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

Abstract

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

Sublattice dynamics and quantum state transfer of doublons in two-dimensional lattices

“…This coexistence, which does not occur in 1D systems with nontrivial topology, allows the direct doublon transfer between edges in a richer manner than in 1D systems via the coherent superpositions of either Shockley or topological edge states. Our analysis is valid for any 2D lattice and can be investigated experimentally in cold-atom lattices [44] or photonic crystals [45]. Developing this work to address a many-particle scenario is an exciting future avenue for research.…”

Effects of local periodic driving on transport and generation of bound states

“…The effects of periodic driving on the stability of a bosonic fractional Chern insulator has been investigated 61 . Interestingly some of these systems have been realized experimentally demonstrating correlated hopping in the Bose Hubbard model 62 and many-body localization 63 , and realizing bound states for two particles in driven photonic systems 64 . Periodic driving can lead to an interesting phenomenon called dynamical localization.…”

Creating topological interfaces and detecting chiral edge modes in a two-dimensional optical lattice

“…In addition, a very recent work [80] has reported on the observation of a point-like edge state, situated at the interface between two geometrically distinct regions, in a one-dimensional optical lattice reminiscent of the Su-Schrieffer-Heeger model [81]. Finally, we point out that topological structures were also identified in other engineered systems, such as photonic lattices [82][83][84][85][86][87], superconducting qubits [88,89], mechanical systems [90] and radio-frequency circuits [91,92]. In 2D systems, topological interfaces consist of boundary lines separating two distinct topologically-ordered regions, where topologically-protected "edge" modes are located and propagate [see Fig.…”

“…We note that similar topological interfaces could be created within photonic crystals, where system parameters (e.g. the hopping amplitudes and on-site potentials entering engineered tight-binding models) can also be precisely addressed in a local manner [86,118].…”