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:1105.2167 · Physical Review A

Dynamics of a tight-binding ring threaded by time-periodic magnetic flux

W. H. Hu, Z. Song

Published Nov 9, 2011• 5 citations
arXivHTMLPDF

Abstract

We analytically study the effects of periodically alternating magnetic fields on the dynamics of a tight-binding ring. It is shown that an arbitrary quantum state can be frozen coherently at will by the very frequent square-wave field as well as the monochromatic-wave field when the corresponding optimal amplitudes are taken. Numerical simulations show that the average fidelity depends on not only the system parameters, but also the features of the quantum state. Moreover, taking the initial zero-momentum Gaussian wave packets as examples, we show the dependence of the threshold frequency on the width of the packet for the given average fidelities. These observations provide a means to perform the quantum-state engineering.

DOI
10.1103/physreva.84.052310

Related papers

Bloch oscillations in interacting systems driven by a time-dependent magnetic field

H. P. Zhang, Z. Song

According to Faraday's law in classical physics, a varying magnetic field stimulates an electric eddy field. Intuitively, when a classical field is constant and imposed on a lattice, the Wannier-Stark ladders (WSL) can be established, resulting in Bloch oscillations. In this work, we investigate the dynamics of an interacting system on a (generalized) ring lattice threaded by a varying magnetic flux. Based on the rigorious results, we demonstrate that there exist many invariant subspaces in which the dynamics is periodic when the flux varies linearly over time. Nevertheless, for a given initial state, the evolved state differs from that driven by a linear field. However, the probability distributions of the two states are identical, referred to as the quantum analogue of Faraday's law. Our results are ubiquitous for a wide variety of interacting systems. We demonstrate these results through numerical simulations in an extended fermi-Hubbard model.

arXiv:2503.08000•Physical review. B./Physical review. B•Jun 16, 2025•3 citations

Time dynamics of electron wave functions of 3d quantum ring in alternating magnetic field

Alexander Anatolievich Bryzgalov, F. I. Karmanov

Three-dimensional axially symmetrical exactly soluble model of quantum ring has been considered in the constant magnetic field. Potential, which restricts particle movement in the system in two directions, has been used. By applying method of splitting into physical processes, an electron wave functions and a quasi-stationary energy levels values have been obtained. Also a qualitative description of wave packet movement has been given for the case of quantum ring threading by alternating magnetic field.

•Mar 1, 2011•0 citations

Mesoscopic ring under the influence of time-periodical flux: Aharonov-Bohm oscillations and transmission of wave packets

Evgeny N. Bulgakov, Almas F. Sadreev

The Aharonov-Bohm oscillations in the transmission probability of a one-dimensional mesoscopic ring between two electrodes are considered numerically where a time-periodical flux \ensuremath{\gamma}(t)=\ensuremath{\gamma}+\ensuremath{\lambda} cos\ensuremath{\omega}t is applied. Such a flux simulates a phase-coherent inelastic scattering due to the absorption/emission processes of modulation quanta. An increase of alternating flux amplitude \ensuremath{\lambda} drastically changes the Aharonov-Bohm oscillations of the transmission though the exact period remains ${\mathrm{\ensuremath{\varphi}}}_{0}$=hc/e. A frequency dependence of the transmission has abrupt steps at \ensuremath{\omega}=(E-${\mathit{E}}_{\mathit{F}}$)/n, caused by the locking of the transmission in the nth channel where ${\mathit{E}}_{\mathit{F}}$ is the Fermi level. Moreover, for transmission of a narrow wave packet the time-periodical flux gives rise to two effects. The first is a fractioning of the input wave packet by the ring in such a way that the output wave function consists of a few separate wave packets. Their number, distance apart, and height essentially depend on the static flux \ensuremath{\gamma}. The second effect is a strong space squeezing of the output wave packet.

Physical review. B, Condensed matter•Oct 15, 1995•8 citations

Tight-binding lattices with an oscillating imaginary gauge field

Stefano Longhi

We consider non-Hermitian dynamics of a quantum particle hopping on a one-dimensional tight-binding lattice made of $N$ sites with asymmetric hopping rates induced by a time-periodic oscillating imaginary gauge field. A deeply different behavior is found depending on the lattice topology. While in a linear chain (open boundary conditions) an oscillating field can lead to a complex quasienergy spectrum via a multiple parametric resonance; in a ring topology (Born--von Karman periodic boundary conditions) an entirely real quasienergy spectrum can be found and the dynamics is pseudo-Hermitian. In the large-$N$ limit, parametric instability and pseudo-Hermitian dynamics in the two different lattice topologies are physically explained on the basis of a simple picture of wave-packet propagation.

arXiv:1603.09245•Physical Review A•Aug 1, 2016•25 citations

Pumping through a Luttinger liquid ring threaded by a time-varying magnetic field

Enrico Perfetto, Michele Cini, Stefano Bellucci A

We consider a quantum ring laterally connected to open one-dimensional leads described within the Luttinger liquid (LL) model and subject to a time-dependent driving magnetic field $\ensuremath{\phi}(t)$. The closed loop is obtained by connecting two points of the LL by a weak link, which is treated exactly to lowest order in perturbation theory. Analytical results for the current across the weak link, as well as in the external circuit and inside the loop, are obtained. We pay special attention to the case of smooth magnetic pulses such that the response of the system is approximately adiabatic. We find that the response to the flux $\ensuremath{\phi}$ is linear only if $\ensuremath{\phi}$ is a small fraction of a flux quantum ${\ensuremath{\phi}}_{0}$. By inserting whole quanta, a current goes in the external wires as two bunches, separated by a time proportional to the length of the loop, and a net pumped current in the external wires is produced. This kind of pumping is consistent with the predictions of the corresponding tight-binding model in the uncorrelated limit, but is not destroyed by electron-electron interactions.

Physical Review B•Jan 10, 2013•8 citations

Freezing a quantum magnet by repeated quantum interference: An experimental realization

Swathi S. Hegde, Hemant Katiyar, T. S. Mahesh +1 more

We experimentally demonstrate the phenomenon of dynamical many-body freezing in a periodically driven Ising chain. Theoretically [A. Das, Phys. Rev. B 82, 172402 (2010)], for certain values of the drive parameters all fundamental degrees of freedom contributing to the response dynamics freeze for all time and for arbitrary initial state. Also, since the condition of freezing involves only the drive parameters and not the quantization of the momentum (i.e., the system size), our simulation with a small (3-spin) chain captures all salient features of the freezing phenomenon predicted for the infinite chain. Using optimal control techniques, we realize high-fidelity cosine-modulated drive, and observe nonmonotonic freezing of magnetization at specific frequencies of modulation. Time evolution of the excitations in momentum space has been tracked directly through magnetization measurements.

arXiv:1307.8219•Physical Review B•Nov 7, 2014•71 citations
We analytically study the effects of periodically alternating magnetic fields on the dynamics of a tight-binding ring. It is shown that an arbitrary quantum state can be frozen coherently at will by the very frequent square-wave field as well as the monochromatic-wave field when the corresponding optimal amplitudes are taken. Numerical simulations show that the average fidelity depends on not only the system parameters, but also the features of the quantum state. Moreover, taking the initial zero-momentum Gaussian wave packets as examples, we show the dependence of the threshold frequency on the width of the packet for the given average fidelities. These observations provide a means to perform the quantum-state engineering.
According to Faraday's law in classical physics, a varying magnetic field stimulates an electric eddy field. Intuitively, when a classical field is constant and imposed on a lattice, the Wannier-Stark ladders (WSL) can be established, resulting in Bloch oscillations. In this work, we investigate the dynamics of an interacting system on a (generalized) ring lattice threaded by a varying magnetic flux. Based on the rigorious results, we demonstrate that there exist many invariant subspaces in which the dynamics is periodic when the flux varies linearly over time. Nevertheless, for a given initial state, the evolved state differs from that driven by a linear field. However, the probability distributions of the two states are identical, referred to as the quantum analogue of Faraday's law. Our results are ubiquitous for a wide variety of interacting systems. We demonstrate these results through numerical simulations in an extended fermi-Hubbard model.
Three-dimensional axially symmetrical exactly soluble model of quantum ring has been considered in the constant magnetic field. Potential, which restricts particle movement in the system in two directions, has been used. By applying method of splitting into physical processes, an electron wave functions and a quasi-stationary energy levels values have been obtained. Also a qualitative description of wave packet movement has been given for the case of quantum ring threading by alternating magnetic field.
The Aharonov-Bohm oscillations in the transmission probability of a one-dimensional mesoscopic ring between two electrodes are considered numerically where a time-periodical flux \ensuremath{\gamma}(t)=\ensuremath{\gamma}+\ensuremath{\lambda} cos\ensuremath{\omega}t is applied. Such a flux simulates a phase-coherent inelastic scattering due to the absorption/emission processes of modulation quanta. An increase of alternating flux amplitude \ensuremath{\lambda} drastically changes the Aharonov-Bohm oscillations of the transmission though the exact period remains ${\mathrm{\ensuremath{\varphi}}}_{0}$=hc/e. A frequency dependence of the transmission has abrupt steps at \ensuremath{\omega}=(E-EF{\mathit{E}}_{\mathit{F}}EF​)/n, caused by the locking of the transmission in the nth channel where EF{\mathit{E}}_{\mathit{F}}EF​ is the Fermi level. Moreover, for transmission of a narrow wave packet the time-periodical flux gives rise to two effects. The first is a fractioning of the input wave packet by the ring in such a way that the output wave function consists of a few separate wave packets. Their number, distance apart, and height essentially depend on the static flux \ensuremath{\gamma}. The second effect is a strong space squeezing of the output wave packet.
We consider non-Hermitian dynamics of a quantum particle hopping on a one-dimensional tight-binding lattice made of NNN sites with asymmetric hopping rates induced by a time-periodic oscillating imaginary gauge field. A deeply different behavior is found depending on the lattice topology. While in a linear chain (open boundary conditions) an oscillating field can lead to a complex quasienergy spectrum via a multiple parametric resonance; in a ring topology (Born--von Karman periodic boundary conditions) an entirely real quasienergy spectrum can be found and the dynamics is pseudo-Hermitian. In the large-NNN limit, parametric instability and pseudo-Hermitian dynamics in the two different lattice topologies are physically explained on the basis of a simple picture of wave-packet propagation.
We consider a quantum ring laterally connected to open one-dimensional leads described within the Luttinger liquid (LL) model and subject to a time-dependent driving magnetic field $\ensuremath{\phi}(t)$. The closed loop is obtained by connecting two points of the LL by a weak link, which is treated exactly to lowest order in perturbation theory. Analytical results for the current across the weak link, as well as in the external circuit and inside the loop, are obtained. We pay special attention to the case of smooth magnetic pulses such that the response of the system is approximately adiabatic. We find that the response to the flux $\ensuremath{\phi}$ is linear only if $\ensuremath{\phi}$ is a small fraction of a flux quantum ${\ensuremath{\phi}}_{0}$. By inserting whole quanta, a current goes in the external wires as two bunches, separated by a time proportional to the length of the loop, and a net pumped current in the external wires is produced. This kind of pumping is consistent with the predictions of the corresponding tight-binding model in the uncorrelated limit, but is not destroyed by electron-electron interactions.
We experimentally demonstrate the phenomenon of dynamical many-body freezing in a periodically driven Ising chain. Theoretically [A. Das, Phys. Rev. B 82, 172402 (2010)], for certain values of the drive parameters all fundamental degrees of freedom contributing to the response dynamics freeze for all time and for arbitrary initial state. Also, since the condition of freezing involves only the drive parameters and not the quantization of the momentum (i.e., the system size), our simulation with a small (3-spin) chain captures all salient features of the freezing phenomenon predicted for the infinite chain. Using optimal control techniques, we realize high-fidelity cosine-modulated drive, and observe nonmonotonic freezing of magnetization at specific frequencies of modulation. Time evolution of the excitations in momentum space has been tracked directly through magnetization measurements.