Flat bands, Dirac cones, and atom dynamics in an optical lattice

Apaja, V.; Hyrkäs, Markku; Manninen, M.

doi:10.1103/physreva.82.041402

Cited by 166 publications

(160 citation statements)

References 27 publications

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“…Their vanishing group velocity and strong degeneracy can be directly observed via the existence of strongly localized yet propagation invariant (nondiffracting) wavepackets [51,52,56]. This nondiffracting behavior leads to a strong sensitivity to further perturbations such as disorder or interactions [45,47,73], analogous to slow light-enhanced nonlinear optical effects. Flat bands can also be generated by pairs of fermionic Dirac cones, where they appear as bands of surface states linking pairs of cones [17,21].…”

Section: Applicationsmentioning

confidence: 99%

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Conical intersections for light and matter waves

Leykam

Desyatnikov

2016

Advances in Physics: X

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We review the design, theory, and applications of two dimensional periodic lattices hosting conical intersections in their energy-momentum spectrum. The best known example is the Dirac cone, where propagation is governed by an effective Dirac equation, with electron spin replaced by a "fermionic" half-integer pseudospin. However, in many systems such as metamaterials, modal symmetries result in the formation of higher order conical intersections with integer or "bosonic" pseudospin. The ability to engineer lattices with these qualitatively different singular dispersion relations opens up many applications, including superior slab lasers, generation of orbital angular momentum, zeroindex metamaterials, and quantum simulation of exotic phases of relativistic matter.

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Section: Applicationsmentioning

confidence: 99%

“…In this case, the prototypical example for studying the properties of integer pseudospin intersections has been the square-like "Lieb lattice" shown in Fig. 1(c), originally proposed for cold atoms [43,[45][46][47] and recently realized as a photonic lattice [48][49][50][51][52].…”

Section: Designmentioning

confidence: 99%

Conical intersections for light and matter waves

Leykam

Desyatnikov

2016

Advances in Physics: X

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“…There exists a large number of different lattice structures which in the simple tight-binding model, with only one state per lattice site and only the nearest-neighbor hopping, exhibit band structures with one or more flat bands [3,4,17]. Often the reason for the flat band is a solution where the singleparticle wave function is zero at some connecting sites of the lattice, making it impossible for the particles to move through the lattice.…”

Section: Quasi-one-dimensional Flat-band Latticesmentioning

confidence: 99%

“…Our motivation is the fast development in the research of atoms trapped in optical lattices, which has shown that surprisingly complicated lattice structures can be manufactured, such as the kagomé lattice [16]. Recently, we suggested how a flat band exhibiting a 2D edge-centered square lattice could be made [17]. Such systems can be quite accurately described with a Hubbard Hamiltonian with contact interaction between the atoms.…”

Section: Introductionmentioning

confidence: 99%

Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices

2013

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The difference between boson and fermion dynamics in quasi-one-dimensional lattices is studied by calculating the persistent current in small quantum rings and by exact simulations of the timeevolution of the many-particle state in two cases: Expansion of a localized cloud, and collisions in a Newtons cradle. We consider three different lattices which in the tight binding model exhibit flat bands. The physical realization is considered to be an optical lattice with bosonic or fermionic atoms. The atoms are assumed to interact with a repulsive short range interaction. The different statistics of bosons and fermions lead to different dynamics. Spinless fermions are easily trapped in the flat-band states due to the Pauli exclusion principle, which prevents them from interacting, while bosons are able to push each other out from the flat-band states.

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“…When β = 0, the two slopes are identical, whereas as β → 1, the J − band becomes flat, and the J + band remains as a cone. Several authors recently considered lattice models for cold atoms that are equivalent to the β = 1 limit of our model, in which there are three bands, one flat, and one Dirac like [12,13]. When β = 1, the underlying Dirac structure of the problem is exposed, allowing us to understand this unusual dispersion from a symmetry point of view [14].…”

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confidence: 99%

Birefringent breakup of Dirac fermions on a square optical lattice

et al. 2011

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We generalize a proposal by Sørensen et al. [Phys. Rev. Lett. 94, 086803 (2005)] for creating an artificial magnetic field in a cold atom system on a square optical lattice. This leads us to an effective lattice model with tunable spatially periodic modulation of the artificial magnetic field and the hopping amplitude. When there is an average flux of half a flux quantum per plaquette the spectrum of low-energy excitations can be described by massless Dirac fermions in which the usually doubly degenerate Dirac cones split into cones with different "speeds of light" which can be tuned to give a single Dirac cone and a flat band. These gapless birefringent Dirac fermions arise because of broken chiral symmetry in the kinetic energy term of the effective low energy Hamiltonian. We characterize the effects of various perturbations to the low-energy spectrum, including staggered potentials, interactions, and domain wall topological defects. PACS numbers: 71.10.Fd, 37.10.Jk, 05.30.Fk, 71.10.Pm With the discovery of graphene [1] and topological insulators [2] there has been much recent interest in systems in which low energy excitations can be described using Dirac fermions. A parallel area of interest has been the exploration of the possibility of generating artificial magnetic fields for cold atoms confined in an optical lattice. Neutral bosonic cold atoms cannot couple to a magnetic field directly, so there have been numerous proposals [3-6] of approaches to couple atoms to an artificial magnetic field, several of which have been implemented experimentally [7,8].The problem of the spectrum of quantum particles in a uniform magnetic field on a lattice has the well-known Hofstadter spectrum [9]. Our modification of the proposal by Sørensen et al. [6] leads to an effective Hamiltonian with a tunable Hofstadter-like spectrum that arises from the combination of hopping and an artificial magnetic field with a non-zero average that are both periodically modulated in the x and the y directions. The presence of spatial periodicity in the amplitude as well as the phase of the hopping is the key difference between the model we consider here and previous work on the spectrum of particles in the presence of magnetic fields that are periodic in both the x and y directions [10]. This difference facilitates the unusual Dirac-like spectrum that we discuss in this Letter. In our effective model, when there is an average of half a flux quantum per plaquette, and at half-filling, the low energy degrees of freedom can be described by a Dirac Hamiltonian with the unusual property that chiral symmetry is broken in the kinetic energy rather than via mass terms. This has the consequence that the doubly degenerate Dirac cone for massless fermions splits into two cones with tunable distinct slopes, analagous to a situation in which there are two speeds of light for fermionic excitations, similar to birefringence of light in crystals such as calcite. We discuss the meaning of broken chiral symmetry in our effective model and explore the ef...

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Flat bands, Dirac cones, and atom dynamics in an optical lattice

Cited by 166 publications

References 27 publications

Conical intersections for light and matter waves

Conical intersections for light and matter waves

Many-particle dynamics of bosons and fermions in quasi-one-dimensional flat-band lattices

Birefringent breakup of Dirac fermions on a square optical lattice

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