Edge states of photon pairs in cavity arrays with spatially modulated nonlinearity

Lyubarov, Mark; Poddubny, Alexander N.

doi:10.1103/physreva.100.053813

Cited by 4 publications

(2 citation statements)

References 37 publications

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“…These two-body states, which are stable even for repulsive interactions due to the finite bandwidth of the singleparticle kinetic energy [9], have been observed [10][11][12][13] and extensively analyzed [14][15][16][17][18][19][20][21][22][23][24][25] in optical lattices, and have also been emulated in photonic systems [26,27] and in topolectrical circuits [28]. Motivated in part by these advances, several recent works have focused on the topological properties of two-body states [13,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], with the long-term aim of paving the path to a better comprehension of topological phases in a full many-body interacting scenario. A distinctive advantage that these small-sized systems offer is that it is often possible to map the problem of two interacting particles in a lattice into a single-particle model defined in a different lattice, the topological characterization of which can then be performed with well-established techniques [31][32][33]36,40,…”

Section: Introductionmentioning

confidence: 99%

Interaction-induced topological properties of two bosons in flat-band systems

Pelegrí

Marques

Ahufinger

et al. 2020

Phys. Rev. Research

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In flat-band systems, destructive interference leads to the localization of noninteracting particles and forbids their motion through the lattice. However, in the presence of interactions the overlap between neighboring single-particle localized eigenstates may enable the propagation of bound pairs of particles. In this work, we show how these interaction-induced hoppings can be tuned to obtain a variety of two-body topological states. In particular, we consider two interacting bosons loaded into the orbital angular momentum l = 1 states of a diamond-chain lattice, wherein an effective π flux may yield a completely flat single-particle energy landscape. In the weakly interacting limit, we derive effective single-particle models for the two-boson quasiparticles which provide an intuitive picture of how the topological states arise. By means of exact diagonalization calculations, we benchmark these states and we show that they are also present for strong interactions and away from the strict flat-band limit. Furthermore, we identify a set of doubly localized two-boson flat-band states that give rise to a special instance of Aharonov-Bohm cages for arbitrary interactions.

show abstract

Section: Introductionmentioning

confidence: 99%

Interaction-induced topological properties of two bosons in flat-band systems

Pelegrí

Marques

Ahufinger

et al. 2020

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

“…These two-body states, which are stable even for repulsive interactions due to the finite bandwidth of the single-particle kinetic energy [9], have been observed [10][11][12][13] and extensively analyzed [14][15][16][17][18][19][20][21][22][23][24][25] in optical lattices, and have also been emulated in photonic systems [26,27] and in topolectrical circuits [28]. Motivated in part by these advances, several recent works have focused on the topological properties of two-body states [13,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], with the long-term aim of paving the path to a better comprehension of topological phases in a full many-body interacting scenario. A distinctive advantage that these small-sized systems offer is that it is often possible to map the prob-lem of two interacting particles in a lattice into a singleparticle model defined in a different lattice, the topological characterization of which can then be performed with well-established techniques [31-33, 36, 40, 41].…”

Section: Introductionmentioning

confidence: 99%

Interaction-induced topological properties of two bosons in flat-band systems

Pelegrí,

Marques,

Ahufinger

et al. 2020

Preprint

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In flat-band systems, destructive interference leads to the localization of non-interacting particles and forbids their motion through the lattice. However, in the presence of interactions the overlap between neighbouring single-particle localized eigenstates may enable the propagation of bound pairs of particles. In this work, we show how these interaction-induced hoppings can be tuned to obtain a variety of two-body topological states. In particular, we consider two interacting bosons loaded into the orbital angular momentum l = 1 states of a diamond-chain lattice, wherein an effective π flux may yield a completely flat single-particle energy landscape. In the weakly-interacting limit, we derive effective single-particle models for the two-boson quasiparticles which provide an intuitive picture of how the topological states arise. By means of exact diagonalization calculations, we benchmark these states and we show that they are also present for strong interactions and away from the strict flat-band limit. Furthermore, we identify a set of doubly localized two-boson flat-band states that give rise to a special instance of Aharonov-Bohm cages for arbitrary interactions.

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Few-body bound topological and flat-band states in a Creutz ladder

Pelegrí,

Flannigan,

Daley

2024

Phys. Rev. B

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We investigate the properties of a few interacting bosons in a Creutz ladder, which has become a standard model for topological systems, and which can be realized in experiments with cold atoms in optical lattices. At the single-particle level, this system may exhibit a completely flat energy landscape with nontrivial topological properties. In this scenario, we identify topological two-body edge states resulting from the bonding of single-particle edge and flat-band states. We also explore the formation of two- and three-body bound states in the strongly interacting limit, and we show how these quasiparticles can be engineered to replicate the flat-band and topological features of the original single-particle model. Furthermore, we show that in this geometry perfect Aharonov-Bohm caging of two-body bound states may occur for arbitrary interaction strengths, and we provide numerical evidence that the main features of this effect are preserved in an interacting many-body scenario resulting in many-body Aharonov-Bohm caging. Published by the American Physical Society 2024

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Edge states of photon pairs in cavity arrays with spatially modulated nonlinearity

Cited by 4 publications

References 37 publications

Interaction-induced topological properties of two bosons in flat-band systems

Interaction-induced topological properties of two bosons in flat-band systems

Interaction-induced topological properties of two bosons in flat-band systems

Few-body bound topological and flat-band states in a Creutz ladder

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