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:2202.04973 · Physical Review Research

Floquet-Landau-Zener interferometry: Usefulness of the Floquet theory in pulse-laser-driven systems

Tatsuhiko N. Ikeda, Satoshi Tanaka, Yōsuke Kayanuma

Published Jul 25, 2022• 32 citations
arXivHTMLPDF

Abstract

We develop the Landau-Zener transfer matrix theory for the instantaneous Floquet states (IFSs) for quantum systems driven by a strong pulse laser. Applying this theory to the pulse excitation probability in two-level quantum systems, we show unexpectedly good quantitative agreement for few-cycle pulses. This approach enables us to qualitatively understand the probability's peculiar behaviors as quantum path interference between IFSs. We also study the pulse-width dependence, finding that this Floquet-state interpretation remains useful for shorter pulses down to two-cycle ones in the present model. These results imply that the Floquet theory is meaningful in experimental few-cycle lasers if applied appropriately in the sense of IFSs.

DOI
10.1103/physrevresearch.4.033075

Related papers

Controlling Floquet states on ultrashort time scales

Matteo Lucchini, Fabio Medeghini, Yingxuan Wu +10 more

The advent of ultrafast laser science offers the unique opportunity to combine Floquet engineering with extreme time resolution, further pushing the optical control of matter into the petahertz domain. However, what is the shortest driving pulse for which Floquet states can be realised remains an unsolved matter, thus limiting the application of Floquet theory to pulses composed by many optical cycles. Here we ionized Ne atoms with few-femtosecond pulses of selected time duration and show that a Floquet state can be observed already with a driving field that lasts for only 10 cycles. For shorter pulses, down to 2 cycles, the finite lifetime of the driven state can still be explained using an analytical model based on Floquet theory. By demonstrating that the amplitude and number of Floquet-like sidebands in the photoelectron spectrum can be controlled not only with the driving laser pulse intensity and frequency, but also by its duration, our results add a new lever to the toolbox of Floquet engineering.

arXiv:2205.00788•Nature Communications•Nov 19, 2022•30 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

Floquet perturbation theory: formalism and application to low-frequency limit

M Rodriguez-Vega, M Lentz, Babak Seradjeh

We develop a low-frequency perturbation theory in the extended Floquet Hilbert space of a periodically driven quantum systems, which puts the high- and low-frequency approximations to the Floquet theory on the same footing. It captures adiabatic perturbation theories recently discussed in the literature as well as diabatic deviation due to Floquet resonances. For illustration, we apply our Floquet perturbation theory to a driven two-level system as in the Schwinger–Rabi and the Landau-Zener–Stückelberg–Majorana models. We reproduce some known expressions for transition probabilities in a simple and systematic way and clarify and extend their regime of applicability. We then apply the theory to a periodically-driven system of fermions on the lattice and obtain the spectral properties and the low-frequency dynamics of the system.

arXiv:1805.01190•New Journal of Physics•Aug 31, 2018•72 citations

Floquet perturbation theory: formalism and application to low-frequency limit

Martin Rodriguez-Vega, Meghan Lentz, Babak Seradjeh

We develop a low-frequency perturbation theory in the extended Floquet Hilbert space of a periodically driven quantum systems, which puts the high- and low-frequency approximations to the Floquet theory on the same footing. It captures adiabatic perturbation theories recently discussed in the literature as well as diabatic deviation due to Floquet resonances. For illustration, we apply our Floquet perturbation theory to a driven two-level system as in the Schwinger-Rabi and the Landau-Zener-Stuckelberg-Majorana models. Were produce some known expressions for transition probabilities in a simple and systematic way and clarify and extend their regime of applicability. We then apply the theory to a periodically-driven system of fermions on the lattice and obtain the spectral properties and the low-frequency dynamics of the system.

•Sep 24, 2018•56 citations

Floquet state depletion in ac-driven circuit QED

Mingbo Chen, Bao‐Chuan Wang, Sigmund Kohler +9 more

We perform Floquet spectroscopy in a GaAs double quantum dot system coupled to a high-impedance superconducting resonator. By applying microwave-induced consecutive passages under a double-resonance condition, we observe Landau-Zener-St\"uckelberg-Majorana interference patterns that stem from a cavity-assisted interference pattern modified by the depletion of the ground state. Our experimental results reveal the stationary state behavior of a strongly driven two-level system and are consistent with the simulations based on our theoretical model. This study provides an excellent platform for investigating the dynamics of Floquet states in the presence of strong driving.

arXiv:2011.03697•Physical review. B./Physical review. B•May 28, 2021•19 citations

Strong-Drive Floquet Engineering of Interacting Qudits: From Finite-Duration Controls to Emergent Symmetry

Ryan Scott, V. W. Scarola

Floquet driving uses periodic controls to tailor the behavior of quantum systems, with applications in quantum analogue simulation, sensing, and the protection of quantum information. Most approaches are designed using idealized, instantaneous pulses, even though experiments necessarily use pulses with finite duration and shape. This mismatch becomes especially challenging for interacting $d$-level systems, or qudits, because the number of possible controls grows rapidly with the number of levels. We develop a strong-drive Floquet theory that incorporates experimentally realizable pulse waveforms directly into the design of the effective interactions. The pulse duration, amplitude, and shape therefore become useful control parameters rather than sources of error. We show that systems with more than two levels offer capabilities unavailable in qubit systems: finite-duration driving can create new interactions that are absent from the original system and can substantially change its symmetries. We demonstrate these capabilities for interacting three-level systems. A single pulse transforms a diagonal interaction into a quantum spin-1 model dominated by nematic interactions, while pulse protocols motivated by trapped ultracold polar molecules produce models with enlarged $SU(2)\times U(1)$ and $SU(3)$ symmetries. Numerical tests of both short-time evolution and many-body dynamics confirm the accuracy of the resulting description. Our results provide a scalable analytical framework for designing finite-duration controls in interacting qudit platforms.

quant-pharXiv:2609.04309•Sep 7, 2026•0 citations
We develop the Landau-Zener transfer matrix theory for the instantaneous Floquet states (IFSs) for quantum systems driven by a strong pulse laser. Applying this theory to the pulse excitation probability in two-level quantum systems, we show unexpectedly good quantitative agreement for few-cycle pulses. This approach enables us to qualitatively understand the probability's peculiar behaviors as quantum path interference between IFSs. We also study the pulse-width dependence, finding that this Floquet-state interpretation remains useful for shorter pulses down to two-cycle ones in the present model. These results imply that the Floquet theory is meaningful in experimental few-cycle lasers if applied appropriately in the sense of IFSs.
The advent of ultrafast laser science offers the unique opportunity to combine Floquet engineering with extreme time resolution, further pushing the optical control of matter into the petahertz domain. However, what is the shortest driving pulse for which Floquet states can be realised remains an unsolved matter, thus limiting the application of Floquet theory to pulses composed by many optical cycles. Here we ionized Ne atoms with few-femtosecond pulses of selected time duration and show that a Floquet state can be observed already with a driving field that lasts for only 10 cycles. For shorter pulses, down to 2 cycles, the finite lifetime of the driven state can still be explained using an analytical model based on Floquet theory. By demonstrating that the amplitude and number of Floquet-like sidebands in the photoelectron spectrum can be controlled not only with the driving laser pulse intensity and frequency, but also by its duration, our results add a new lever to the toolbox of Floquet engineering.
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 develop a low-frequency perturbation theory in the extended Floquet Hilbert space of a periodically driven quantum systems, which puts the high- and low-frequency approximations to the Floquet theory on the same footing. It captures adiabatic perturbation theories recently discussed in the literature as well as diabatic deviation due to Floquet resonances. For illustration, we apply our Floquet perturbation theory to a driven two-level system as in the Schwinger–Rabi and the Landau-Zener–Stückelberg–Majorana models. We reproduce some known expressions for transition probabilities in a simple and systematic way and clarify and extend their regime of applicability. We then apply the theory to a periodically-driven system of fermions on the lattice and obtain the spectral properties and the low-frequency dynamics of the system.
We develop a low-frequency perturbation theory in the extended Floquet Hilbert space of a periodically driven quantum systems, which puts the high- and low-frequency approximations to the Floquet theory on the same footing. It captures adiabatic perturbation theories recently discussed in the literature as well as diabatic deviation due to Floquet resonances. For illustration, we apply our Floquet perturbation theory to a driven two-level system as in the Schwinger-Rabi and the Landau-Zener-Stuckelberg-Majorana models. Were produce some known expressions for transition probabilities in a simple and systematic way and clarify and extend their regime of applicability. We then apply the theory to a periodically-driven system of fermions on the lattice and obtain the spectral properties and the low-frequency dynamics of the system.
We perform Floquet spectroscopy in a GaAs double quantum dot system coupled to a high-impedance superconducting resonator. By applying microwave-induced consecutive passages under a double-resonance condition, we observe Landau-Zener-St\"uckelberg-Majorana interference patterns that stem from a cavity-assisted interference pattern modified by the depletion of the ground state. Our experimental results reveal the stationary state behavior of a strongly driven two-level system and are consistent with the simulations based on our theoretical model. This study provides an excellent platform for investigating the dynamics of Floquet states in the presence of strong driving.
Floquet driving uses periodic controls to tailor the behavior of quantum systems, with applications in quantum analogue simulation, sensing, and the protection of quantum information. Most approaches are designed using idealized, instantaneous pulses, even though experiments necessarily use pulses with finite duration and shape. This mismatch becomes especially challenging for interacting ddd-level systems, or qudits, because the number of possible controls grows rapidly with the number of levels. We develop a strong-drive Floquet theory that incorporates experimentally realizable pulse waveforms directly into the design of the effective interactions. The pulse duration, amplitude, and shape therefore become useful control parameters rather than sources of error. We show that systems with more than two levels offer capabilities unavailable in qubit systems: finite-duration driving can create new interactions that are absent from the original system and can substantially change its symmetries. We demonstrate these capabilities for interacting three-level systems. A single pulse transforms a diagonal interaction into a quantum spin-1 model dominated by nematic interactions, while pulse protocols motivated by trapped ultracold polar molecules produce models with enlarged SU(2)×U(1)SU(2)\times U(1)SU(2)×U(1) and SU(3)SU(3)SU(3) symmetries. Numerical tests of both short-time evolution and many-body dynamics confirm the accuracy of the resulting description. Our results provide a scalable analytical framework for designing finite-duration controls in interacting qudit platforms.