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:2205.07489 · Physical review. B./Physical review. B

Dynamic generation of nonequilibrium superconducting states in a Kitaev chain

Youguo Shi, K. L. Zhang, Z. Song

Published Nov 14, 2022• 9 citations
arXivHTMLPDF

Abstract

A nonequilibrium state shares macroscopic properties, such as conductivity and superconductivity, with a static state when the two states exhibit an identical average value of an observable over a period. We studied the quench dynamics of a Kitaev chain on the basis of two types of order parameters associated with two channels of pairing: local pairing in real space and Bardeen-Cooper-Schrieffer (BCS)-like pairing in momentum space. Based on the exact solution, we found that the two order parameters were identical for the ground state, which indicated a balance between the two pairing channels and would help determine the quantum phase diagram. However, for a nonequilibrium state obtained through time evolution from an initially prepared vacuum state, the two parameters varied, but both parameters could still help determine the phase diagram. In the region of nontrivial topological phases, nonequilibrium states favored BCS-like pairing. In this paper, we present an alternative approach to dynamically generate a superconducting state from a trivial empty state and illuminate the pairing mechanism.

DOI
10.1103/physrevb.106.184505

Related papers

Emerging topological characterization in nonequilibrium states of quenched Kitaev chains

Youguo Shi, X. Z. Zhang, Z. Song

Topological characteristics of quantum systems are typically determined by the closing of a gap, while the dynamical quantum phase transition (DQPT) during quantum real-time evolution has emerged as a nonequilibrium analog to the quantum phase transition (QPT). In this paper, we illustrate that the system dynamics can be elucidated by considering the precession of a collection of free pseudospins under a magnetic field based on the exact results of extended Kitaev chains. The topology of the driven Hamiltonian is determined by the average winding number of the nonequilibrium state. Furthermore, we establish that the singularity of the DQPT arises from two perpendicular pseudospin vectors associated with the pre- and postquenched Hamiltonians. Moreover, we investigate the distinct behaviors of the dynamic pairing order parameter in both topological and nontopological regions. These findings offer valuable insights into the non-equilibrium behavior of topological superconductors, contributing to the understanding of the resilience of topological properties in driven quantum systems.

arXiv:2311.08056•Physical review. B./Physical review. B•Nov 19, 2024•3 citations

Nonequilibrium dynamics of superconductivity in the Hatsugai-Kohmoto model

Ádám Bácsi, Balázs Dóra

We study the nonequilibrium dynamics of the superconducting order parameter in the Hatsugai-Kohmoto (HK) model. In the absence of superconductivity, its ground state is a non-Fermi liquid, whose properties are controlled by the HK interaction. Our protocol involves quantum quenching the HK interaction but leaving the interaction responsible for superconductivity unchanged. We map out the nonequilibrium dynamical phase diagram of the interacting model which contains three phases where, at long times, the order parameter amplitude vanishes, approaches a constant value, or persistently oscillates. We also investigate the Loschmidt echo in searching for dynamical quantum phase transition and find that its nonanalytic temporal behavior is close but does not match exactly the vanishing of the order parameter. The momentum space entanglement entropy between positive and negative momentum modes, relevant for Cooper pairing, is calculated. Counterintuitively, this momentum space entanglement does not change significantly during the quench dynamics and its value remains reasonably large even for a vanishing superconducting order parameter. Nevertheless, its derivative with respect to the HK interaction signals the dynamical phase transition associated to the late time vanishing of superconductivity.

arXiv:2410.14424•Physical review. B./Physical review. B•Feb 6, 2025•2 citations

Resonant generation of a p -wave Cooper pair in a non-Hermitian Kitaev chain at the exceptional point

X. M. Yang, Z. Song

We investigate a non-Hermitian extension of a Kitaev chain by considering imaginary $p$-wave pairing amplitudes. The exact solution shows that the phase diagram consists of two phases with real and complex Bogoliubov--de Gennes spectra, associated with the $\mathcal{PT}$-symmetry breaking, which is separated by a hyperbolic exceptional line. The exceptional points (EPs) correspond to a specific Cooper pair state $(1+{c}_{k}^{\ifmmode\dagger\else\textdagger\fi{}}{c}_{\ensuremath{-}k}^{\ifmmode\dagger\else\textdagger\fi{}})\left|0\right\ensuremath{\rangle}$ with movable $k$ when the parameters vary along the exceptional line. The non-Hermiticity around EP supports resonant generation of such a pair state from the vacuum state $\left|0\right\ensuremath{\rangle}$ of fermions via the critical dynamic process. In addition, we propose a scheme to generate a superconducting state through a dynamic method.

arXiv:1912.07227•Physical Review A•Aug 19, 2020•13 citations

Cavity-QED Quantum Simulator of Dynamical Phases of a Bardeen-Cooper-Schrieffer Superconductor

Robert J. Lewis-Swan, Diego Barberena, Julia Cline +3 more

We propose to simulate dynamical phases of a BCS superconductor using an ensemble of cold atoms trapped in an optical cavity. Effective Cooper pairs are encoded via the internal states of the atoms, and attractive interactions are realized via the exchange of virtual photons between atoms coupled to a common cavity mode. Control of the interaction strength combined with a tunable dispersion relation of the effective Cooper pairs allows exploration of the full dynamical phase diagram of the BCS model as a function of system parameters and the prepared initial state. Our proposal paves the way for the study of the nonequilibrium features of quantum magnetism and superconductivity by harnessing atom-light interactions in cold atomic gases.

arXiv:2011.13007•Physical Review Letters•Apr 27, 2021•30 citations

Real-space decomposition of p-wave Kitaev chain

D. K. He, E. S. Ma, Z. Song

Abstract We propose an extended Bogoliubov transformation in real space for spinless fermions, based on which a class of Kitaev chains of length 2N with zero chemical potential can be mapped to two independent Kitaev chains of length N. It provides an alternative way to investigate a complicated system from the result of relatively simple systems. We demonstrate the implications of this decomposition by a Su–Schrieffer–Heeger Kitaev model, which supports rich quantum phases. The features of the system, including the groundstate topology and nonequilibrium dynamics, can be revealed directly from that of sub-Kitaev chains. Based on this connection, two types of Bardeen–Cooper–Schrieffer (BCS)-pair order parameters are introduced to characterize the phase diagram, showing the ingredient of two different BCS pairing modes. Analytical analysis and numerical simulations show that the real-space decomposition for the ground state still holds true approximately in presence of finite chemical potential in the gapful regions.

arXiv:2310.05006•New Journal of Physics•Jan 30, 2024•0 citations

Consequences of integrability breaking in quench dynamics of pairing Hamiltonians

Jasen A. Scaramazza, Pietro Smacchia, Emil A. Yuzbashyan

We study the collisionless dynamics of two classes of nonintegrable pairing models. One is a Bardeen-Cooper-Schrieffer model with separable energy-dependent interactions, and the other is a two-dimensional topological superconductor with spin-orbit coupling and a band-splitting external field. The long-time quantum quench dynamics at integrable points of these models are well understood. Namely the squared magnitude of the time-dependent order parameter $\mathrm{\ensuremath{\Delta}}(t)$ can vanish (Phase I), reach a nonzero constant (Phase II), or periodically oscillate as an elliptic function (Phase III). We demonstrate that nonintegrable models, too, exhibit some or all of these nonequilibrium phases. Remarkably, elliptic periodic oscillations persist, even though both their amplitude and functional form change drastically with integrability breaking. Striking new phenomena accompany loss of integrability. First, an extremely long timescale emerges in the relaxation to Phase III, such that short-time numerical simulations risk erroneously classifying the asymptotic state. This timescale diverges near integrable points. Second, an entirely new Phase IV of quasiperiodic oscillations of $|\mathrm{\ensuremath{\Delta}}|$ emerges in the quantum quench phase diagrams of nonintegrable pairing models. As integrability techniques do not apply for the models we study, we develop the concept of asymptotic self-consistency and a linear stability analysis of the asymptotic phases. With the help of these new tools, we determine the phase boundaries, characterize the asymptotic state, and clarify the physical meaning of the quantum quench phase diagrams of BCS superconductors. We also propose an explanation of these diagrams in terms of bifurcation theory.

arXiv:1812.04410•Physical review. B./Physical review. B•Feb 28, 2019•15 citations
A nonequilibrium state shares macroscopic properties, such as conductivity and superconductivity, with a static state when the two states exhibit an identical average value of an observable over a period. We studied the quench dynamics of a Kitaev chain on the basis of two types of order parameters associated with two channels of pairing: local pairing in real space and Bardeen-Cooper-Schrieffer (BCS)-like pairing in momentum space. Based on the exact solution, we found that the two order parameters were identical for the ground state, which indicated a balance between the two pairing channels and would help determine the quantum phase diagram. However, for a nonequilibrium state obtained through time evolution from an initially prepared vacuum state, the two parameters varied, but both parameters could still help determine the phase diagram. In the region of nontrivial topological phases, nonequilibrium states favored BCS-like pairing. In this paper, we present an alternative approach to dynamically generate a superconducting state from a trivial empty state and illuminate the pairing mechanism.
Topological characteristics of quantum systems are typically determined by the closing of a gap, while the dynamical quantum phase transition (DQPT) during quantum real-time evolution has emerged as a nonequilibrium analog to the quantum phase transition (QPT). In this paper, we illustrate that the system dynamics can be elucidated by considering the precession of a collection of free pseudospins under a magnetic field based on the exact results of extended Kitaev chains. The topology of the driven Hamiltonian is determined by the average winding number of the nonequilibrium state. Furthermore, we establish that the singularity of the DQPT arises from two perpendicular pseudospin vectors associated with the pre- and postquenched Hamiltonians. Moreover, we investigate the distinct behaviors of the dynamic pairing order parameter in both topological and nontopological regions. These findings offer valuable insights into the non-equilibrium behavior of topological superconductors, contributing to the understanding of the resilience of topological properties in driven quantum systems.
We study the nonequilibrium dynamics of the superconducting order parameter in the Hatsugai-Kohmoto (HK) model. In the absence of superconductivity, its ground state is a non-Fermi liquid, whose properties are controlled by the HK interaction. Our protocol involves quantum quenching the HK interaction but leaving the interaction responsible for superconductivity unchanged. We map out the nonequilibrium dynamical phase diagram of the interacting model which contains three phases where, at long times, the order parameter amplitude vanishes, approaches a constant value, or persistently oscillates. We also investigate the Loschmidt echo in searching for dynamical quantum phase transition and find that its nonanalytic temporal behavior is close but does not match exactly the vanishing of the order parameter. The momentum space entanglement entropy between positive and negative momentum modes, relevant for Cooper pairing, is calculated. Counterintuitively, this momentum space entanglement does not change significantly during the quench dynamics and its value remains reasonably large even for a vanishing superconducting order parameter. Nevertheless, its derivative with respect to the HK interaction signals the dynamical phase transition associated to the late time vanishing of superconductivity.
We investigate a non-Hermitian extension of a Kitaev chain by considering imaginary ppp-wave pairing amplitudes. The exact solution shows that the phase diagram consists of two phases with real and complex Bogoliubov--de Gennes spectra, associated with the PT\mathcal{PT}PT-symmetry breaking, which is separated by a hyperbolic exceptional line. The exceptional points (EPs) correspond to a specific Cooper pair state $(1+{c}_{k}^{\ifmmode\dagger\else\textdagger\fi{}}{c}_{\ensuremath{-}k}^{\ifmmode\dagger\else\textdagger\fi{}})\left|0\right\ensuremath{\rangle}$ with movable kkk when the parameters vary along the exceptional line. The non-Hermiticity around EP supports resonant generation of such a pair state from the vacuum state $\left|0\right\ensuremath{\rangle}$ of fermions via the critical dynamic process. In addition, we propose a scheme to generate a superconducting state through a dynamic method.
We propose to simulate dynamical phases of a BCS superconductor using an ensemble of cold atoms trapped in an optical cavity. Effective Cooper pairs are encoded via the internal states of the atoms, and attractive interactions are realized via the exchange of virtual photons between atoms coupled to a common cavity mode. Control of the interaction strength combined with a tunable dispersion relation of the effective Cooper pairs allows exploration of the full dynamical phase diagram of the BCS model as a function of system parameters and the prepared initial state. Our proposal paves the way for the study of the nonequilibrium features of quantum magnetism and superconductivity by harnessing atom-light interactions in cold atomic gases.
Abstract We propose an extended Bogoliubov transformation in real space for spinless fermions, based on which a class of Kitaev chains of length 2N with zero chemical potential can be mapped to two independent Kitaev chains of length N. It provides an alternative way to investigate a complicated system from the result of relatively simple systems. We demonstrate the implications of this decomposition by a Su–Schrieffer–Heeger Kitaev model, which supports rich quantum phases. The features of the system, including the groundstate topology and nonequilibrium dynamics, can be revealed directly from that of sub-Kitaev chains. Based on this connection, two types of Bardeen–Cooper–Schrieffer (BCS)-pair order parameters are introduced to characterize the phase diagram, showing the ingredient of two different BCS pairing modes. Analytical analysis and numerical simulations show that the real-space decomposition for the ground state still holds true approximately in presence of finite chemical potential in the gapful regions.
We study the collisionless dynamics of two classes of nonintegrable pairing models. One is a Bardeen-Cooper-Schrieffer model with separable energy-dependent interactions, and the other is a two-dimensional topological superconductor with spin-orbit coupling and a band-splitting external field. The long-time quantum quench dynamics at integrable points of these models are well understood. Namely the squared magnitude of the time-dependent order parameter $\mathrm{\ensuremath{\Delta}}(t)$ can vanish (Phase I), reach a nonzero constant (Phase II), or periodically oscillate as an elliptic function (Phase III). We demonstrate that nonintegrable models, too, exhibit some or all of these nonequilibrium phases. Remarkably, elliptic periodic oscillations persist, even though both their amplitude and functional form change drastically with integrability breaking. Striking new phenomena accompany loss of integrability. First, an extremely long timescale emerges in the relaxation to Phase III, such that short-time numerical simulations risk erroneously classifying the asymptotic state. This timescale diverges near integrable points. Second, an entirely new Phase IV of quasiperiodic oscillations of $|\mathrm{\ensuremath{\Delta}}|$ emerges in the quantum quench phase diagrams of nonintegrable pairing models. As integrability techniques do not apply for the models we study, we develop the concept of asymptotic self-consistency and a linear stability analysis of the asymptotic phases. With the help of these new tools, we determine the phase boundaries, characterize the asymptotic state, and clarify the physical meaning of the quantum quench phase diagrams of BCS superconductors. We also propose an explanation of these diagrams in terms of bifurcation theory.