In this dissertation, I present my work on ground state entanglement in Bose-Hubbard-type models. Bose-Hubbard-type models form a wide class of bosonic lattice models and describe systems that can be realized by cold atoms or molecules trapped in optical lattices. By studying ground state entanglement, one can understand quantum phases and phase transitions among them from a microscopic point of view. I will first introduce the two-component Bose-Hubbard model describing Bose-Bose mixtures, and discuss the role played by the interspecies entanglement in the Mott-insulator-to-superfluid phase transition of one component in the presence of a second component. I will show that interspecies entanglement provides a new perspective to understand quantum phases in mixtures. Then I will discuss long-range spatial entanglement in single-species Bose-Hubbard-type models. Specifically, I will build a generic framework for understanding under which conditions these models harbor certain types of topological order. My results provide guidance for future numerical studies which can pave the way for searching experimentally realizable bosonic lattice models harboring nontrivial topological order.In this dissertation, I present my work on ground state entanglement in Bose-Hubbard-type models. Bose-Hubbard-type models form a wide class of bosonic lattice models and describe systems that can be realized by cold atoms or molecules trapped in optical lattices. By studying ground state entanglement, one can understand quantum phases and phase transitions among them from a microscopic point of view. I will first introduce the two-component Bose-Hubbard model describing Bose-Bose mixtures, and discuss the role played by the interspecies entanglement in the Mott-insulator-to-superfluid phase transition of one component in the presence of a second component. I will show that interspecies entanglement provides a new perspective to understand quantum phases in mixtures. Then I will discuss long-range spatial entanglement in single-species Bose-Hubbard-type models. Specifically, I will build a generic framework for understanding under which conditions these models harbor certain types of topological order. My results provide guidance for future numerical studies which can pave the way for searching experimentally realizable bosonic lattice models harboring nontrivial topological order.

Jan 1, 20170 citations

The Bose-Hubbard model: from Josephson junction arrays to optical lattices

Christoph Bruder, Rosario Fazio, Gerd Schön

Annalen der PhysikAug 18, 200551 citations

Phase-separated charge-density-wave phase in the two-species extended Bose-Hubbard model

Tapan Mishra, B. K. Sahoo, Ramesh V. Pai

We study the quantum phase transitions in a two component Bose mixture in a one-dimensional optical lattice. The calculations have been performed in the framework of the extended Bose-Hubbard model using the finite size density matrix renormalization group method. We obtain different phase transitions for the system for integer filling. When the interspecies on-site and the nearest-neighbor interactions are larger than the intraspecies on-site and also the nearest-neighbor interaction, the system exhibits a phase separated charge-density-wave order that is characterized by the two species being spatially separated and existing in the density-wave phases.We study the quantum phase transitions in a two component Bose mixture in a one-dimensional optical lattice. The calculations have been performed in the framework of the extended Bose-Hubbard model using the finite size density matrix renormalization group method. We obtain different phase transitions for the system for integer filling. When the interspecies on-site and the nearest-neighbor interactions are larger than the intraspecies on-site and also the nearest-neighbor interaction, the system exhibits a phase separated charge-density-wave order that is characterized by the two species being spatially separated and existing in the density-wave phases.

arXiv:0804.1930Physical Review AJul 24, 200812 citations

Ground state properties of one- and two-component Bose-Hubbard model

Barbara Capogrosso-Sansone, Şebnem Güneş Söyler, Nikolay V. Prokof'ev +1 more

Bulletin of the American Physical SocietyMar 12, 20080 citations

Progress towards quantum simulating the classical O(2) model

Haiyuan Zou, Yuzhi Liu A, Chen-Yen Lai +8 more

We connect explicitly the classical $\text{O}(2)$ model in $1+1$ dimensions, a model sharing important features with $\text{U}(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization-group formulation, we take the time continuum limit and check that finite-dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite-dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a $^{87}\mathrm{Rb}$ and $^{41}\mathrm{K}$ Bose-Bose mixture.We connect explicitly the classical $\text{O}(2)$ model in $1+1$ dimensions, a model sharing important features with $\text{U}(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization-group formulation, we take the time continuum limit and check that finite-dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite-dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a $^{87}\mathrm{Rb}$ and $^{41}\mathrm{K}$ Bose-Bose mixture.

arXiv:1403.5238Physical Review ADec 1, 201441 citations

We connect explicitly the classical

\text{O}(2)

model in

1+1

dimensions, a model sharing important features with

\text{U}(1)

lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization-group formulation, we take the time continuum limit and check that finite-dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite-dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a

^{87}\mathrm{Rb}

and

^{41}\mathrm{K}

Bose-Bose mixture.