Topologically protected edge states in small Rydberg systems

We propose a simple setup of Rydberg atoms in a honeycomb lattice which gives rise to topologically protected edge states. The proposal is based on the combination of dipolar exchange interaction, which couples the internal angular momentum and the orbital degree of freedom of a Rydberg excitation, and a static magnetic field breaking time reversal symmetry. We demonstrate that for realistic experimental parameters, signatures of topologically protected edge states are present in small systems with as few as 10 atoms. Our analysis paves the way for the experimental realization of Rydberg systems characterized by a topological invariant, providing a promising setup for future application in quantum information.We propose a simple setup of Rydberg atoms in a honeycomb lattice which gives rise to topologically protected edge states. The proposal is based on the combination of dipolar exchange interaction, which couples the internal angular momentum and the orbital degree of freedom of a Rydberg excitation, and a static magnetic field breaking time reversal symmetry. We demonstrate that for realistic experimental parameters, signatures of topologically protected edge states are present in small systems with as few as 10 atoms. Our analysis paves the way for the experimental realization of Rydberg systems characterized by a topological invariant, providing a promising setup for future application in quantum information.

arXiv:1803.05293Quantum Science and TechnologyJun 5, 201833 citations

Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms

Sylvain de Léséleuc, Vincent Lienhard, Pascal Scholl +6 more

The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.

arXiv:1810.13286ScienceAug 1, 2019552 citations

Experimentally accessible scheme for a fractional Chern insulator in Rydberg atoms

S. M. Weber, Rukmani Bai, Nastasia Makki +6 more

We present a setup with Rydberg atoms for the realization of a bosonic fractional Chern insulator in artificial matter. The suggested setup relies on Rydberg atoms arranged in a honeycomb lattice, where excitations hop through the lattice by dipolar exchange interactions, and can be interpreted as hard-core bosons. The quantum many-body Hamiltonian is studied within exact diagonalization and DMRG. We identify experimentally accessible parameters where all signatures indicate the appearance of a fractional state with the same topological properties as the $ν=1/2$ bosonic Laughlin state. We demonstrate an adiabatic ramping procedure, which allows for the preparation of the topological state in a finite system, and demonstrate an experimentally accessible smoking gun signature for the fractional excitations.We present a setup with Rydberg atoms for the realization of a bosonic fractional Chern insulator in artificial matter. The suggested setup relies on Rydberg atoms arranged in a honeycomb lattice, where excitations hop through the lattice by dipolar exchange interactions, and can be interpreted as hard-core bosons. The quantum many-body Hamiltonian is studied within exact diagonalization and DMRG. We identify experimentally accessible parameters where all signatures indicate the appearance of a fractional state with the same topological properties as the $ν=1/2$ bosonic Laughlin state. We demonstrate an adiabatic ramping procedure, which allows for the preparation of the topological state in a finite system, and demonstrate an experimentally accessible smoking gun signature for the fractional excitations.

arXiv:2202.00699Feb 1, 20220 citations

Experimentally Accessible Scheme for a Fractional Chern Insulator in Rydberg Atoms

Sebastian Weber, Rukmani Bai, Nastasia Makki +6 more

We present a setup with Rydberg atoms for the realization of a bosonic fractional Chern insulator in artificial matter. The suggested setup relies on Rydberg atoms arranged in a honeycomb lattice, where excitations hop through the lattice by dipolar exchange interactions and can be interpreted as hard-core bosons. The quantum many-body Hamiltonian is studied within exact diagonalization and the density-matrix renormalization group. We identify experimentally accessible parameters where all signatures indicate the appearance of a fractional state with the same topological properties as the ν=1/2 bosonic Laughlin state. We demonstrate an adiabatic ramping procedure, which allows for the preparation of the topological state in a finite system, and demonstrate an experimentally accessible smoking-gun signature for the fractional excitations.We present a setup with Rydberg atoms for the realization of a bosonic fractional Chern insulator in artificial matter. The suggested setup relies on Rydberg atoms arranged in a honeycomb lattice, where excitations hop through the lattice by dipolar exchange interactions and can be interpreted as hard-core bosons. The quantum many-body Hamiltonian is studied within exact diagonalization and the density-matrix renormalization group. We identify experimentally accessible parameters where all signatures indicate the appearance of a fractional state with the same topological properties as the ν=1/2 bosonic Laughlin state. We demonstrate an adiabatic ramping procedure, which allows for the preparation of the topological state in a finite system, and demonstrate an experimentally accessible smoking-gun signature for the fractional excitations.

PRX QuantumJul 5, 202229 citations

Topological bands in the continuum using Rydberg states

Sebastian Weber, Przemysław Bienias, Hans Peter Büchler

The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a two-dimensional cloud of atoms dressed to Rydberg states, where excitations propagate by dipolar exchange interaction, while the Rydberg blockade phenomenon naturally gives rise to a characteristic length scale, suppressing the hopping on short distances. Then, the system becomes independent of the atoms' spatial arrangement and can be described by a continuum model. We demonstrate the appearance of a topological band structure in the continuum characterized by a Chern number $C=2$ and show that edge states appear at interfaces tunable by the atomic density.The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a two-dimensional cloud of atoms dressed to Rydberg states, where excitations propagate by dipolar exchange interaction, while the Rydberg blockade phenomenon naturally gives rise to a characteristic length scale, suppressing the hopping on short distances. Then, the system becomes independent of the atoms' spatial arrangement and can be described by a continuum model. We demonstrate the appearance of a topological band structure in the continuum characterized by a Chern number $C=2$ and show that edge states appear at interfaces tunable by the atomic density.

arXiv:2101.08363Jan 20, 20210 citations

Z 2 Topological Quantum Paramagnet on a honeycomb bilayer

Darshan G. Joshi, Andreas P. Schnyder

Topological quantum paramagnets are exotic states of matter, whose magnetic excitations have a topological band structure, while the ground state is topologically trivial. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts a time-reversal-symmetry protected ${\mathbb{Z}}_{2}$ topological quantum paramagnet (topological triplon insulator) in the presence of spin-orbit coupling. The excitation spectrum of this quantum paramagnet consists of three triplon bands, two of which carry a nontrivial ${\mathbb{Z}}_{2}$ index. As a consequence, there appear two counterpropagating triplon excitation modes at the edge of the system. We compute the triplon edge state spectrum and the ${\mathbb{Z}}_{2}$ index for various parameter choices. We further show that upon making one of the Heisenberg couplings stronger, the system undergoes a topological quantum phase transition, where the ${\mathbb{Z}}_{2}$ index vanishes, to a different topological quantum paramagnet. In this case the counterpopagating triplon edge modes are disconnected from the bulk excitations and are protected by a chiral and a unitary symmetry. We discuss possible realizations of our model in real materials, in particular ${d}^{4}$ Mott insulators, and their potential applications.Topological quantum paramagnets are exotic states of matter, whose magnetic excitations have a topological band structure, while the ground state is topologically trivial. Here we show that a simple model of quantum spins on a honeycomb bilayer hosts a time-reversal-symmetry protected ${\mathbb{Z}}_{2}$ topological quantum paramagnet (topological triplon insulator) in the presence of spin-orbit coupling. The excitation spectrum of this quantum paramagnet consists of three triplon bands, two of which carry a nontrivial ${\mathbb{Z}}_{2}$ index. As a consequence, there appear two counterpropagating triplon excitation modes at the edge of the system. We compute the triplon edge state spectrum and the ${\mathbb{Z}}_{2}$ index for various parameter choices. We further show that upon making one of the Heisenberg couplings stronger, the system undergoes a topological quantum phase transition, where the ${\mathbb{Z}}_{2}$ index vanishes, to a different topological quantum paramagnet. In this case the counterpopagating triplon edge modes are disconnected from the bulk excitations and are protected by a chiral and a unitary symmetry. We discuss possible realizations of our model in real materials, in particular ${d}^{4}$ Mott insulators, and their potential applications.

Bulletin of the American Physical SocietyMar 5, 20181 citation

ν=1/2

bosonic Laughlin state. We demonstrate an adiabatic ramping procedure, which allows for the preparation of the topological state in a finite system, and demonstrate an experimentally accessible smoking gun signature for the fractional excitations.

C=2

and show that edge states appear at interfaces tunable by the atomic density.

{\mathbb{Z}}_{2}

topological quantum paramagnet (topological triplon insulator) in the presence of spin-orbit coupling. The excitation spectrum of this quantum paramagnet consists of three triplon bands, two of which carry a nontrivial

{\mathbb{Z}}_{2}

index. As a consequence, there appear two counterpropagating triplon excitation modes at the edge of the system. We compute the triplon edge state spectrum and the

{\mathbb{Z}}_{2}

index for various parameter choices. We further show that upon making one of the Heisenberg couplings stronger, the system undergoes a topological quantum phase transition, where the

{\mathbb{Z}}_{2}

index vanishes, to a different topological quantum paramagnet. In this case the counterpopagating triplon edge modes are disconnected from the bulk excitations and are protected by a chiral and a unitary symmetry. We discuss possible realizations of our model in real materials, in particular

{d}^{4}

Mott insulators, and their potential applications.