained using ytterbium atoms. We show that atomic states are highly number squeezed owing to strong interatomic interactions as the lattice potential becomes deeper. Furthermore, the calculated inhomogeneous collisional broadening of spectroscopic line shapes agrees well with high-resolution spectra measured by using the ultranarrow magnetic quadrupole 1S0\ensuremath−3P2 transition.
We compare effects of particle interaction on Bose-Einstein condensation in inhomogeneous traps with and without optical lattice inside. Interaction pushes normal particles away from the condensate droplet, which is located in the center of the trap, toward the periphery of the trap where the trapping potential is large. In the end, the remaining normal particles are squeezed to a quasi-two-dimensional (2D) shell around the condensate droplet, thus changing the effective dimensionality of the system. In the absence of the optical lattice, the index in the temperature dependence of the condensate density at the later stages of the process is close to 2 with a weak dependence on the number of trapped particles. In the presence of the lattice inside the trap, this simple picture breaks down and the index acquires a strong dependence on the number of particles inside the trap, gradually falling from a three-dimensional to a 2D value with an increase in the number of particles. This change in index is explained by the lattice-driven spread of the condensate droplet and the localization of the narrow-band particles by the trap potential.
We study the dynamics of Bose–Einstein condensed atoms in a one-dimensional (1D) optical lattice potential in a regime where the collective (Josephson) tunnelling energy is comparable with the on-site interaction energy, and the number of particles per lattice site is mesoscopically large. By directly imaging the motion of atoms in the lattice, we observe an abrupt suppression of atom transport through the array for a critical ratio of these energies, consistent with quantum fluctuation induced localization. Directly below the onset of localization, the frequency of the observed superfluid transport can be explained by a phonon excitation but deviates substantially from that predicted by the hydrodynamic/Gross–Pitaevskii equations.
We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.
Ultracold atoms in optical lattices are a powerful platform for the study of quantum many-body physics. The combination of a high degree of isolation from the environment and external control over all relevant parameters makes these systems ideal candidates for the quantum simulation of fundamental lattice models. However, since the atoms are trapped in standing waves of interfering laser beams, the available trap geometries are constrained to regular lattices and single-site control is limited. In this thesis, an alternative experimental platform is investigated. Here, the combination of a microlens array and a spatial light modulator is used to provide a two-dimensional optical microtrap array for ultracold atoms. This setup allows for versatile trap geometries and comprehensive single-site control. The experimental feasibility of the described platform is investigated in the following way. First, the light field generating the microtrap array is simulated using a detailed model of the optical setup. The computed intensity distribution is proportional to the optical dipole potential for the atoms. Second, the simulation results are used to obtain the Hubbard parameters for multiple alkalies from numerical calculations as well as approximative analytical methods. It is shown that the strongly correlated regimes of the Bose-Hubbard model can be reached at sufficiently large tunneling rates. In addition, the impact of fluctuations in the trap parameters is investigated. Third, two approaches are considered for the preparation of low-entropy many-body states. On the one hand, a loading scheme is investigated which starts from a Bose-Einstein condensate and is used in optical lattice experiments. Here, the depth of the microtrap array is increased adiabatically. On the other hand, an array of isolated traps, which is initialized with one atom per site in the respective motional ground state, is considered as starting point. The itinerant regime of the Hubbard model is accessed by an adiabatic decrease of the trap depth. An analysis of ramp-induced excitations and external heating processes shows the feasibility of both approaches. Demonstrating the potential of the investigated platform, two applications are described. On the one hand, the tunneling dynamics of ultracold atoms between weakly coupled ring lattices is analyzed. Controlled by the interaction strength, multiple phenomena can be observed: Josephson oscillations exhibiting collapse and revival, inter-action-induced self-trapping, and tunneling resonances. On the other hand, the implementation of a scheme for universal quantum computing based on time-continuous quantum walks of interacting particles is proposed. Here, the information is encoded into the position of atomic wave packets moving through a planar graph which is built from optical microtraps and implements a quantum circuit. Details of an experimental implementation are discussed for both applications using the results derived in the preceding parts of this thesis.
High-resolution laser spectroscopy of a Bose–Einstein condensate (BEC) was performed by using the ultranarrow magnetic quadrupole (6s 2 ) 1 S 0 ↔(6s6p) 3 P 2 transition of ytterbium (Yb). The transition from the Doppler-broadened spectrum of thermal atoms to the asymmetric spectrum, reflecting the inhomogeneous density distribution of a BEC in a harmonic trap, was observed. The role of the inter-atomic interaction was highlighted by performing spectroscopy of a BEC loaded in a one-dimensional (1D) optical lattice.
We study the ground-state properties of spin-1 bosonic atoms trapped in a one-dimensional optical lattice with harmonic confinement. We have developed a highly efficient numerical method based on the Gutzwiller approximation to clarify the inhomogeneous magnetic phases induced by the harmonic confining potential. A quantum phase transition from a superfluid to a Mott insulator is examined for the respective cases with antiferromagnetic and ferromagnetic interactions. It is shown that the profile of local spins over the lattice sites changes as a function of the interaction strength forming the characteristic structures, which closely correlates with the average number of atoms at the sites. For antiferromagnetic cases, we find that there is a crossover from a superfluid polar condensate to Mott-insulator domains consisting of either a spin-singlet pair or a single spin at each site.