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AIP conference proceedings

Two-photon topological States in the array of qubits caused by the effective photon-photon interaction

Andrei A. Stepanenko, Mark D. Lyubarov, Maxim A. Gorlach

Published Jan 1, 2020• 0 citations
Publisher

Abstract

We investigate two-photon topological states in the array of nearest-neighbor coupled qubits for two model systems based on the extended version of the Bose-Hubbard Hamiltonian, one of which includes direct two-photon tunneling and an- other one incorporates density-dependent hopping. For both models, we demonstrate that the effective photon-photon interaction gives rise to the topological bandgap and topologically protected edge states of bound photon pairs. We design effective density- dependent hopping by inserting auxiliary frequency-detuned qubits in the appropriate positions in the array, which is feasible to realize, for instance, in existing arrays of transmon qubits. Furthermore, we map our system onto the paradigmatic Su-Schrieffer- Heeger model in the limiting cases illustrating our conclusions by the results of numerical simulations.

DOI
10.1063/5.0031720

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We investigate two-photon topological states in the array of nearest-neighbor coupled qubits for two model systems based on the extended version of the Bose-Hubbard Hamiltonian, one of which includes direct two-photon tunneling and an- other one incorporates density-dependent hopping. For both models, we demonstrate that the effective photon-photon interaction gives rise to the topological bandgap and topologically protected edge states of bound photon pairs. We design effective density- dependent hopping by inserting auxiliary frequency-detuned qubits in the appropriate positions in the array, which is feasible to realize, for instance, in existing arrays of transmon qubits. Furthermore, we map our system onto the paradigmatic Su-Schrieffer- Heeger model in the limiting cases illustrating our conclusions by the results of numerical simulations.
Topological states of light open up exciting possibilities in quantum photonics, promising the topological protection of quantum entanglement. Here, we put forward an approach to realizing the topological states of photon pairs mediated by the effective density-dependent coupling, which is manifested as the dependence of the tunneling amplitude on the number of photons. As a specific platform, we investigate the arrays of nearest-neighbor coupled transmon qubits, where the effective density-dependent coupling is engineered by inserting auxiliary frequency-detuned resonators. We prove the topological origin of the designed model by the direct evaluation of the Zak phase, highlighting the feasibility of our proposal for state-of-the-art fabrication technologies.
Topological protection of quantum correlations opens new horizons and opportunities in quantum technologies. A variety of topological effects has recently been observed in qubit networks. However, the experimental identification of the topological phase still remains challenging, especially in the entangled many-body case. Here, we propose an approach to independently probe single- and two-photon topological invariants from the time evolution of the two-photon state in a one-dimensional array of qubits. Extending the bulk-boundary correspondence to the two-photon scenario, we show that an appropriate choice of the initial state enables the retrieval of the topological invariant for the different types of the two-photon states in the interacting Su-Schrieffer-Heeger model. Our analysis of the Zak phase reveals additional facets of topological protection in the case of collapse of bound photon pairs.
We consider an array of Ne{N}_{e}Ne​ noninteracting qubits or emitters that are coupled to a one-dimensional cavity array with tunneling energy JJJ and nonlinearity of strength UUU. The number of cavities is assumed to be larger than the number of qubits. Working in the two-excitation manifold, we focus on the band-gap regime where the energy of two excited qubits is off-resonant with the two-photon bound state band. A two-step adiabatic elimination of the photonic degrees of freedom gives rise to a one-dimensional spin Hamiltonian with effective interactions; specifically, the Hamiltonian features constrained single-qubit hopping and pair hopping interactions not only between nearest neighbors but also between next-to-nearest and next-to-next-to-nearest spins. For a regularly arranged qubit array, we identify parameter combinations for which the system supports droplet-like bound states whose characteristics depend critically on the pair hopping. The droplet-like states can be probed dynamically. The bound states identified in our work for off-resonance conditions are distinct from localized hybridized states that emerge for on-resonance conditions.
We investigate the influence of long-range hoppings in a structured photonic bath on atom-photon interactions. Considering a system comprising a two-leg giant atom coupled to an extended Su-Schrieffer-Heeger (SSH) model incorporating beyond-nearest-neighbor hoppings while preserving chiral symmetry, we demonstrate the formation of an unconventional bound state in the continuum (BIC) when the atomic transition frequency resonates with a mode inside the propagation band. In particular, the spatial distribution of the photoinc wavefunction of the BIC can be modified by the long-range hoppings. Consequently, when multiple identical giant atoms are included in the system, the resulting decoherence-free interactions between them are rendered less sensitive to the specific topological configuration (e.g., braided, separated, or nested) of the emitters. Furthermore, we propose two efficient and controllable quantum state transfer protocols enabled by the extended SSH model coupled to normal atoms. We show that by appropriately engineering the long-range hopping strengths, perfect excitation transfer can be achieved between two atoms coupled to the edge sites of an infinite SSH chain. In a second scheme, a single atom coupled to the center of a finite SSH chain can transfer its excitation to one of the topological edge modes. Our paper provides a method for controlling atom-photon interactions with significant implications for quantum information transfer and processing.
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.
Quantum technologies, holding the promise of exponentially superior performance in comparison to their classical counterparts for certain tasks, have consistently encountered challenges, including instability in quantum light sources, quantum decoherence, and vulnerability to losses that topological photonics happens to adeptly address. Here, we theoretically put forth a quantum Su-Schrieffer-Heeger-type chain designed to greatly enhance single-photon blockade (single PB) effect with topological protection. By designing the deliberate coupling strengths, the quantum level lattices take the form of a one-dimensional array with a topological edge state in single-excitation space and a two-dimensional square breathing lattice with topological corner states in two-excitation space, resulting in enhanced single-photon excitation and the suppression of two-photon transitions. Therefore, the second-order correlation function is diminished by up to 2 orders of magnitude at the cavity resonance frequency, accompanied by stronger brightness. Furthermore, the PB effect is robust to local perturbations in cavity-qubit coupling and qubit frequency, benefitting from topological protection.