Two-body physics in the Su-Schrieffer-Heeger model

Liberto, Marco Di; Recati, Alessio; Carusotto, Iacopo; Menotti, C.

doi:10.1103/physreva.94.062704

Cited by 100 publications

(123 citation statements)

References 36 publications

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“…Our experiment paves the way for simulating few-body physics in low-dimensional lattices with a clean nearest-neighbor-only hopping, for both static and periodically-driven (or Floquet) Hamiltonians. Successful implementation of similar photonic setups will enable us to experimentally simulate other intriguing problems such as N particles in a double-well potential [29], the dynamics of the correlated particles in a random potential [52,53], dissipation-induced correlation [34] and twobody Su-Schrieffer-Heeger model [54].…”

Section: Discussionmentioning

confidence: 99%

Observation of pair tunneling and coherent destruction of tunneling in arrays of optical waveguides

et al. 2016

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We report on the experimental realization of a photonic system that simulates the one-dimensional two-particle Hubbard model. This analogy is realized by means of two-dimensional arrays of coupled optical waveguides, fabricated using femtosecond laser inscription. By tuning the analogous "interaction strength", we reach the strongly-interacting regime of the Hubbard Hamiltonian, and demonstrate the suppression of standard tunneling for individual "particles". In this regime, the formation of bound states is identified through the direct observation of pair tunneling. We then demonstrate the coherent destruction of tunneling (CDT) for the paired particles in the presence of an engineered oscillating force of high frequency. The precise control over the analogous "interaction strength" and driving force offered by our experimental system opens an exciting route towards quantum simulation of few-body physics in photonics.Introduction. Elucidating the physics of interacting electrons in crystalline solids constitutes one of the most challenging problems in modern physics, with direct implications for our understanding of quantum magnetism and superconductivity. Theoretical toy models, such as the Hubbard model [1], can be used to examine these problems, but challenging issues can arise, especially in the intermediate to strong coupling regimes where perturbation theory fails. However, the one-dimensional Hubbard model is exactly solvable by means of Bethe Ansatz techniques [2,3]. In particular, the two-particle solution in the singlet sector -the triplet sector is noninteracting -shows both scattering and bound states for any value of the interaction strength. Remarkably, bound state solutions, known as doublons, exist even in the presence of repulsive interactions. This phenomenon can be understood in terms of the band gap, or the boundedness of the spectrum in the Hubbard model, which implies that two repulsively interacting particles, initially occupying the same lattice well, will have no available scattering energies to dissociate into. This can be further explained by an exact symmetry between attractive and repulsive interactions reported in [4][5][6]. These repulsively bound states were experimentally observed using both bosonic [7] and fermionic [8] particles in optical lattices. These experiments triggered an intense activity exploring the physics of few particles in optical lattices, including the two-body [9][10][11][12][13][14][15][16][17][18][19] and three-body [20,21] problems, in which certain phenomena that have no analogy in free space occur. For example, the Mattis-Gallinar effect [22], due to the absence of Galilean invariance, states that the effective mass of a lattice bound pair is higher than its free-space analogue, and was observed for excitons [23]. Three-body composites in bosonic [21] or mass-imbalanced one-dimensional fermionic systems [20] can also exist due to an effective exchange mechanism

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Section: Discussionmentioning

confidence: 99%

Observation of pair tunneling and coherent destruction of tunneling in arrays of optical waveguides

et al. 2016

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“…Here we will consider two nonlinear systems supporting edge states: classical nonlinear SSH array with the tunneling constants depending on intensity [7,8], and the SSH model in quantum two-particle regime with the effective photon-photon interaction [9,10].…”

Section: Nonlinear Ssh Modelsmentioning

confidence: 99%

“…Another interesting system is the two-particle SSH model described by the Bose-Hubbard Hamiltonian [9,10]: The U term takes into account Kerr-type nonlinearity of the medium inside the resonators. This nonlinearity induces effective photon-photon interactions and gives rise to the photon binding (Fig.…”

Section: Nonlinear Ssh Modelsmentioning

confidence: 99%

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Nonlinear topological states in the Su–Schrieffer–Heeger model

Gorlach¹,

Slobozhanyuk²

2017

Nanosystems: Phys. Chem. Math.

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Topological photonics offers unique functionalities in light manipulation at the nanoscale by means of the so-called topological states which are robust against various forms of disorder. One of the simplest one-dimensional models supporting topological states is the Su-Schrieffer-Heeger model. In this paper, we review the physics of the Su-Schrieffer-Heeger model and its nonlinear counterparts exhibiting self-induced, tunable and many-particle edge states. We discuss the robustness of these states, highlighting their rich potential for nanophotonic and quantum optics applications.

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“…To implement the first quantization Hilbert space corresponding to the two‐particle 1D system, a 2D system is needed. This is a well‐known method of treating the degrees of freedom in low‐dimensional systems, and has been employed for both conventional and topological materials …”

Section: Creutz‐hubbard Laddermentioning

confidence: 99%

Topology and Interactions in the Photonic Creutz and Creutz‐Hubbard Ladders

2019

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The latest advances in the field of photonics have enabled the simulation of an increasing number of quantum models in photonic systems, turning them into an important tool for realizing exotic quantum phenomena. In this paper, different ways in which these systems can be used to study the interplay between flat band dynamics, topology, and interactions in a well‐known quasi‐1D topological insulator—the Creutz ladder—are suggested. First, a simple experimental protocol is proposed to observe the Aharonov–Bohm localization in the noninteracting system, and the different experimental setups that might be used for this are reviewed. The inclusion of a repulsive Hubbard‐type interaction term, which can give rise to repulsively bound pairs termed doublons, is then considered. The dynamics of these quasiparticles are studied for different points of the phase diagram, including a regime in which pairs are localized and particles are free to move. Finally, a scheme for the photonic implementation of a two‐particle bosonic Creutz‐Hubbard model is presented.

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Two-body physics in the Su-Schrieffer-Heeger model

Cited by 100 publications

References 36 publications

Observation of pair tunneling and coherent destruction of tunneling in arrays of optical waveguides

Observation of pair tunneling and coherent destruction of tunneling in arrays of optical waveguides

Nonlinear topological states in the Su–Schrieffer–Heeger model

Topology and Interactions in the Photonic Creutz and Creutz‐Hubbard Ladders

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