20 April 2010
New ICFO PhD Graduate

Dr. Christian Trefzger

Thesis Committee

Dr. Christian Trefzger obtained his PhD with a thesis on ultracold dipolar gases.
Dr. Christian Trefzger graduated in Physics from the Università degli studi di Trento, Italy, in 2005. That year he joined ICFO to work in the field of Quantum Optics Theory.

Dr. Trefzger\'s thesis, \' Ultracold Dipolar Gases in Optical Lattices \', was supervised by ICFO group leader and ICREA Prof. Maciej Lewenstein.

ABSTRACT

This thesis is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules, cooled below the quantum degeneracy temperature, typically in the nK range. In such conditions, in a three-dimensional (3D) harmonic trap, weakly interacting bosons condense and form a Bose-Einstein Condensate (BEC). When a BEC is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur. These systems realize then Hubbard-type models and can be brought to a strongly correlated regime.

In 1989, M. Fisher et al. predicted that the homogeneous Bose-Hubbard model (BH) exhibits the Superfluid-Mott insulator (SF-MI) quantum phase transition. In 2002, the transition between these two phases was observed experimentally for the first time in the group of T. Esslinger and I. Bloch. The experimental realisation of a dipolar BEC of Chromium by the group of T. Pfau, and the recent progresses in trapping and cooling of dipolar molecules by the groups of D. Jin and J. Ye, have opened the path towards ultra-cold quantum gases with dominant dipole interactions. A natural evolution, and present challenge, on the experimental side is then to load dipolar BECs into optical lattices and study strongly correlated ultracold dipolar lattice gases.

Before this PhD work, studies of BH models with interactions extended to nearest neighbors had pointed out that novel quantum phases, like supersolid (SS) and checkerboard phases (CB) are expected. Due to the long-range character of the dipole-dipole interaction, which decays as the inverse cubic power of the distance, it is necessary to include more than one nearest neighbor to have a faithful quantitative description of dipolar systems. In fact, longer-range interactions tend to allow for and stabilize more novel phases.

In this thesis we study BH models with dipolar interactions, going beyond the ground state search. We consider a two-dimensional (2D) lattice where the dipoles are polarized perpendicularly to the 2D plane, resulting in an isotropic repulsive interaction. We use the mean-field approximations and a Gutzwiller ansatz which are quite accurate and suitable to describe this system. We find that dipolar bosonic gas in 2D exhibits a multitude of insulating metastable states, often competing with the ground state, similarly as in a disordered system. We study in detail the fate of these metastable states: how can they be prepared on demand, how they can be detected, what is their lifetime due to tunnelling, and what is their role in various cooling schemes. Moreover, we find that the ground state is characterized by insulating checkerboard-like states with fractional filling factors (average number of particles per site) that depend on the cut-off used for the interaction range. We confirm this prediction by studying the same system with Quantum Monte Carlo methods (the worm algorithm). In this case no cut-off is used, and we find evidence for a Devil\'s staircase in the ground state, i.e. where insulating phases appear at all rational filling factors of the underlying lattice. We also find regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies.

In this work, we also investigate how the previous scenario changes in 3D. We focus on the simplest 3D lattice composed of two 2D layers in which the dipoles are polarized perpendicularly to the planes; the dipolar interaction is then repulsive for particles laying on the same plane, while it is attractive for particles at the same lattice site on different layers. Instead we consider inter-layer tunnelling to be suppressed, which makes the system analogous to a bosonic mixture in a 2D lattice. Our calculations show that particles pair into composites, and demonstrate the existence of the novel Pair Super Solid (PSS) quantum phase. Currently, we are studying a 2D lattice where the dipoles are free to point in both directions perpendicularly to the plane, which results in a nearest neighbour repulsive (attractive) interaction for aligned (anti-aligned) dipoles. We find regions of parameters where the ground state is ferromagnetic or anti-ferromagnetic, and find evidences for the existence of a Counterflow Super Solid (CSS) quantum phase.

Our predictions have direct experimental consequences, and we hope that they will be soon checked in experiments with ultracold dipolar atomic and molecular gases.

Dr. Trefzger\'s thesis, \' Ultracold Dipolar Gases in Optical Lattices \', was supervised by ICFO group leader and ICREA Prof. Maciej Lewenstein.

ABSTRACT

This thesis is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules, cooled below the quantum degeneracy temperature, typically in the nK range. In such conditions, in a three-dimensional (3D) harmonic trap, weakly interacting bosons condense and form a Bose-Einstein Condensate (BEC). When a BEC is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur. These systems realize then Hubbard-type models and can be brought to a strongly correlated regime.

In 1989, M. Fisher et al. predicted that the homogeneous Bose-Hubbard model (BH) exhibits the Superfluid-Mott insulator (SF-MI) quantum phase transition. In 2002, the transition between these two phases was observed experimentally for the first time in the group of T. Esslinger and I. Bloch. The experimental realisation of a dipolar BEC of Chromium by the group of T. Pfau, and the recent progresses in trapping and cooling of dipolar molecules by the groups of D. Jin and J. Ye, have opened the path towards ultra-cold quantum gases with dominant dipole interactions. A natural evolution, and present challenge, on the experimental side is then to load dipolar BECs into optical lattices and study strongly correlated ultracold dipolar lattice gases.

Before this PhD work, studies of BH models with interactions extended to nearest neighbors had pointed out that novel quantum phases, like supersolid (SS) and checkerboard phases (CB) are expected. Due to the long-range character of the dipole-dipole interaction, which decays as the inverse cubic power of the distance, it is necessary to include more than one nearest neighbor to have a faithful quantitative description of dipolar systems. In fact, longer-range interactions tend to allow for and stabilize more novel phases.

In this thesis we study BH models with dipolar interactions, going beyond the ground state search. We consider a two-dimensional (2D) lattice where the dipoles are polarized perpendicularly to the 2D plane, resulting in an isotropic repulsive interaction. We use the mean-field approximations and a Gutzwiller ansatz which are quite accurate and suitable to describe this system. We find that dipolar bosonic gas in 2D exhibits a multitude of insulating metastable states, often competing with the ground state, similarly as in a disordered system. We study in detail the fate of these metastable states: how can they be prepared on demand, how they can be detected, what is their lifetime due to tunnelling, and what is their role in various cooling schemes. Moreover, we find that the ground state is characterized by insulating checkerboard-like states with fractional filling factors (average number of particles per site) that depend on the cut-off used for the interaction range. We confirm this prediction by studying the same system with Quantum Monte Carlo methods (the worm algorithm). In this case no cut-off is used, and we find evidence for a Devil\'s staircase in the ground state, i.e. where insulating phases appear at all rational filling factors of the underlying lattice. We also find regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies.

In this work, we also investigate how the previous scenario changes in 3D. We focus on the simplest 3D lattice composed of two 2D layers in which the dipoles are polarized perpendicularly to the planes; the dipolar interaction is then repulsive for particles laying on the same plane, while it is attractive for particles at the same lattice site on different layers. Instead we consider inter-layer tunnelling to be suppressed, which makes the system analogous to a bosonic mixture in a 2D lattice. Our calculations show that particles pair into composites, and demonstrate the existence of the novel Pair Super Solid (PSS) quantum phase. Currently, we are studying a 2D lattice where the dipoles are free to point in both directions perpendicularly to the plane, which results in a nearest neighbour repulsive (attractive) interaction for aligned (anti-aligned) dipoles. We find regions of parameters where the ground state is ferromagnetic or anti-ferromagnetic, and find evidences for the existence of a Counterflow Super Solid (CSS) quantum phase.

Our predictions have direct experimental consequences, and we hope that they will be soon checked in experiments with ultracold dipolar atomic and molecular gases.