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

Journal of Physics Conference Series

Quasi-energies of coupled qubits: Magnus-Floquet states and their probing by weak signal

M. V. Bastrakova, N. V. Klenov, Сатанин Аркадий Михайлович

Published Feb 1, 2019• 0 citations
Publisher

Abstract

The behaviour of two coupled qubits in a periodic electromagnetic field of arbitrary amplitude was investigated. Quasienergy levels of the system as a function of the driving field parameters and the qubit coupling energy were found on the basis of the Floquet theory and the Magnus approximation. It is shown that the quasienergy levels may intersect depending on the control parameters. This fact can manifest itself as appearance of the novel resonances and interesting nonlinear phenomena.

DOI
10.1088/1742-6596/1163/1/012075

Related papers

Amplitude spectroscopy of two coupled qubits

Сатанин Аркадий Михайлович, M. V. Denisenko, Sahel Ashhab +1 more

We study the effect of a time-dependent driving field with a high amplitude on a system composed of two coupled qubits (two-level systems). Using the rotating-wave approximation (RWA) makes it possible to find simple conditions for resonant excitation of the four-level system. We find that the resonance conditions include the coupling strength between the qubits. Numerical simulations confirm the qualitative conclusions following from the RWA. To reveal the peculiarities of resonant transitions caused by the quasilevel motion and crossing in a periodic driving field, we use Floquet states, which determine the precise intermediate states of the system. Calculating the quasienergy states of the multilevel system makes it possible to find the transition probabilities and build interference patterns for the transition probabilities. The interference patterns demonstrate the possibility of obtaining various pieces of information about the qubits, since the positions of transition-probability maxima depend on various system parameters, including the coupling strength between the qubits.

arXiv:1201.1901•Physical Review B•May 18, 2012•43 citations

Floquet Engineering of Two Weakly Coupled Superconducting Flux Qubits

Wan-Lu Song, Jia-Bin You, J.K. Xu +2 more

We explore the periodically driven dynamics of two weakly coupled flux qubits and propose a scheme to generate a maximally entangled state based on Floquet engineering. The periodic driving modifies the quasienergy spectrum of the system and induces crossing of quasienergies, and the weak coupling between them lifts the degeneracy of quasienergies. It is found that the phenomena of entanglement resonance of Floquet state appear at certain values of the driving parameters, which could be demonstrated by virtue of the Rabi-frequency spectrum and average concurrence during one driving period. Our scheme relaxes the experimental difficulty in adjusting the static parameters of the system to establish entanglement, and may open interesting perspectives for devising active decoherence-immune quantum-information devices.

Physical Review Applied•Nov 19, 2020•6 citations

Probe spectroscopy of quasienergy states

Matti Silveri, Jani Tuorila, Mika Kemppainen +1 more

The present qubit technology, in particular, in Josephson qubits, allows an unprecedented control of discrete energy levels. This motivates a new study of the old pump-probe problem, where a discrete quantum system is driven by a strong drive and simultaneously probed by a weaker one. The strong drive is included by the Floquet method and the resulting quasienergy states are then studied with the probe. We study a qubit where the harmonic drive has a significant longitudinal component relative to the static equilibrium state of the qubit. Both analytical and numerical methods are used to solve the problem. We present calculations with realistic parameters and compare the results with recent experimental results. A short introduction to the Floquet method and the probe absorption is given.

arXiv:1301.0230•Physical Review B•Apr 8, 2013•30 citations

Dipole-dipole interaction of floquet states

Tim Ehret

We formulate a Floquet-Markov master equation, which combines an open quantum system approach with Floquet theory, for two spatially separated two-level atoms driven by a strong electromagnetic field and coupled to a common electromagnetic bath. This equation features a modified form of dipole-dipole interactions compared to the case of weakly driven atoms, giving rise to new, previously undescribed shifts of the Floquet quasienergies. We provide a detailed physical interpretation of the modified dipole-dipole interactions of two-level atoms, discuss their manifestations in two-atom resonance fluorescence, and extract the distance dependence of the dipole-dipole force between the atoms. The extensive discussion of two-level atoms is complemented by a brief study of one-dimensional hydrogen atoms (otherwise essentially described without approximations), with focus on the dipole-dipole interactions of periodically driven atoms whose electronic degrees of freedom are locked in non-dispersive wave packet states.

•Apr 15, 2026•0 citations

Dynamics of a two-level system under strong driving: Quantum-gate optimization based on Floquet theory

Chunqing Deng, Feiruo Shen, Sahel Ashhab +1 more

We consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If the pulse amplitude varies very slowly, the system adiabatically follows the instantaneous Floquet states, which acquire dynamical phases that depend on the evolution of the quasienergies over time. The difference between the phases acquired by the two Floquet states corresponds to a qubit state rotation, generalizing the notion of Rabi oscillations to the case of large driving amplitudes. If the pulse amplitude changes very fast, the evolution is nonadiabatic, with transitions taking place between the Floquet states. We quantify and analyze the nonadiabatic transitions during the pulse by employing adiabatic perturbation theory and exact numerical simulations. We find that, for certain combinations of pulse rise and fall times and maximum driving amplitude, a destructive interference effect leads to a remarkably strong suppression of transitions between the Floquet states. This effect provides the basis of a quantum control protocol, which we name Floquet interference efficient suppression of transitions in the adiabatic basis (FIESTA), that can be used to design ultrafast high-fidelity single-qubit quantum gates.

arXiv:1605.08826•Physical Review A•Sep 27, 2016•45 citations

Entanglement resonances of driven multi-partite quantum systems

Simeon Sauer, Florian Mintert, Clemens Gneiting +1 more

We show how to create maximally entangled dressed states of a weakly interacting multi-partite quantum system by suitably tuning an external, periodic driving field. Floquet theory allows us to relate, in a transparent manner, the occurrence of entanglement resonances to avoided crossings in the spectrum of quasi-energies, tantamount of well-defined conditions for the controlled, resonant interaction of particles. We demonstrate the universality of the phenomenon for periodically driven, weakly interacting two-level systems, by considering different interaction mechanisms and driving profiles. In particular, we show that entanglement resonances are a generic feature of driven, multi-partite systems, widely independent of the details of the interaction mechanism. Our results are therefore particularly relevant for experiments on interacting two-level systems, in which the microscopic realization of the inter-particle coupling is unknown.

arXiv:1101.1671•Journal of Physics B Atomic Molecular and Optical Physics•Jul 30, 2012•17 citations
The behaviour of two coupled qubits in a periodic electromagnetic field of arbitrary amplitude was investigated. Quasienergy levels of the system as a function of the driving field parameters and the qubit coupling energy were found on the basis of the Floquet theory and the Magnus approximation. It is shown that the quasienergy levels may intersect depending on the control parameters. This fact can manifest itself as appearance of the novel resonances and interesting nonlinear phenomena.
We study the effect of a time-dependent driving field with a high amplitude on a system composed of two coupled qubits (two-level systems). Using the rotating-wave approximation (RWA) makes it possible to find simple conditions for resonant excitation of the four-level system. We find that the resonance conditions include the coupling strength between the qubits. Numerical simulations confirm the qualitative conclusions following from the RWA. To reveal the peculiarities of resonant transitions caused by the quasilevel motion and crossing in a periodic driving field, we use Floquet states, which determine the precise intermediate states of the system. Calculating the quasienergy states of the multilevel system makes it possible to find the transition probabilities and build interference patterns for the transition probabilities. The interference patterns demonstrate the possibility of obtaining various pieces of information about the qubits, since the positions of transition-probability maxima depend on various system parameters, including the coupling strength between the qubits.
We explore the periodically driven dynamics of two weakly coupled flux qubits and propose a scheme to generate a maximally entangled state based on Floquet engineering. The periodic driving modifies the quasienergy spectrum of the system and induces crossing of quasienergies, and the weak coupling between them lifts the degeneracy of quasienergies. It is found that the phenomena of entanglement resonance of Floquet state appear at certain values of the driving parameters, which could be demonstrated by virtue of the Rabi-frequency spectrum and average concurrence during one driving period. Our scheme relaxes the experimental difficulty in adjusting the static parameters of the system to establish entanglement, and may open interesting perspectives for devising active decoherence-immune quantum-information devices.
The present qubit technology, in particular, in Josephson qubits, allows an unprecedented control of discrete energy levels. This motivates a new study of the old pump-probe problem, where a discrete quantum system is driven by a strong drive and simultaneously probed by a weaker one. The strong drive is included by the Floquet method and the resulting quasienergy states are then studied with the probe. We study a qubit where the harmonic drive has a significant longitudinal component relative to the static equilibrium state of the qubit. Both analytical and numerical methods are used to solve the problem. We present calculations with realistic parameters and compare the results with recent experimental results. A short introduction to the Floquet method and the probe absorption is given.
We formulate a Floquet-Markov master equation, which combines an open quantum system approach with Floquet theory, for two spatially separated two-level atoms driven by a strong electromagnetic field and coupled to a common electromagnetic bath. This equation features a modified form of dipole-dipole interactions compared to the case of weakly driven atoms, giving rise to new, previously undescribed shifts of the Floquet quasienergies. We provide a detailed physical interpretation of the modified dipole-dipole interactions of two-level atoms, discuss their manifestations in two-atom resonance fluorescence, and extract the distance dependence of the dipole-dipole force between the atoms. The extensive discussion of two-level atoms is complemented by a brief study of one-dimensional hydrogen atoms (otherwise essentially described without approximations), with focus on the dipole-dipole interactions of periodically driven atoms whose electronic degrees of freedom are locked in non-dispersive wave packet states.
We consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If the pulse amplitude varies very slowly, the system adiabatically follows the instantaneous Floquet states, which acquire dynamical phases that depend on the evolution of the quasienergies over time. The difference between the phases acquired by the two Floquet states corresponds to a qubit state rotation, generalizing the notion of Rabi oscillations to the case of large driving amplitudes. If the pulse amplitude changes very fast, the evolution is nonadiabatic, with transitions taking place between the Floquet states. We quantify and analyze the nonadiabatic transitions during the pulse by employing adiabatic perturbation theory and exact numerical simulations. We find that, for certain combinations of pulse rise and fall times and maximum driving amplitude, a destructive interference effect leads to a remarkably strong suppression of transitions between the Floquet states. This effect provides the basis of a quantum control protocol, which we name Floquet interference efficient suppression of transitions in the adiabatic basis (FIESTA), that can be used to design ultrafast high-fidelity single-qubit quantum gates.
We show how to create maximally entangled dressed states of a weakly interacting multi-partite quantum system by suitably tuning an external, periodic driving field. Floquet theory allows us to relate, in a transparent manner, the occurrence of entanglement resonances to avoided crossings in the spectrum of quasi-energies, tantamount of well-defined conditions for the controlled, resonant interaction of particles. We demonstrate the universality of the phenomenon for periodically driven, weakly interacting two-level systems, by considering different interaction mechanisms and driving profiles. In particular, we show that entanglement resonances are a generic feature of driven, multi-partite systems, widely independent of the details of the interaction mechanism. Our results are therefore particularly relevant for experiments on interacting two-level systems, in which the microscopic realization of the inter-particle coupling is unknown.