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Register a new userRealizing Su-Schrieffer-Heeger topological edge states in Rydberg-atom synthetic dimensions
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We demonstrate a platform for synthetic dimensions based on coupled Rydberg levels in ultracold atoms, and we implement the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian. Rydberg levels are interpreted as synthetic lattice sites, with tunneling introduced through resonant millimeter-wave couplings. Tunneling amplitudes are controlled through the millimeter-wave amplitudes, and on-site potentials are controlled through detunings of the millimeter waves from resonance. Using alternating weak and strong tunneling with weak tunneling to edge lattice sites, we attain a configuration with symmetry-protected topological edge states. The band structure is probed through optical excitation to the Rydberg levels from the ground state, which reveals topological edge states at zero energy. We verify that edge-state energies are robust to perturbation of tunneling-rates, which preserves chiral symmetry, but can be shifted by the introduction of on-site potentials.
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We investigate the Su-Schrieffer-Heeger model in presence of an injection and removal of particles, introduced via a master equation in Lindblad form. It is shown that the dynamics of the density matrix follows the predictions of calculations in which the gain and loss are modeled by complex $mathcal{PT}$-symmetric potentials. In particular it is found that there is a clear distinction in the dynamics between the topologically different cases known from the stationary eigenstates.
If a full band gap closes and then reopens when we continuously deform a periodic system while keeping its symmetry, a topological phase transition usually occurs. A common model demonstrating such a topological phase transition in condensed matter physics is the Su-Schrieffer-Heeger (SSH) model. As well known, two distinct topological phases emerge when the intracell hopping is tuned from smaller to larger with respect to the intercell hopping in the model. The former case is topologically trivial, while the latter case is topologically non-trivial. Here, we design a 1D periodic acoustic system in exact analogy to the SSH model. The unit cell of the acoustic system is composed of two resonators and two junction tubes connecting them. We show that the topological phase transition happens in our acoustic analog when we tune the radii of the junction tubes which control the intercell and intracell hoppings. The topological phase transition is characterized by the abrupt change of the geometric Zak phase. The topological interface states between non-trivial and trivial phases of our acoustic analog are experimentally measured, and the results agree very well with the numerical values. Further, we show that topologically non-trivial phases of our acoustic analog of the SSH model can support edge states, on which the discussion is absent in previous works about topological acoustics. The edge states are robust against localized defects and perturbations.
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 propose a realization of topological quantum interference in a pumped non-Hermitian Su-Schrieffer-Heeger lattice that can be implemented by creation and coherent control of excitonic states of trapped neutral atoms. Our approach is based on realizing sudden delocalization of two localized topological edge states by switching the value of the laser phase controlling the lattice potential to quench the system from the topological to the gapless or trivial non-topological quantum phases of the system. We find interference patterns in the occupation probabilities of excitations on lattice sites, with a transition from a two-excitation interference seen in the absence of pumping to many-excitation interferences in the presence of pumping. Investigation of the excitation dynamics in both the topological and trivial non-topological phases shows that such interference patterns which originate in topology are drastically distinct from interference between non-topological states of the lattice. Our results also reveal that unlike well-known situations where topological states are protected against local perturbations, in these non-Hermitian SSH systems a local dissipation at each lattice site can suppress both the total population of the lattice in the topological phase and the interference of the topological states.
In this paper we study the formation of topological Tamm states at the interface between a semi-infinite one-dimensional photonic-crystal and a metal. We show that when the system is topologically non-trivial there is a single Tamm state in each of the band-gaps, whereas if it is topologically trivial the band-gaps host no Tamm states. We connect the disappearance of the Tamm states with a topological transition from a topologically non-trivial system to a topologically trivial one. This topological transition is driven by the modification of the dielectric functions in the unit cell. Our interpretation is further supported by an exact mapping between the solutions of Maxwells equations and the existence of a tight-binding representation of those solutions. We show that the tight-binding representation of the 1D photonic crystal, based on Maxwells equations, corresponds to a Su-Schrieffer-Heeger-type model (SSH-model) for each set of pairs of bands. Expanding this representation near the band edge we show that the system can be described by a Dirac-like Hamiltonian. It allows one to characterize the topology associated with the solution of Maxwells equations via the winding number. In addition, for the infinite system, we provide an analytical expression for the photonic bands from which the band-gaps can be computed.
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