Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2412.15286 · Physical review. B./Physical review. B

Adiabatic preparation of a number-conserving atomic Majorana phase

Benjamin Michen, Tim Pokart, Jan Carl Budich

Published Jun 24, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/dqsb-nzx1

Related papers

Floquet-Engineered Hybrid Topological Orders with Majorana Edge Modes in Number-Conserving Fermionic Quantum Simulators

Zhi Lin, Song, Qi, Yue, Sheng +3 more

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.

arXiv:2502.06569•Feb 10, 2025•0 citations

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

Anaïs Defossez, Laurens Vanderstraeten, Lucila Peralta Gavensky +1 more

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.

arXiv:2412.14886•Physical Review Research•May 27, 2025•6 citations

Nudging Quantum Matter over the Edge of Topological Order

Benjamin Michen

This thesis explores multiple ways of nudging quantum matter over the edge of topological order and is divided into two parts. The first part offers an overview of the theoretical foundations for the original results presented in the second part. These results first focus on non-standard dynamical paths between trivial and topological phases with applications to adiabatic state preparation in atomic quantum simulators. We commence with the adiabatic preparation of a fractional Chern insulator from a one-dimensional charge density wave. To achieve this, we show analytically how an anisotropy of the hopping amplitudes can effectively change the aspect ratio of the system and induce a so-called ``thin-torus'' limit. The analytical results are corroborated using numerical exact diagonalization. Subsequently, we investigate the adiabatic preparation of a number-conserving Majorana phase protected by a parity symmetry that emerges at a critical point of a two-leg ladder subject to a pair-hopping interaction. For this purpose, we design a symmetry-breaking flux term that can gap out the critical target state and devise a protocol that ramps down the flux term with a power law adapted to system size so as to enable an optimal (linear) scaling of preparation time. To design the flux term, we treat the system in the framework of constructive bosonization. The results are supported numerically using matrix product state techniques to calculate excitation gaps, correlation functions, and time evolutions. Then, we shift the focus to the identification of minimal requirements for topological effects and demonstrate how an integer quantum Hall phase can form in a topologically completely trivial band structure at the onset of disorder. These results are confirmed through extensive numerical simulations with the software package Kwant. Finally, we investigate a Floquet system in an anomalous topological phase that is subjected to nonlinear effects. Specifically, we demonstrate a nonlinearity induced scattering of an edge state off a circulating bulk mode by calculating the exact dynamics of the system through a numerical solution of the nonlinear Schrödinger equation. Notably, we find that the scattering amplitude is determined by interference effects between the two pulses and therefore highly sensitive to their initial relative phase.

•Nov 20, 2025•0 citations

Adiabatic preparation of a fractional quantum Hall fluid by coherently pumping atoms from a Bose-Einstein condensate

Alberto Tabarelli de Fatis, Christof Weitenberg, Alexander Schnell +2 more

We propose a protocol to adiabatically prepare a many-particle fractional quantum Hall fluid of bosonic ultracold atoms exploiting a time-dependent coherent coupling of a strongly interacting atomic state with a large dilute Bose-Einstein condensate. Starting from an empty cloud, atoms with well-defined angular momentum are coherently pumped into the fluid by Raman beams with a Laguerre-Gauss profile. Compared to number-conserving schemes which rely on finite-size-induced topological gaps, we identify an adiabatic path in the Fock space which avoids crossing topological phase transitions and thus maintains a sizable adiabatic gap open at all times. The efficiency of our preparation protocol is numerically assessed for typical experimental parameters up to particle numbers that largely exceed the experimental state-of-the-art. The crucial advantage of including an anharmonic confinement is finally highlighted.

cond-mat.quant-gasCross-listedarXiv:2606.15951•Jun 16, 2026•0 citations

Absence of gapless Majorana edge modes in few-leg bosonic flux ladders

Felix A. Palm, Cécile Repellin, Nathan Goldman +1 more

The search for Majorana excitations has seen tremendous efforts in recent years, ultimately aiming for their individual controllability in future topological quantum computers. A promising framework to realize such exotic Majorana fermions are topologically ordered non-Abelian phases of matter, such as certain fractional quantum Hall states. Quantum simulators provide unprecedented controllability and versatility to investigate such states, and developing experimentally feasible schemes to realize and identify them is of immediate relevance. Motivated by recent experiments, we consider bosons on coupled chains, subjected to a magnetic flux and experiencing Hubbard repulsion. At magnetic filling factor ν = 1 , similar systems on cylinders have been found to host the non-Abelian Moore-Read Pfaffian state in the bulk. Here, we address the question of whether more realistic few-leg ladders can host this exotic state and its chiral Majorana edge states. To this end, we perform extensive density-matrix renormalization-group simulations and determine the central charge of the ground state. While we do not find any evidence of gapless Majorana edge modes in systems of up to six legs, exact diagonalization of small systems reveals evidence for the Pfaffian state in the entanglement structure. By systematically varying the number of legs and monitoring the appearance and disappearance of this signal, our work highlights the importance of finite-size effects for the realization of exotic states in experimentally realistic systems.

arXiv:2407.18873•Physical Review Research•Jan 6, 2025•1 citation

Majorana zero modes in fermionic wires coupled by Aharonov-Bohm cages

Niklas Tausendpfund, Sebastian Diehl, Matteo Rizzi

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.

arXiv:2208.09382•Physical review. B./Physical review. B•Jan 17, 2023•4 citations
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.
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 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.
This thesis explores multiple ways of nudging quantum matter over the edge of topological order and is divided into two parts. The first part offers an overview of the theoretical foundations for the original results presented in the second part. These results first focus on non-standard dynamical paths between trivial and topological phases with applications to adiabatic state preparation in atomic quantum simulators. We commence with the adiabatic preparation of a fractional Chern insulator from a one-dimensional charge density wave. To achieve this, we show analytically how an anisotropy of the hopping amplitudes can effectively change the aspect ratio of the system and induce a so-called ``thin-torus'' limit. The analytical results are corroborated using numerical exact diagonalization. Subsequently, we investigate the adiabatic preparation of a number-conserving Majorana phase protected by a parity symmetry that emerges at a critical point of a two-leg ladder subject to a pair-hopping interaction. For this purpose, we design a symmetry-breaking flux term that can gap out the critical target state and devise a protocol that ramps down the flux term with a power law adapted to system size so as to enable an optimal (linear) scaling of preparation time. To design the flux term, we treat the system in the framework of constructive bosonization. The results are supported numerically using matrix product state techniques to calculate excitation gaps, correlation functions, and time evolutions. Then, we shift the focus to the identification of minimal requirements for topological effects and demonstrate how an integer quantum Hall phase can form in a topologically completely trivial band structure at the onset of disorder. These results are confirmed through extensive numerical simulations with the software package Kwant. Finally, we investigate a Floquet system in an anomalous topological phase that is subjected to nonlinear effects. Specifically, we demonstrate a nonlinearity induced scattering of an edge state off a circulating bulk mode by calculating the exact dynamics of the system through a numerical solution of the nonlinear Schrödinger equation. Notably, we find that the scattering amplitude is determined by interference effects between the two pulses and therefore highly sensitive to their initial relative phase.
We propose a protocol to adiabatically prepare a many-particle fractional quantum Hall fluid of bosonic ultracold atoms exploiting a time-dependent coherent coupling of a strongly interacting atomic state with a large dilute Bose-Einstein condensate. Starting from an empty cloud, atoms with well-defined angular momentum are coherently pumped into the fluid by Raman beams with a Laguerre-Gauss profile. Compared to number-conserving schemes which rely on finite-size-induced topological gaps, we identify an adiabatic path in the Fock space which avoids crossing topological phase transitions and thus maintains a sizable adiabatic gap open at all times. The efficiency of our preparation protocol is numerically assessed for typical experimental parameters up to particle numbers that largely exceed the experimental state-of-the-art. The crucial advantage of including an anharmonic confinement is finally highlighted.
The search for Majorana excitations has seen tremendous efforts in recent years, ultimately aiming for their individual controllability in future topological quantum computers. A promising framework to realize such exotic Majorana fermions are topologically ordered non-Abelian phases of matter, such as certain fractional quantum Hall states. Quantum simulators provide unprecedented controllability and versatility to investigate such states, and developing experimentally feasible schemes to realize and identify them is of immediate relevance. Motivated by recent experiments, we consider bosons on coupled chains, subjected to a magnetic flux and experiencing Hubbard repulsion. At magnetic filling factor ν = 1 , similar systems on cylinders have been found to host the non-Abelian Moore-Read Pfaffian state in the bulk. Here, we address the question of whether more realistic few-leg ladders can host this exotic state and its chiral Majorana edge states. To this end, we perform extensive density-matrix renormalization-group simulations and determine the central charge of the ground state. While we do not find any evidence of gapless Majorana edge modes in systems of up to six legs, exact diagonalization of small systems reveals evidence for the Pfaffian state in the entanglement structure. By systematically varying the number of legs and monitoring the appearance and disappearance of this signal, our work highlights the importance of finite-size effects for the realization of exotic states in experimentally realistic systems.
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.