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arXiv:2007.06395 · Physical Review Applied

Topological States in Qubit Arrays Induced by Density-Dependent Coupling

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

Published Dec 14, 2020• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevapplied.14.064040

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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.
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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.
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The efficient generation of non-classical light at the micro- and nanoscale is central to the development of quantum technologies. Integrated photonic structures offer new opportunities for increasing the generation efficiency and control of the quantum state of non-classical light. Recently, photonic structures based on topology conservation have been proposed as platforms to overcome issues associated with disorder and fabrication imperfections. For instance, it has been suggested that topological edge states can be exploited for the generation of photon pairs having robust spectral correlations [1]. More recently, the effect of topology on path correlations of photon pairs generated by spontaneous four-wave mixing (SFWM) in waveguide arrays has also been investigated [2].
Hybrid photonic nanostructures allow the engineering of novel interesting states of light. One recent example is topological photonic crystals where a nontrivial Berry phase of the photonic band structure gives rise to topologically protected unidirectionally-propagating (chiral) edge states of photons. Here we demonstrate that by coupling an array of emitters to the chiral photonic edge state one can create strongly correlated states of photons in a highly controllable way. These are topologically protected and have a number of remarkable universal properties: the outcome of scattering does not depend on the positions of emitters and is given only by universal numbers, the zeroes of Laguerre polynomials; two-photon correlation functions manifest a well-pronounced even–odd effect with respect to the number of emitters; and the result of scattering is robust with respect to fluctuations in the emitters' transition frequencies.