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arXiv:2412.14886 · Physical Review Research

Dynamic realization of Majorana zero modes in a particle-conserving ladder

Anaïs Defossez, Laurens Vanderstraeten, Lucila Peralta Gavensky, Nathan Goldman

Published May 27, 2025• 6 citations
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Abstract

We present a scheme to realize a topological superconducting system supporting Majorana zero modes, within a number-conserving framework suitable for optical-lattice experiments. Our approach builds on the engineering of pair-hopping processes on a ladder geometry, using a sequence of pulses that activate single-particle hopping in a time-periodic manner. We demonstrate that this dynamic setting is well captured by an effective Hamiltonian that preserves the parity symmetry, a key requirement for the stabilization of Majorana zero modes. The phase diagram of our system is determined using a bosonization theory, which is then validated by a numerical study of the topological bulk gap and entanglement spectrum using matrix product states. Our results indicate that Majorana zero modes can be stabilized in a large parameter space, accessible in optical-lattice experiments.

DOI
10.1103/physrevresearch.7.023183

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We present a scheme to realize a topological superconducting system supporting Majorana zero modes, within a number-conserving framework suitable for optical-lattice experiments. Our approach builds on the engineering of pair-hopping processes on a ladder geometry, using a sequence of pulses that activate single-particle hopping in a time-periodic manner. We demonstrate that this dynamic setting is well captured by an effective Hamiltonian that preserves the parity symmetry, a key requirement for the stabilization of Majorana zero modes. The phase diagram of our system is determined using a bosonization theory, which is then validated by a numerical study of the topological bulk gap and entanglement spectrum using matrix product states. Our results indicate that Majorana zero modes can be stabilized in a large parameter space, accessible in optical-lattice experiments.
We devise a number-conserving scheme for the realization of Majorana zero modes in an interacting fermionic ladder coupled by Aharonov-Bohm cages. The latter provide an efficient mechanism to cancel single-particle hopping by destructive interference. The crucial parity symmetry in each wire is thus encoded in the geometry of the setup, in particular, its translation invariance. A generic nearest-neighbor interaction generates the desired correlated hopping of pairs. We exhibit the presence of an extended topological region in parameter space, first in a simplified effective model via bosonization techniques, and subsequently in a larger parameter regime with matrix-product-states numerical simulations. We demonstrate the adiabatic connection to previous models, including exactly solvable ones, and we briefly comment on possible experimental realizations in synthetic quantum platforms, like cold atomic samples.
We construct a protocol to adiabatically prepare the ground state of a widely discussed number-conserving model Hamiltonian for ultracold atoms in optical lattices that supports Majorana edge states. In particular, we introduce a symmetry breaking mass term that amounts to threading a commensurate (artificial) magnetic flux through the plaquettes of the considered two-leg ladder which opens a constant bulk gap. This enables the preparation of the topological Majorana phase from a trivial Mott insulator state with optimal asymptotic scaling of the ramp time in system size, which is linear owing to the critical nature of the target state. Using constructive bosonization techniques that account for both finite size effects and global fermion number conservation, we are able to fully explain with theory the somewhat counterintuitive necessity of the aforementioned commensurate flux for a controlled bulk gap. Our analytical predictions are corroborated and quantified by unbiased numerical matrix product states (MPS) simulations. Directly building up on previous experimental work, the crucial flux-term of the proposed protocol is feasible with state-of-the-art experimental techniques in atomic quantum simulators.
One promising avenue to study one-dimensional (1D) topological phases is to realize them in synthetic materials such as cold atomic gases. Intriguingly, it is possible to realize Majorana boundary modes in a 1D number-conserving system consisting of two fermionic chains coupled only by pair-hopping processes [C. V. Kraus et al., Phys. Rev. Lett. 111, 173004 (2013)]. It is commonly believed that significant interchain single-particle tunneling necessarily destroys these Majorana modes, as it spoils the Z2{\mathbb{Z}}_{2}Z2​ fermion-parity symmetry that protects them. In this Rapid Communication, we present a mechanism to overcome this obstacle, by piercing a (synthetic) magnetic $\ensuremath{\pi}$ flux through each plaquette of the Fermi ladder. Using bosonization, we show that in this case there exists an exact leg-interchange symmetry that is robust to interchain hopping, and acts as fermion parity at long wavelengths. We utilize density matrix renormalization group and exact diagonalization to verify that the resulting model exhibits Majorana boundary modes up to large single-particle tunnelings, comparable to the intrachain hopping strength. Our work highlights the unusual impacts of different topologically trivial band structures on these interaction-driven topological phases, and identifies a distinct route to stabilizing Majorana boundary modes in 1D fermionic ladders.
We develop an experimental protocol based on Floquet-engineered ultracold fermions in optical lattices, enabling the emulation of pair-hopping and competing singlet/triplet pairing interactions. Through large-scale density matrix renormalization group (DMRG) simulations, we uncover three emergent topological phases: (i) A Majorana-enabled spin-density-wave (MS) phase featuring exponentially localized edge charges, non-local fermionic edge correlations, and doubly degenerate entanglement spectra; (ii) A z-axis polarized triplet superconducting (TS) phase exhibiting fractionalized edge spins (S=1/4 per edge), two-fold ground state degeneracy and a bulk single-particle gap; (iii) A hybrid x-directional triplet superconducting (XTS) phase that uniquely combines fractional spin textures and Majorana-type edge correlations, defining a new universality class of hybrid orders in number-conserving systems. These findings establish a universal framework for engineering non-Abelian topological matter, crucially bypassing the need for external pairing fields while maintaining experimental feasibility with current cold-atom techniques.
We show the presence of Majorana edge modes in an interacting fermionic ladder with spin in a number-conserved setting. The interchain single-particle hopping is suppressed and only a pair hopping is present between the different chains of the ladder. Additionally, the hopping along the chains is spin imbalanced and a transverse magnetic field is applied breaking time-reversal invariance. We study the robustness of the topological phase with respect to an on-site interaction between the spin-up and spin-down fermions and the spin-dependent imbalance of the hopping. The main result of the present work is that the topological phase survives for a finite region in the parameter space in the presence of interactions. The localized Majorana edge modes seem to be more stable in the case when the on-site interaction is an attraction.
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.