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Multi-species systems in optical lattices: From orbital physics in excited bands to effects of disorder
Stockholm University, Faculty of Science, Department of Physics.
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we explore different aspects of the physics of multi-species atomic systems in optical lattices. In the first part we will study cold gases in the first and second excited bands of optical lattices - the p and d bands. The multi-species character of the physics in excited bands lies in the existence of an additional orbital degree of freedom, which gives rise to qualitative properties that are different from what is known for the systems in the ground band. We will introduce the orbital degree of freedom in the context of optical lattices and we will study the many-body systems both in the weakly interacting and in the strongly correlated regimes.

We start with the properties of single particles in excited bands, from where we investigate the weakly interacting regime of the many-body p- and d-orbital systems in Chapters 2 and 3. This presents part of the theoretical framework to be used throughout this thesis, and covers part of the content of Paper I and of Preprint II. In Chapter 4, we study Bose-Einstein condensates in the p band, confined by a harmonic trap. This includes the finite temperature study of the ideal gas and the characterization of the superfluid phase of the interacting system at zero temperature for both symmetric and asymmetric lattices. This material is the content of Paper I.

We continue with the strongly correlated regime in Chapter 5, where we investigate the Mott insulator phase of various systems in the p and d bands in terms of effective spin models. This covers the results of Paper II, of Preprint I and parts of Preprint II. More specifically, we show that the Mott phase with a unit filling of bosons in the p and in the d bands can be mapped, in two dimensions, to different types of XYZ Heisenberg models. In addition, we show that the effective Hamiltonian of the Mott phase with a unit filling in the p band of three-dimensional lattices has degrees of freedom that are the generators of the SU(3) group. Here we discuss both the bosonic and fermionic cases.

In the second part, consisting of Chapter 6, we will change gears and study effects of disorder in generic systems of two atomic species. This is the content of Preprint III, where we consider different systems of non-interacting but randomly coupled Bose-Einstein condensates in 2D, regardless of an orbital degree of freedom. We characterize spectral properties and discuss the occurrence of Anderson localization in different cases, belonging to the different chiral orthogonal, chiral unitary, Wigner-Dyson orthogonal and Wigner-Dyson unitary symmetry classes. We show that the different properties of localization in the low-lying excited states of the models in the chiral and the Wigner-Dyson classes can be understood in terms of an effective model, and we characterize the excitations in these systems. Furthermore, we discuss the experimental relevance of the Hamiltonians presented here in connection to the Anderson and the random-flux models.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University , 2015. , 117 p.
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-116436ISBN: 978-91-7649-188-1 (print)OAI: oai:DiVA.org:su-116436DiVA: diva2:806345
Public defence
2015-05-22, sal FB52, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Submitted. Paper 4: Accepted. Paper 5: Submitted.

Available from: 2015-04-29 Created: 2015-04-20 Last updated: 2015-06-16Bibliographically approved
List of papers
1. Confined p-band Bose-Einstein condensates
Open this publication in new window or tab >>Confined p-band Bose-Einstein condensates
2012 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 85, no 3, 033638Article in journal (Refereed) Published
Abstract [en]

We study bosonic atoms on the p band of a two-dimensional optical square lattice in the presence of a confining trapping potential. Using a mean-field approach, we show how the anisotropic tunneling for p-band particles affects the cloud of condensed atoms by characterizing the ground-state density and the coherence properties of the atomic states both between sites and atomic flavors. In contrast to the usual results based on the local-density approximation, the atomic density can become anisotropic. This anisotropic effect is especially pronounced in the limit of weak atom-atom interactions and of weak lattice amplitudes, i.e., when the properties of the ground state are mainly driven by the kinetic energies. We also investigate how the trap influences known properties of the nontrapped case. In particular, we focus on the behavior of the antiferromagnetic vortex-antivortex order, which for the confined system is shown to disappear at the edges of the condensed cloud.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-76124 (URN)10.1103/PhysRevA.85.033638 (DOI)000301970900008 ()
Note

3

Available from: 2012-05-10 Created: 2012-05-09 Last updated: 2017-12-07Bibliographically approved
2. XYZ Quantum Heisenberg Models with p-Orbital Bosons
Open this publication in new window or tab >>XYZ Quantum Heisenberg Models with p-Orbital Bosons
2013 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 111, no 20, 205302Article in journal (Refereed) Published
Abstract [en]

We demonstrate how the spin-1/2 XYZ quantum Heisenberg model can be realized with bosonic atoms loaded in the p band of an optical lattice in the Mott regime. The combination of Bose statistics and the symmetry of the p-orbital wave functions leads to a nonintegrable Heisenberg model with antiferro-magnetic couplings. Moreover, the sign and relative strength of the couplings characterizing the model are shown to be experimentally tunable. We display the rich phase diagram in the one-dimensional case and discuss finite size effects relevant for trapped systems. Finally, experimental issues related to preparation, manipulation, detection, and imperfections are considered.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-98090 (URN)10.1103/PhysRevLett.111.205302 (DOI)000327243600016 ()
Funder
Swedish Research Council
Note

AuthorCount:4;

Available from: 2013-12-27 Created: 2013-12-27 Last updated: 2017-12-06Bibliographically approved
3. p orbitals in 3D lattices; fermions, bosons and (exotic) models of magnetism
Open this publication in new window or tab >>p orbitals in 3D lattices; fermions, bosons and (exotic) models of magnetism
(English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622Article in journal (Refereed) Submitted
Abstract [en]

We demonstrate how different types of SU(3)  Heisenberg models can be implemented with the use of the p  orbitals of three dimensional optical lattices. By considering a Mott insulator with unit filling, the dynamics is well described by an effective model derived from the perturbative treatment of the tunneling elements relative to the onsite interaction terms. This yields systems with degrees of freedom that are generators of the SU(3)  group, which extends the Heisenberg models frequently used to analyze quantum magnetism. Due to the different character of interactions in the bosonic and fermionic cases, the choice of atom determines what type of anisotropies will appear in the couplings of the corresponding effective Hamiltonians. Experimental schemes for detection and manipulation of these systems are presented, and properties of the ground states of selected examples are discussed.

National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-116297 (URN)
Available from: 2015-04-18 Created: 2015-04-18 Last updated: 2017-12-04
4. Phases of d-orbital bosons in optical lattices
Open this publication in new window or tab >>Phases of d-orbital bosons in optical lattices
2015 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 17, 053004Article in journal (Refereed) Published
Abstract [en]

We explore the properties of bosonic atoms loaded into the d bands of an isotropic square optical lattice. Following the recent experimental success reported in [Y. Zhai et al., Phys. Rev. A 87, 063638 (2013)], in which populating d bands with a 99% fidelity was demonstrated, we present a theoretical study of the possible phases that can appear in this system. Using the Gutzwiller ansatz for the three d band orbitals we map the boundaries of the Mott insulating phases. For not too large occupation, two of the orbitals are predominantly occupied, while the third, of a slightly higher energy, remains almost unpopulated. In this regime, in the superfluid phase we find the formation of a vortex lattice, where the vortices come in vortex/anti-vortex pairs with two pairs locked to every site. Due to the orientation of the vortices time-reversal symmetry is spontaneously broken. This state also breaks a discrete Z2-symmetry. We further derive an effective spin-1/2 model that describe the relevant physics of the lowest Mott-phase with unit filling. We argue that the corresponding two dimensional phase diagram should be rich with several different phases. We also explain how to generate antisymmetric spin interactions that can give rise to novel effects like spin canting.

National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-116299 (URN)10.1088/1367-2630/17/5/053004 (DOI)
Available from: 2015-04-18 Created: 2015-04-18 Last updated: 2017-12-04Bibliographically approved
5. Disordered cold atoms in different symmetry classes
Open this publication in new window or tab >>Disordered cold atoms in different symmetry classes
(English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622Article in journal (Refereed) Submitted
Abstract [en]

We consider an experimentally realizable model of non-interacting but randomly coupled atoms in a two-dimensional optical lattice. By choosing appropriate real or complex-valued random fields and species-dependent energy offsets, this system can be used to analyze effects of disorder in four different classes: The chiral BDI and AIII, and the A and AI symmetry classes. These chiral classes are known to support a metallic phase at zero energy, which here, due to the inevitable finite size of the system, should also persist in a neighborhood of non-zero energies. As we discuss, this is of particular interest for experiments involving quenches. Away from the centre of the spectrum, we find that excitations appear as domain walls in the cases with time-reversal symmetry, or as vortices in the cases where time-reversal symmetry is absent. Therefore, a quench in a system with uniform density would lead to the formation of either vortices or domain walls depending on the symmetry class. For the non-chiral models in the A and AI classes, a population imbalance between the two atomic species naturally occurs. In these cases, one of the two species is seen to favour a more uniform density. We also study the onset of localization as the disorder strength is increased for the different classes, and by deriving an effective model for the non-chiral cases we show how their eigenstates remain extended for larger values of the coupling with the disorder, if compared to the non-chiral ones.

National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-116298 (URN)
Available from: 2015-04-18 Created: 2015-04-18 Last updated: 2017-12-04

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