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Bulletin of the American Physical Society

Observation of qubit-photon bound states in a rectangular waveguide QED system

Pradeepkumar Nandakumar, Andrés Rosario Hamann, Rohit Navarathna, Maximilian Zanner, Mikhail Pletyukhov, Arkady Fedorov

Published Mar 15, 2021• 0 citations
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Waveguide quantum electrodynamic (waveguide QED) systems (arrays of qubits coupled to a waveguide) can exhibit a vast array of phenomena from collective effects, non-trivial topology to novel localisation effects. This thesis is the first study of a long-range coupled topological waveguide QED system. The existence of topological edge states for when one photon is incident on a spatially modulated qubit array is numerically verified and the results are analogous to a photonic crystal set-up in Ref. [1]. This thesis then goes beyond the single photon regime to consider the effect of interactions for when two photons are incident in the qubit array. Bound photon pairs and bound pair edge states are readily observed. Numerical results suggest that the bound pair edge states are topologically non-trivial, however, a topological invariant should be calculated before making stronger conclusive statements. Even more interestingly, the two-photon qubit array can also exhibit a self-induced localised state. This appears to be a completely unexplored effect that can connect many body physics, collective effects as well as topological properties. The exotic topological properties of these waveguide QED systems are promising developments in the growing field of quantum topological photonics which is said to have large potential for quantum computing technologies. The novel localised states also reveals that the physics of waveguide QED systems are richer than expected with many unexplored phenomena.

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Light-matter interaction at the single-quantum level is the heart of many regimes of high fundamental importance to modern quantum technologies. Strong interaction of a qubit with a single photon of an electromagnetic field mode is described by the cavity/circuit electrodynamics (QED) regime which is one of the most advanced platforms for quantum computing. The opposite regime of the waveguide QED, where qubits interact with a continuum of modes in an infinite one-dimensional space, is also at the focus of recent research revealing novel quantum phenomena. Despite the demonstration of several key features of waveguide QED, the transition from an experimentally realizable finite-size system to the theoretically assumed infinite device size is neither rigorously justified nor fully understood. In this paper, we formulate a unifying theory which under a minimal set of standard approximations accounts for physical boundaries of a system in all parameter domains. Considering two qubits in a rectangular waveguide which naturally exhibits a low frequency cutoff we are able to account for infinite number of modes and obtain an accurate description of the waveguide transmission, a life-time of a qubit-photon bound state and the exchange interaction between two qubit-photon bounds states. For verification, we compare our theory to experimental data obtained for two superconducting qubits in a rectangular waveguide demonstrating how the infinite size limit of waveguide QED emerges in a finite-size system. Our theory can be straightforwardly extended to other waveguides such as the photonic crystal and coupled cavity arrays.
When the energy of a quantum emitter aligns with the photonic bandgap of the waveguide, variety of distinct quantum optical phenomena emerges. The paradigmatic example of such nontrivial interaction results in the formation of a qubit-photon bound state (QPBS) where a single photon is exponentially localized around the qubit position. Superconducting quantum circuits has been extensively used for studying QPBS where the photonic band gaps are generated in two-dimensional periodic structures such as photonic crystals and metamaterials. Nonetheless, in all the experiments reported so far, the exponential nature of the bound state wave function is justified by making two assumptions (1) that the waveguide is infinite in length and (2) the coupling to the external ports are absent. These assumptions are difficult to achieve for a physical device and the transition from an experimentally realizable finite-size system to the theoretically assumed infinite device size has never been thoroughly understood. Here, we have realized an alternative platform based on a three-dimensional (3D) rectangular waveguide that has a naturally occurring low-frequency cutoff for generating QPBS as proposed in Shahmoon and Kurizki [Phys. Rev. A 87, 033831 (2013)]. In its theoretical description, we explicitly take into consideration the finite nature of the 3D waveguide arising due to its metallic boundaries and coupling to microwave ports and demonstrate how the infinite waveguide limit arises in such a finite system.
Waveguide quantum electrodynamic (waveguide QED) systems (arrays of qubits coupled to a waveguide) can exhibit a vast array of phenomena from collective effects, non-trivial topology to novel localisation effects. This thesis is the first study of a long-range coupled topological waveguide QED system. The existence of topological edge states for when one photon is incident on a spatially modulated qubit array is numerically verified and the results are analogous to a photonic crystal set-up in Ref. [1]. This thesis then goes beyond the single photon regime to consider the effect of interactions for when two photons are incident in the qubit array. Bound photon pairs and bound pair edge states are readily observed. Numerical results suggest that the bound pair edge states are topologically non-trivial, however, a topological invariant should be calculated before making stronger conclusive statements. Even more interestingly, the two-photon qubit array can also exhibit a self-induced localised state. This appears to be a completely unexplored effect that can connect many body physics, collective effects as well as topological properties. The exotic topological properties of these waveguide QED systems are promising developments in the growing field of quantum topological photonics which is said to have large potential for quantum computing technologies. The novel localised states also reveals that the physics of waveguide QED systems are richer than expected with many unexplored phenomena.