Abstract I analyze the emergence of Majorana zero modes (MZM) in a one dimensional ultracold fermionic system confined by an optical lattice inside a high-Q cavity. This forms a quantum optical lattice due to the cavity backaction, with emergent long range interactions controlled by the light pumped into the system and thus long range pairing. I investigate the possibility of formation and emergence of edge modes using exact diagonalization with self-consistent order parameters and singular value decomposition of the Hamiltonian in the Majorana representation. I analyze the spectral properties of the system, the mass gap and amplitude of the MZM with a unified framework. The interplay of cavity induced interactions and effective p -wave short range interactions controls the emergence of the signatures of MZM. I find that under certain conditions MZM distinctively emerge leading to superradiant topological phases of matter. These MZM have potential applications for quantum information as they are topologically protected analogous to the behavior of the Kitaev chain. The techniques employed lead to a scheme based on the Majorana representation and exact diagonalization with self consistent conditions using Hartree–Fock–Bogoliubov theory in real space for finite systems that can be applied to other fermionic and analog systems termed Light-Matter-Majorana. A promising landscape for the exploration of short range and long range topological order with superradiance is found.
Abstract I analyze the emergence of Majorana zero modes (MZM) in a one dimensional ultracold fermionic system confined by an optical lattice inside a high-Q cavity. This forms a quantum optical lattice due to the cavity backaction, with emergent long range interactions controlled by the light pumped into the system and thus long range pairing. I investigate the possibility of formation and emergence of edge modes using exact diagonalization with self-consistent order parameters and singular value decomposition of the Hamiltonian in the Majorana representation. I analyze the spectral properties of the system, the mass gap and amplitude of the MZM with a unified framework. The interplay of cavity induced interactions and effective p -wave short range interactions controls the emergence of the signatures of MZM. I find that under certain conditions MZM distinctively emerge leading to superradiant topological phases of matter. These MZM have potential applications for quantum information as they are topologically protected analogous to the behavior of the Kitaev chain. The techniques employed lead to a scheme based on the Majorana representation and exact diagonalization with self consistent conditions using Hartree–Fock–Bogoliubov theory in real space for finite systems that can be applied to other fermionic and analog systems termed Light-Matter-Majorana. A promising landscape for the exploration of short range and long range topological order with superradiance is found.
I analyze the emergence of Majorana zero modes (MZM) in a one dimensional ultracold fermionic system confined by an optical lattice inside a high-Q cavity. This forms a quantum optical lattice due to the cavity backaction, with emergent long range interactions controlled by the light pumped into the system and thus long range pairing. I investigate the possibility of formation and emergence of edge modes using exact diagonalization and singular value decomposition of the Hamiltonian in the Majorana representation, while computing the mass gap of the MZM and its spectral properties. The interplay of cavity induced interactions and effective p-wave short range interactions controls the emergence of the signatures of MZM. I find that under certain conditions MZM distinctively emerge leading to a superradiant topological phase of matter. These MZM have potential applications for quantum information as they are topologically protected analogous to the behaviour of the Kitaev chain. The techniques employed lead to a scheme based on the Majorana representation and exact diagonalization with self consistent conditions that can be applied to other fermionic and analog systems termed Light-Matter-Majorana.
Long-range interactions can fundamentally alter properties in gapped topological phases such as emergent massive edge modes. However, recent research has shifted attention to topological nontrivial critical points or phases, and it is natural to explore how long-range interactions influence them. In this work, we investigate the topological behavior at the quantum critical point of extended Kitaev chains with long-range interactions, which can be derived from the critical Ising model via the Jordan-Wigner transformation in the short-range limit. Specifically, we analytically find that the critical edge modes at the critical point remain stable against long-range interactions. More importantly, we observe that these critical edge modes remain massless even when long- range interactions become very strong. As a by-product, we numerically find that the critical behavior of the long-range model belongs to the free-Majorana-fermion universality class, which is entirely different from the long-range universality class in the usual long-range spin models. Our work could shed new light on the interplay between long-range interactions (frustrated) and the gapless topological phases of matter.
Abstract Topological excitations, such as Majorana zero modes, are a promising route for encoding quantum information. Topologically protected gates of Majorana qubits, based on their braiding, will require some form of network. Here, we propose to build such a network by entangling Majorana matter with light in a microwave cavity QED set-up. Our scheme exploits a light-induced interaction which is universal to all the Majorana nanoscale circuit platforms. This effect stems from a parametric drive of the light-matter coupling in a one-dimensional chain of physical Majorana modes. Our set-up enables all the basic operations needed in a Majorana quantum computing platform such as fusing, braiding, the crucial T-gate, the read-out, and importantly, the stabilization or correction of the physical Majorana modes.
Quantum matter at ultralow temperatures offers a test bed for analyzing and controlling desired properties in strongly correlated systems. Under typical conditions the nature of the atoms fixes the magnetic character of the system. Beyond classical light potentials leading to optical lattices and short-range interactions, high-Q cavities introduce novel dynamics into the system via the quantumness of light. Here we propose a theoretical model and we analyze it using exact diagonalization and density matrix renormalization group simulations. We explore the effects of cavity mediated long-range magnetic interactions and optical lattices in ultracold matter. We find that global interactions modify the underlying magnetic character of the system while introducing competition scenarios. Antiferromagnetic correlated bosonic matter emerges in conditions beyond what nature typically provides. These allow new alternatives toward the design of robust mechanisms for quantum information purposes, exploiting the properties of magnetic phases of strongly correlated quantum matter.
Topological phases in one-dimensional superconducting systems are commonly characterized by symmetry-protected invariants. These invariants determine the number of Majorana zero-energy boundary modes but do not specify their corresponding spatial structure. In this work, we present an analytical study of Majorana zero modes (MZMs) in an extended Kitaev chain with nearest- and next-nearest-neighbor couplings. By expressing the Hamiltonian in the Majorana basis, we derive a recursion relation whose characteristic roots completely determine the spatial structure of the zero modes and yield closed-form expressions for their amplitudes. We show that, even within a single topological phase, the MZMs can exhibit qualitatively distinct decay behaviors-monotonic decay, oscillatory decay, and perfectly localized states. Remarkably, boundary-origin MZMs need not have their maximum probability at the edge of the chain. They can instead exhibit maxima at interior lattice sites with an exponentially decaying envelope from either side of the maxima. Furthermore, the characteristic roots determine the length scale required for finite chains to reproduce the semi-infinite MZM structure, providing a direct link between Hamiltonian parameters, finite-size effects, and experimentally observable spatial profiles.
The realization and manipulation of topological Majorana zero modes (MZMs) have been pivotal in both theoretical and experimental research. In this paper, we present a symmetry enhanced topological model that supports stable, localized MZMs in a one-dimensional interacting fermionic system. The MZMs in our model, induced by particle-number conserving interactions, are fully decoupled from the chain's interior and remain degenerate regardless of chain length, allowing for simulations in extremely short fermionic chains. The topological phase transition is driven by changes in coupling parameters, transitioning to a trivial phase without affecting the MZMs' independence or degeneracy, only their topological protection. Additionally, local symmetries in the model enhance MZMs' stability and reveal unique odd-even effects across different chain lengths.