We present a robust scheme by which fractional quantum Hall states of bosons can be achieved for ultracold atomic gases.We describe a new form of optical flux lattice, suitable for commonly used atomic species with ground state angular momentum J g ¼ 1, for which the lowest energy band is topological and nearly dispersionless.Through exact diagonalization studies, we show that, even for moderate interactions, the many-body ground states consist of bosonic fractional quantum Hall states, including the Laughlin state and the Moore-Read (Pfaffian) state.These phases are shown to have energy gaps that are larger than temperature scales achievable in ultracold gases.We present a robust scheme by which fractional quantum Hall states of bosons can be achieved for ultracold atomic gases.We describe a new form of optical flux lattice, suitable for commonly used atomic species with ground state angular momentum J g ¼ 1, for which the lowest energy band is topological and nearly dispersionless.Through exact diagonalization studies, we show that, even for moderate interactions, the many-body ground states consist of bosonic fractional quantum Hall states, including the Laughlin state and the Moore-Read (Pfaffian) state.These phases are shown to have energy gaps that are larger than temperature scales achievable in ultracold gases.

arXiv:1305.7070PhysicsApr 29, 20133 citations

Interacting bosons in topological optical flux lattices

Antoine Sterdyniak, Bogdan Andrei Bernevig, Nigel R. Cooper +1 more

An interesting route to the realization of topological Chern bands in ultracold atomic gases is through the use of optical flux lattices. These models differ from the tight-binding real-space lattice models of Chern insulators that are conventionally studied in solid-state contexts. Instead, they involve the coherent coupling of internal atomic (spin) states, and can be viewed as tight-binding models in reciprocal space. By changing the form of the coupling and the number $N$ of internal spin states, they give rise to Chern bands with controllable Chern number and with nearly flat energy dispersion. We investigate in detail how interactions between bosons occupying these bands can lead to the emergence of fractional quantum Hall states, such as the Laughlin and Moore-Read states. In order to test the experimental realization of these phases, we study their stability with respect to band dispersion and band mixing. We also probe interesting topological phases that emerge in these systems when the Chern number is greater than 1.An interesting route to the realization of topological Chern bands in ultracold atomic gases is through the use of optical flux lattices. These models differ from the tight-binding real-space lattice models of Chern insulators that are conventionally studied in solid-state contexts. Instead, they involve the coherent coupling of internal atomic (spin) states, and can be viewed as tight-binding models in reciprocal space. By changing the form of the coupling and the number $N$ of internal spin states, they give rise to Chern bands with controllable Chern number and with nearly flat energy dispersion. We investigate in detail how interactions between bosons occupying these bands can lead to the emergence of fractional quantum Hall states, such as the Laughlin and Moore-Read states. In order to test the experimental realization of these phases, we study their stability with respect to band dispersion and band mixing. We also probe interesting topological phases that emerge in these systems when the Chern number is greater than 1.

arXiv:1410.0357Physical Review BJan 13, 201525 citations

Optical flux lattices for two-photon dressed states

Nigel R. Cooper, Jean Dalibard

We describe a simple scheme by which "optical flux lattices" can be implemented in ultracold atomic gases using two-photon dressed states. This scheme can be applied, for example, to the ground-state hyperfine levels of commonly used atomic species. The resulting flux lattices simulate a magnetic field with high mean flux density, and have low-energy bands analogous to the lowest Landau level. We show that in practical cases the atomic motion significantly deviates from the adiabatic following of one dressed state, and that this can lead to significant interactions even for fermions occupying a single band. Our scheme allows experiments on cold atomic gases to explore strong correlation phenomena related to the fractional quantum Hall effect, both for fermions and bosons.We describe a simple scheme by which "optical flux lattices" can be implemented in ultracold atomic gases using two-photon dressed states. This scheme can be applied, for example, to the ground-state hyperfine levels of commonly used atomic species. The resulting flux lattices simulate a magnetic field with high mean flux density, and have low-energy bands analogous to the lowest Landau level. We show that in practical cases the atomic motion significantly deviates from the adiabatic following of one dressed state, and that this can lead to significant interactions even for fermions occupying a single band. Our scheme allows experiments on cold atomic gases to explore strong correlation phenomena related to the fractional quantum Hall effect, both for fermions and bosons.

arXiv:1106.0820Europhysics Letters (EPL)Sep 1, 201154 citations

Creating fractional quantum Hall states with atomic clusters using light-assisted insertion of angular momentum

Junyi Zhang, J. Beugnon, Sylvain Nascimbène

We describe a protocol to prepare clusters of ultracold bosonic atoms in strongly interacting states reminiscent of fractional quantum Hall states. Our scheme consists in injecting a controlled amount of angular momentum to an atomic gas using Raman transitions carrying orbital angular momentum. By injecting one unit of angular momentum per atom, one realizes a single-vortex state, which is well described by mean-field theory for large enough particle numbers. We also present schemes to realize fractional quantum Hall states, namely, the bosonic Laughlin and Moore-Read states. We investigate the requirements for adiabatic nucleation of such topological states, in particular comparing linear Landau-Zener ramps and arbitrary ramps obtained from optimized control methods. We also show that this protocol requires excellent control over the isotropic character of the trapping potential.We describe a protocol to prepare clusters of ultracold bosonic atoms in strongly interacting states reminiscent of fractional quantum Hall states. Our scheme consists in injecting a controlled amount of angular momentum to an atomic gas using Raman transitions carrying orbital angular momentum. By injecting one unit of angular momentum per atom, one realizes a single-vortex state, which is well described by mean-field theory for large enough particle numbers. We also present schemes to realize fractional quantum Hall states, namely, the bosonic Laughlin and Moore-Read states. We investigate the requirements for adiabatic nucleation of such topological states, in particular comparing linear Landau-Zener ramps and arbitrary ramps obtained from optimized control methods. We also show that this protocol requires excellent control over the isotropic character of the trapping potential.

arXiv:1608.07460Physical Review AOct 6, 20165 citations

Ideal optical flux lattices

Ophelia Evelyn Sommer, Nigel R. Cooper

The realization of fractional quantum Hall (FQH) states in cold atomic gases is a long-standing goal in quantum simulation. Established approaches, including rapidly rotating gases and tight-binding lattices, are often hampered by low interaction energies and small many-body energy gaps. While optical flux lattices (OFLs) can achieve higher effective magnetic flux densities, standard two-state configurations generate highly non-uniform fields, and extensions to multi-state systems introduce significant experimental complexity. Here, we present a new paradigm for engineering robust FQH phases in OFLs using only two internal atomic states. We show that the introduction of an additional scalar potential provides a generic mechanism for creating Chern bands that are simultaneously essentially flat and ideal.'' These desirable properties arise by tuning lattice parameters to certain $N$ -flat manifolds $(N=1,2,\dots)$ , where the $1$ -flat manifold shares its origin with certainmagic-angle’’ conditions familiar from moiré materials. A central result is the design of a dark-state OFL whose adiabatic Hamiltonian is exactly of Aharonov-Casher (AC) form. This exact AC equivalence guarantees perfectly flat, exactly ideal Chern bands in the adiabatic limit. This method allows for precise tuning of band flatness and stabilizes both Abelian and non-Abelian FQH phases. Our scheme is compatible with existing experimental capabilities using vector polarizability, opening practical routes to exploring strongly correlated topological physics with cold atoms.The realization of fractional quantum Hall (FQH) states in cold atomic gases is a long-standing goal in quantum simulation. Established approaches, including rapidly rotating gases and tight-binding lattices, are often hampered by low interaction energies and small many-body energy gaps. While optical flux lattices (OFLs) can achieve higher effective magnetic flux densities, standard two-state configurations generate highly non-uniform fields, and extensions to multi-state systems introduce significant experimental complexity. Here, we present a new paradigm for engineering robust FQH phases in OFLs using only two internal atomic states. We show that the introduction of an additional scalar potential provides a generic mechanism for creating Chern bands that are simultaneously essentially flat and ideal.'' These desirable properties arise by tuning lattice parameters to certain $N$-flat manifolds $(N=1,2,\dots)$, where the $1$-flat manifold shares its origin with certainmagic-angle’’ conditions familiar from moiré materials. A central result is the design of a dark-state OFL whose adiabatic Hamiltonian is exactly of Aharonov-Casher (AC) form. This exact AC equivalence guarantees perfectly flat, exactly ideal Chern bands in the adiabatic limit. This method allows for precise tuning of band flatness and stabilizes both Abelian and non-Abelian FQH phases. Our scheme is compatible with existing experimental capabilities using vector polarizability, opening practical routes to exploring strongly correlated topological physics with cold atoms.

Oct 1, 20260 citations

Bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices without flat bands

Shiwan Miao, Zhongchi Zhang, Yajuan Zhao +3 more

We propose a scheme to realize bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices. This scheme does not require a very flat band, and the necessary long-range interaction relies on $s$ -wave scattering, which is common in many ultracold-atom experiments. By filling the lattice at 1/4 with identical bosons under Feshbach resonance, two degenerate many-body ground states share one Chern number of 1 and correspond exactly to the fractional quantum Hall conductance of 1/2. Meanwhile, we prove that the fractional quantum Hall state can be prepared by adiabatically turning on the lattice shaking, and the fractional conductance is robust in the shaken lattice. This provides an easy way to initialize and prepare the fractional quantum Hall states in ultracold-atom platforms, and it paves the way to investigate and simulate strongly correlated quantum matters with degenerate quantum gas.We propose a scheme to realize bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices. This scheme does not require a very flat band, and the necessary long-range interaction relies on $s$-wave scattering, which is common in many ultracold-atom experiments. By filling the lattice at 1/4 with identical bosons under Feshbach resonance, two degenerate many-body ground states share one Chern number of 1 and correspond exactly to the fractional quantum Hall conductance of 1/2. Meanwhile, we prove that the fractional quantum Hall state can be prepared by adiabatically turning on the lattice shaking, and the fractional conductance is robust in the shaken lattice. This provides an easy way to initialize and prepare the fractional quantum Hall states in ultracold-atom platforms, and it paves the way to investigate and simulate strongly correlated quantum matters with degenerate quantum gas.

arXiv:2110.11587Physical review. B./Physical review. BAug 22, 20229 citations

N

of internal spin states, they give rise to Chern bands with controllable Chern number and with nearly flat energy dispersion. We investigate in detail how interactions between bosons occupying these bands can lead to the emergence of fractional quantum Hall states, such as the Laughlin and Moore-Read states. In order to test the experimental realization of these phases, we study their stability with respect to band dispersion and band mixing. We also probe interesting topological phases that emerge in these systems when the Chern number is greater than 1.

N

-flat manifolds

(N=1,2,\dots)

, where the

1

-flat manifold shares its origin with certainmagic-angle’’ conditions familiar from moiré materials. A central result is the design of a dark-state OFL whose adiabatic Hamiltonian is exactly of Aharonov-Casher (AC) form. This exact AC equivalence guarantees perfectly flat, exactly ideal Chern bands in the adiabatic limit. This method allows for precise tuning of band flatness and stabilizes both Abelian and non-Abelian FQH phases. Our scheme is compatible with existing experimental capabilities using vector polarizability, opening practical routes to exploring strongly correlated topological physics with cold atoms.

s

-wave scattering, which is common in many ultracold-atom experiments. By filling the lattice at 1/4 with identical bosons under Feshbach resonance, two degenerate many-body ground states share one Chern number of 1 and correspond exactly to the fractional quantum Hall conductance of 1/2. Meanwhile, we prove that the fractional quantum Hall state can be prepared by adiabatically turning on the lattice shaking, and the fractional conductance is robust in the shaken lattice. This provides an easy way to initialize and prepare the fractional quantum Hall states in ultracold-atom platforms, and it paves the way to investigate and simulate strongly correlated quantum matters with degenerate quantum gas.