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arXiv:1808.05989 · Physical Review A

Simulation of two-boson bound states using arrays of driven-dissipative coupled linear optical resonators

Maxim A. Gorlach, Marco Fedele Di Liberto, Alessio Recati, Iacopo Carusotto, Alexander N. Poddubny, Chiara Menotti

Published Dec 20, 2018• 17 citations
arXivHTMLPDF

Abstract

We present a strategy based on two-dimensional arrays of coupled linear optical resonators to investigate the two-body physics of interacting bosons in one-dimensional lattices. In particular, we want to address the bound pairs in topologically nontrivial Su-Schrieffer-Heeger arrays. Taking advantage of the driven-dissipative nature of the resonators, we propose spectroscopic protocols to detect and tomographically characterize bulk doublon bands and doublon edge states from the spatially resolved transmission spectra, and to highlight Feshbach resonance effects in two-body collision processes. We discuss the experimental feasibility using state-of-the-art devices, with a specific eye on arrays of semiconductor micropillar cavities.

DOI
10.1103/physreva.98.063625

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We present a strategy based on two-dimensional arrays of coupled linear optical resonators to investigate the two-body physics of interacting bosons in one-dimensional lattices. In particular, we want to address the bound pairs in topologically nontrivial Su-Schrieffer-Heeger arrays. Taking advantage of the driven-dissipative nature of the resonators, we propose spectroscopic protocols to detect and tomographically characterize bulk doublon bands and doublon edge states from the spatially resolved transmission spectra, and to highlight Feshbach resonance effects in two-body collision processes. We discuss the experimental feasibility using state-of-the-art devices, with a specific eye on arrays of semiconductor micropillar cavities.
We investigate theoretically the Bose-Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called 'doublons', when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities, optical lattices and qubits, and provide perspectives for topological two-particle and many-body physics.
We consider two interacting bosons in a dimerized Su-Schrieffer-Heeger (SSH) lattice. We identify a rich variety of two-body states. In particular, for open boundary conditions and moderate interactions, edge bound states (EBS) are present even for the dimerization that does not sustain single-particle edge states. Moreover, for large values of the interactions, we find a breaking of the standard bulk-boundary correspondence. Based on the mapping of two interacting particles in one dimension onto a single particle in two dimensions, we propose an experimentally realistic coupled optical fibers setup as quantum simulator of the two-body SSH model. This setup is able to highlight the localization properties of the states as well as the presence of a resonant scattering mechanism provided by a bound state that crosses the scattering continuum, revealing the closed-channel population in real time and real space.
We study two-particle states in a Su-Schrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with potential walls along specific edges. The 2D SSH model has a trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D) topological invariant, along specific directions of the lattice, which allow for the presence of topological edge states. Using center-of-mass and relative coordinates, we calculate the energy spectrum of these two-body states for strong interactions and find that, aside from the expected appearance of doublon bands, two extra in-gap bands are present. These are identified as bands of topological states localized at the edges of the internal coordinate, the relative distance between the two particles. As such, the topological states reported here are intrinsically many-body in what concerns their real space manifestation, having no counterpart in single-particle states derived from effective models. Finally, we compare the effect of Hubbard interactions with that of NN interactions to show how the presence of the topological bound states is specific to the latter case.
We theoretically investigate the optical response of a one-dimensional array of strongly nonlinear optical microcavities. When the optical nonlinearity is much larger than both losses and intercavity tunnel coupling, the nonequilibrium steady state of the system is reminiscent of a strongly correlated Tonks-Girardeau gas of impenetrable bosons. Signatures of strong correlations are identified in the transmission spectrum of the system, as well as in the intensity correlations of the transmitted light. Possible experimental implementations in state-of-the-art solid-state devices are discussed.
We study the topological properties of interacting and noninteracting bosons loaded in the orbital angular momentum states l=1l=1l=1 in a lattice of rings with alternating distances. At the single-particle level, the two circulation states within each site lead to two decoupled Su-Schrieffer-Heeger lattices with correlated topological phases. We characterize the topological configuration of these lattices in terms of the alternating distances, as well as their single-particle spectrum and topologically protected edge states. Second, we add on-site interactions for the two-boson case, which lead to the appearance of multiple bound states and edge bound states. We investigate the doublon bands in terms of a strong-link model and we analyze the resulting subspaces using perturbation theory in the limit of strong interactions. All analytical results are benchmarked against exact diagonalization simulations.
Modern experimental platforms such as superconducting circuit arrays call for the exploration of bosonic tight-binding models in unconventional situations with no counterpart in real materials. Here we investigate one such situation in which excitations are driven and damped by pairs, leading to pattern formation and exotic bosonic states emerging from a nonequilibrium quantum many-body system. Focusing on a two-dimensional driven-dissipative Bose-Hubbard model, we find that its steady states are characterized by the condensation of bosons around momenta lying on a "Bose surface," a bosonic analog of the Fermi surface in solid-state systems. The interplay between instabilities generated by the driving, the nonlinear dissipative mode coupling, and the underlying lattice effect allows the system to equilibrate into an exotic superfluid state of bosons condensed on a closed ring in momentum space instead of discrete points. Such an unconventional state with a spatially uniform density distribution goes beyond the traditional scope of pattern formation and thus has no counterpart in the classical literature. In addition, it is a state connected to several open problems in modern condensed-matter physics. Here we provide the means to stabilize it, opening the way to its experimental study. Moreover, we also provide a concrete experimental implementation of our model in currently available superconducting circuit arrays. We also investigate the relaxation spectrum around the condensate, which shows a characteristic purely diffusive behavior.