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arXiv:2211.14145 · Physical review. B./Physical review. B

From edge to bulk: Cavity-induced displacement of topological nonlocal qubits

F. P. M. Méndez-Córdoba, Ferney J. Rodríguez, C. Tejedor, Luis Quiroga

Published Mar 2, 2023• 9 citations
arXivHTMLPDF

Abstract

We investigate the ability of selective cavity coupling to a topological chain for tailoring the connectivity of Majorana fermions. We show how topological qubits (TQs), associated with nonlocal Majorana fermion pairing, can be displaced from the edges to the bulk of a topological chain through selective access to light-matter interaction with specific physical sites. In particular, we present a comprehensive density matrix renormalization group study of ground-state features in different chain-cavity coupling geometries, and we validate analytical insights in the strong-coupling regime. This type of Majorana fermion correlation generation process comes with emergent cavity photon features. Moreover, by considering the time evolution after a sudden quench of the cavity-matter coupling strength, we show that the development of high nontrivial matter (Majorana) correlations leaves behind measurable nonclassical photon imprints in the cavity. Innovative ways to dynamically generate TQ nonlocal correlations in topological chains of arbitrary length are thus provided, opening alternative routes to controllable long-range entanglement in hybrid photonic solid-state systems.

DOI
10.1103/physrevb.107.125104

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We investigate the ability of selective cavity coupling to a topological chain for tailoring the connectivity of Majorana fermions. We show how topological qubits (TQs), associated with nonlocal Majorana fermion pairing, can be displaced from the edges to the bulk of a topological chain through selective access to light-matter interaction with specific physical sites. In particular, we present a comprehensive density matrix renormalization group study of ground-state features in different chain-cavity coupling geometries, and we validate analytical insights in the strong-coupling regime. This type of Majorana fermion correlation generation process comes with emergent cavity photon features. Moreover, by considering the time evolution after a sudden quench of the cavity-matter coupling strength, we show that the development of high nontrivial matter (Majorana) correlations leaves behind measurable nonclassical photon imprints in the cavity. Innovative ways to dynamically generate TQ nonlocal correlations in topological chains of arbitrary length are thus provided, opening alternative routes to controllable long-range entanglement in hybrid photonic solid-state systems.
Abstract We investigate the effects of coupling a local electromagnetic cavity to a segment of a topological Kitaev chain (KC), with particular emphasis on the interplay between photons and Majorana zero modes (MZMs). In addition to the well-known scissor effect-which effectively partitions the chain and isolates free MZMs in the bulk-we provide evidence of non-trivial fusion rules and braiding operations, hallmark signatures of non-Abelian anyons, enabled by spatially selective ultrastrong KC-cavity coupling. We propose that these distinctive MZM properties can be experimentally probed via fermionic parity measurements and photon-induced Berry phases. Furthermore, we demonstrate that, in the so-called sweet-spot regime, the coupled system can be mapped onto a Rabi-like model with a homodyne-rotated quadrature, offering a simplified yet powerful theoretical description. Exploiting the symmetry of fermionic modes within a two-site cavity configuration, we also show the feasibility of generating hybrid MZM-polariton Schrödinger cat states. Our findings offer a novel approach to manipulating topological quantum matter through local light–matter interactions and provide theoretical tools for future experimental realizations in platforms such as quantum materials or superconducting circuits.
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Recent experimental advances in the field of cold atoms led to the development of novel techniques for producing synthetic dimensions and synthetic magnetic fields, thus greatly expanding the utility of cold atomic systems for exploring exotic states of matter. In this paper we investigate the possibility of using experimentally tunable interactions in such systems to mimic the physics of Majorana chains, currently a subject of intense research. Crucially to our proposal, the interactions, which are local in space, appear non-local in the synthetic dimension. We use this fact to induce coupling between counter-propagating edge modes in the quantum Hall regime. For the case of attractive interactions in a system composed of two tunneling-coupled chains, we find a gapless quasi-topological phase with a doubly-degenerate ground state. While the total number of particles in the system is kept fixed, this phase is characterized by strong fluctuations of the pair number in each chain. Each ground state is characterized by the parity of the total particle number in each chain, similar to Majorana wires. However, in our system this degeneracy persists for periodic boundary conditions. For open boundary conditions there is a small splitting of this degeneracy due to the single-particle hopping at the edges. We show how subjecting the system to additional synthetic flux or asymmetric potentials on the two chains can be used to control this nonlocal qubit. We propose experimental probes for testing the nonlocal nature of such a qubit and measuring its state.
Quantum systems inside high-Q cavities offer an excellent testbed for the control of emergent symmetries induced by light and their interplay with quantum matter. Recently several developments in cavity experiments with neutral atoms and other quantum objects such as ions motivate the study of their quantum correlated properties and their entanglement to tailor and control the behavior of the system. Using the enhanced coupling between light and interacting matter we explore the properties of emergent superradiant modes using our newly developed Light-Matter DMRG algorithm with strongly interacting spin chains. We explore a experimentally viable generalization of the transverse Ising chain coupled to the cavity light where it is possible to induce multimode structures tailored by the light pumped into the system. We find a plethora of scenarios can be explored with clear and accesible measurable signatures. This allows to study the physics of emergent orders and strong quantum correlations with quantum spins where the local and long range coupling can be efficiently simulated. We find that quantum spin nematic states with long range order and magnon pairs emerge as the transitions to superradiant phases take place. Notably, we show the cavity field allows the optimization of entanglement between spins for different light induced modes which can be used for quantum state engineering of quantum correlated states. Our methods can be used to model other hybrid quantum systems efficiently.
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 ppp-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.
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.