Tunable Quantum States Emerge from Light-Superconductor Link, Defying Conventional Physics
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Scientists are increasingly exploring the potential of manipulating quantum phenomena through light-matter interactions, and this research details a novel investigation into how photonic cavities affect Majorana bound states (MBS) within a superconducting system. Aksel Kobiałka, Arnob Kumar Ghosh, and Annica M. Black-Schaffer, all from the Department of Physics and Astronomy at Uppsala University, alongside Rodrigo Arouca from the Centro Brasileiro de Pesquisas Físicas, demonstrate that these MBS persist even when coupled to a cavity field, appearing at finite and tunable energies unlike those found in conventional one-dimensional superconductors. This ability to control and stabilise MBS via light-matter coupling represents a significant step towards realising topologically protected quantum computation, offering increased tunability and resilience against disorder. Furthermore, the authors introduce a refined spectral localizer formalism, providing an essential analytical tool for characterising quantum matter within cavity environments and overcoming limitations present in standard approaches. This work investigates how cavity-induced photon fields affect a superconductor hosting MBS, revealing a pathway to tune and stabilize these exotic quantum states. Researchers modelled the system using a Peierls substitution, incorporating the photonic operator into the kinetic and spin-orbit terms of the Hamiltonian, and employed exact diagonalization to analyse the coupled system. The study establishes that MBS persist even when exposed to a cavity field, appearing at finite and tunable energies, a departure from conventional one-dimensional topological superconductors. The energy of these MBS is modified by two distinct processes. The cavity photon energy introduces a constant energy shift, while light-matter interaction generates a pseudo-dispersion, causing the MBS energy to vary with both the strength of the interaction and the applied magnetic field. Importantly, increasing the light-matter interaction suppresses energy oscillations within the MBS, and the system’s stability against disorder remains unaffected. These combined effects offer enhanced tunability and robustness for MBS, potentially advancing their use in quantum computation. Beyond manipulating MBS, this research introduces a modified spectral localizer formalism, a crucial tool for characterizing quantum matter within a cavity environment. The spectral localizer enables characterization at arbitrary energies, essential for probing different photon sectors. Addressing limitations of standard spectral localizers due to hybridization between photon sectors, the team resolved this issue by applying a judicious energy shift. This work thus opens a new avenue for controlling MBS via light-matter coupling and establishes a framework for exploring cavity-modified topological systems. Hamiltonian construction and photonic cavity modelling are crucial for quantum optics research A 1D topological superconductor (1DTSC) coupled to a photonic cavity forms the basis of this study, where researchers investigated the impact of cavity-induced photon fields on Majorana bound states (MBS). The electronic system is described by a Hamiltonian comprising a nanowire term and a superconducting pairing term, incorporating parameters such as chemical potential μ, magnetic field B, hopping amplitude t, and Rashba spin-orbit coupling α. This Hamiltonian, defined for a 100-site nanowire, accounts for electron interactions and the proximity-induced superconducting gap ∆. To model the light-matter interaction, a Peierls substitution of the photonic operator was implemented within the kinetic and spin-orbit terms of the Hamiltonian. This allowed for an exact diagonalization of the Hamiltonian for a finite number of photons, enabling investigation of the coupled system’s properties. Parameters were set to μ = −2t, ∆= α = 0.2t, and B = 0.3t, while the cavity was defined by ω = 6t and γ = 0.4t. This approach revealed that MBS persist even with a cavity field, appearing at finite and tunable energies, a departure from typical 1D superconductors. Furthermore, a modified spectral localizer formalism was established as a crucial tool for characterizing quantum matter within a cavity. This real-space and energy-resolved topological invariant assesses topology at varying energies, essential for probing different photon sectors. Recognizing hybridization between photon sectors in the low-frequency regime, researchers judiciously applied an energy shift to the spectral localizer, resolving issues and enabling clear identification of the topological state of the 1DTSC in the light cavity. The work considers Nph + 1 photon sectors, each containing a copy of the 1DTSC energy spectrum centered around energy ω(Nps + 1/2) and modified by the light-matter coupling γ. Majorana bound state energy modulation via cavity photon interactions and magnetic fields offers potential for topological qubit control Researchers established a modified spectral localizer formalism as an essential tool for characterizing quantum matter within a cavity. The bandwidth of each photon sector of H∞ is approximately 8t. Diagonal blocks HM,M result in a dressing of the electronic Hamiltonian in each photon sector, while HN,M, for all N not equal to M, represents coupling between different photon sectors. The study finds that Majorana bound state (MBS) energies are shifted by two processes, with the cavity photon energy adding a constant energy shift and light-matter interaction inducing additional parameter dependencies. Consequently, MBS experience a pseudo-dispersion as a function of both light-matter interaction and magnetic field. Oscillations in MBS energy are suppressed with increasing light-matter interaction, and disorder stability remains unaffected by this interaction. These combined effects offer additional tunability and stability to the MBS. The research demonstrates that the MBS persist even in the presence of a cavity field, appearing at finite and tunable energy, in contrast to a typical one-dimensional superconductor. The spectral localizer allows characterization at arbitrary energies, crucial for probing different photon sectors. Hybridization between photon sectors in the low-frequency regime initially limits straightforward application of a standard spectral localizer. This limitation is fully resolved by applying a judicious energy shift to the spectral localizer, introducing a new avenue for controlling MBS via light-matter coupling. The localizer gap, σ(x,E), defined as the minimum absolute eigenvalue of Lx,E(X,H∞), vanishes when a topological boundary state exists at a given spatial location and energy. Researchers extract the localizer index, a topological invariant, using the chiral symmetry S of the system, defining the topological invariant ν(x,E) as sig([ X + i(H∞−EI)]S). The topological invariant ν(x,E) is space and energy-resolved, enabling probing of topology under light-matter interactions despite the finite energies of the photon sectors. In the zero-photon case, the spin-conserving and spin-flipping hopping terms remain present, defining the 0th photon sector, H0,0.
Photonic Cavity Control of Majorana Bound State Energies enables tunable superconducting qubit coupling Researchers have demonstrated that coupling a superconductor with Majorana bound states to a photonic cavity introduces tunability and stability to these states. Investigations utilising a Peierls substitution and exact diagonalization reveal that Majorana bound states persist even when exposed to cavity photon fields, appearing at finite and adjustable energies, a departure from typical one-dimensional superconductors. The energy of these states is modified through both a constant shift from the cavity photons and a pseudo-dispersion induced by light-matter interaction, dependent on both the strength of this interaction and an applied magnetic field. Furthermore, oscillations in the Majorana bound state energy are suppressed as light-matter interaction increases, without compromising the system’s stability against disorder. This work establishes a novel method for controlling Majorana bound states through light-matter coupling, offering an additional degree of freedom for manipulating these potentially useful quantum components. A modified spectral localizer formalism was also developed, serving as a valuable tool for characterizing quantum matter within a cavity environment, enabling analysis at various energy levels. However, the authors acknowledge limitations stemming from hybridization between photon sectors at low frequencies, which they addressed through a judicious energy shift applied to the spectral localizer. Future research could explore the potential of this light-matter coupling approach for applications in quantum information processing and the creation of more robust topological quantum systems. 👉 More information 🗞 Topology and energy dependence of Majorana bound states in a photonic cavity 🧠 ArXiv: https://arxiv.org/abs/2602.03553 Tags: