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:1811.06388

Field Induced Oscillation of Two Majorana Modes in a Quantum Ring

Yue Yu, Kwok Yip Szeto

Published Nov 14, 2018• 0 citations
arXivHTMLPDF

Abstract

We calculate the topological boundary modes found for quantum wire for a quantum ring. For the symmetric ring we find analytical solutions for two quasi-particles identifiable as the Majorana states and for asymmetric ring, we have also find approximate solution. By turning on a small field at time zero, we find a field induced oscillation of the Majorana states that was initially localized. The range of validity of our solution, the relation between the period of oscillation and the coin parameter and field strength, and the encoding of a message of the on/off of the field using the Majorana states are discussed. Our results suggest ways to reduce decoherence for small systems, thereby providing a good candidate for quantum memory and computing as the Majorana qubit is topologically protected.

DOI
10.48550/arxiv.1811.06388

Related papers

Field Induced Oscillation of Two Majorana Modes for a finite Quantum Wire

Yue Yu, Kwok Yip Szeto

The evolution of quantum walk on a finite wire under a small increment of vector potential $α$ can exhibit intrinsic quantum oscillation of the two topologically protected bound states corresponding to the Majorana modes. By tuning an external electric field corresponding to the addition of an $α$ impulse at the end of each intrinsic period, the intrinsic oscillation is enveloped by a beat modulation with a longer period. This beat oscillation is useful in the preparation of decoherence-free qubit in trapped ion chain and may be observed in several experiments.

arXiv:1611.00634•Nov 2, 2016•0 citations

Stability of Floquet Majorana Box Qubits

Anne Matthies, Jinhong Park, Erez Berg +1 more

In one-dimensional topological superconductors driven periodically with the frequency ω, two types of topological edge modes may appear, the well-known Majorana zero mode and a Floquet Majorana mode located at the quasienergy ℏω/2. We investigate two Josephson-coupled topological quantum wires in the presence of Coulomb interactions, forming a so-called Majorana box qubit. An oscillating gate voltage can induce Floquet Majorana modes in both wires. This allows for the encoding of three qubits in a sector with fixed electron parity. If such a system is prepared by increasing the amplitude of oscillations adiabatically, it is inherently unstable as interactions resonantly create quasiparticles. This can be avoided by using instead a protocol where the oscillation frequency is increased slowly. In this case, one can find a parameter regime where the system remains stable.

arXiv:2110.05281•Physical Review Letters•Mar 24, 2022•15 citations

Ansatz for Majorana modes for a quantum walk in a finite wire

Ho Tat Lam, Yue Yu, Kwok Yip Szeto

The topological phases in a one-dimensional quantum walk can be classified by the coin parameters. By solving for the general exact solutions of bound states in a one-dimensional quantum walk with boundaries specified by different coin parameters, we show that these bound states are Majorana modes with quasienergy $E=0,\ensuremath{\pi}$. These modes are qualitatively different for different boundary conditions used. For systems with two boundaries, such as finite wires, we find the same exact solution as the single boundary system if the boundary condition is antisymmetric. For a two-boundary system with symmetric boundary conditions in a finite wire, the interaction energy between two Majorana bound states can be computed as a function of the length of the wire and the coin parameter in the wire. Suggestions of observing these modes are provided.

arXiv:1508.07528•Physical Review A•May 16, 2016•8 citations

Stability of Floquet Majorana Box Qubits

Anne Matthies, Jinhong Park, Erez Berg +1 more

In one-dimensional topological superconductors driven periodically with the frequency omega, two types of topological edge modes may appear, the well-known Majorana zero mode and a Floquet Majorana mode located at the quasienergy PLANCK CONSTANT OVER TWO PI omega/2. We investigate two Josephson-coupled topological quantum wires in the presence of Coulomb interactions, forming a so-called Majorana box qubit. An oscillating gate voltage can induce Floquet Majorana modes in both wires. This allows for the encoding of three qubits in a sector with fixed electron parity. If such a system is prepared by increasing the amplitude of oscillations adiabatically, it is inherently unstable as interactions resonantly create quasiparticles. This can be avoided by using instead a protocol where the oscillation frequency is increased slowly. In this case, one can find a parameter regime where the system remains stable.

•Jan 1, 2022•11 citations

Majorana Zero Modes in Synthetic Dimensions

Or Golan, Eran Sela, Kirill Shtengel

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.

arXiv:1711.11064•Nov 29, 2017•0 citations

Majorana oscillations and parity crossings in semiconductor nanowire-based transmon qubits

J. Ávila, E. Prada, P. San-Jose +1 more

We show that the microwave (MW) spectra in semiconductor-nanowire-based transmon qubits provide a strong signature of the presence of Majorana bound states in the junction.This occurs as an external magnetic field tunes the wire into the topological regime and the energy splitting of the emergent Majorana modes oscillates around zero energy owing to their wave function spatial overlap in finite-length wires.In particular, we discuss how these Majorana oscillations, and the concomitant fermion parity switches in the ground state of the junction, result in distinct spectroscopic features-in the form of an intermittent visibility of absorption lines-that strongly deviate from standard transmon behavior.In contrast, nonoscillating zero modes, such as topologically trivial Andreev bound states resulting from sufficiently smooth potentials, exhibit an overall standard transmon response.These differences in the MW response could help determine whether the junction contains topological Majoranas or not.

arXiv:2003.02858•Physical Review Research•Sep 25, 2020•25 citations
We calculate the topological boundary modes found for quantum wire for a quantum ring. For the symmetric ring we find analytical solutions for two quasi-particles identifiable as the Majorana states and for asymmetric ring, we have also find approximate solution. By turning on a small field at time zero, we find a field induced oscillation of the Majorana states that was initially localized. The range of validity of our solution, the relation between the period of oscillation and the coin parameter and field strength, and the encoding of a message of the on/off of the field using the Majorana states are discussed. Our results suggest ways to reduce decoherence for small systems, thereby providing a good candidate for quantum memory and computing as the Majorana qubit is topologically protected.
The evolution of quantum walk on a finite wire under a small increment of vector potential ααα can exhibit intrinsic quantum oscillation of the two topologically protected bound states corresponding to the Majorana modes. By tuning an external electric field corresponding to the addition of an ααα impulse at the end of each intrinsic period, the intrinsic oscillation is enveloped by a beat modulation with a longer period. This beat oscillation is useful in the preparation of decoherence-free qubit in trapped ion chain and may be observed in several experiments.
In one-dimensional topological superconductors driven periodically with the frequency ω, two types of topological edge modes may appear, the well-known Majorana zero mode and a Floquet Majorana mode located at the quasienergy ℏω/2. We investigate two Josephson-coupled topological quantum wires in the presence of Coulomb interactions, forming a so-called Majorana box qubit. An oscillating gate voltage can induce Floquet Majorana modes in both wires. This allows for the encoding of three qubits in a sector with fixed electron parity. If such a system is prepared by increasing the amplitude of oscillations adiabatically, it is inherently unstable as interactions resonantly create quasiparticles. This can be avoided by using instead a protocol where the oscillation frequency is increased slowly. In this case, one can find a parameter regime where the system remains stable.
The topological phases in a one-dimensional quantum walk can be classified by the coin parameters. By solving for the general exact solutions of bound states in a one-dimensional quantum walk with boundaries specified by different coin parameters, we show that these bound states are Majorana modes with quasienergy $E=0,\ensuremath{\pi}$. These modes are qualitatively different for different boundary conditions used. For systems with two boundaries, such as finite wires, we find the same exact solution as the single boundary system if the boundary condition is antisymmetric. For a two-boundary system with symmetric boundary conditions in a finite wire, the interaction energy between two Majorana bound states can be computed as a function of the length of the wire and the coin parameter in the wire. Suggestions of observing these modes are provided.
In one-dimensional topological superconductors driven periodically with the frequency omega, two types of topological edge modes may appear, the well-known Majorana zero mode and a Floquet Majorana mode located at the quasienergy PLANCK CONSTANT OVER TWO PI omega/2. We investigate two Josephson-coupled topological quantum wires in the presence of Coulomb interactions, forming a so-called Majorana box qubit. An oscillating gate voltage can induce Floquet Majorana modes in both wires. This allows for the encoding of three qubits in a sector with fixed electron parity. If such a system is prepared by increasing the amplitude of oscillations adiabatically, it is inherently unstable as interactions resonantly create quasiparticles. This can be avoided by using instead a protocol where the oscillation frequency is increased slowly. In this case, one can find a parameter regime where the system remains stable.
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.
We show that the microwave (MW) spectra in semiconductor-nanowire-based transmon qubits provide a strong signature of the presence of Majorana bound states in the junction.This occurs as an external magnetic field tunes the wire into the topological regime and the energy splitting of the emergent Majorana modes oscillates around zero energy owing to their wave function spatial overlap in finite-length wires.In particular, we discuss how these Majorana oscillations, and the concomitant fermion parity switches in the ground state of the junction, result in distinct spectroscopic features-in the form of an intermittent visibility of absorption lines-that strongly deviate from standard transmon behavior.In contrast, nonoscillating zero modes, such as topologically trivial Andreev bound states resulting from sufficiently smooth potentials, exhibit an overall standard transmon response.These differences in the MW response could help determine whether the junction contains topological Majoranas or not.