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

New Journal of Physics

Floquet dynamics of ultracold atoms in optical lattices with a parametrically modulated trapping potential

Usman Ali, Martin Holthaus, T. Meier

Published Dec 1, 2024• 1 citation
Publisher

Abstract

Abstract Experiments with ultracold atoms in optical lattices usually involve a weak parabolic trapping potential which merely serves to confine the atoms, but otherwise remains negligible. In contrast, we suggest a different class of experiments in which the presence of a stronger trap is an essential part of the set-up. Because the trap-modified on-site energies exhibit a slowly varying level spacing, similar to that of an anharmonic oscillator, an additional time-periodic trap modulation with judiciously chosen parameters creates nonlinear resonances which enable efficient Floquet engineering. We employ a Mathieu approximation for constructing the near-resonant Floquet states in an accurate manner and demonstrate the emergence of effective ground states from the resonant trap eigenstates. Moreover, we show that the population of the Floquet states is strongly affected by the phase of a sudden turn-on of the trap modulation, which leads to significantly modified and rich dynamics. As a guideline for further studies, we argue that the deliberate population of only the resonance-induced effective ground states will allow one to realize Floquet condensates which follow classical periodic orbits, thus providing challenging future perspectives for the investigation of the quantum–classical correspondence.

DOI
10.1088/1367-2630/ad9b47

Related papers

Floquet dynamics of ultracold atoms in optical lattices with a parametrically modulated trapping potential

Ali, Usman, Martin Holthaus, T. Meier

Experiments with ultracold atoms in optical lattices usually involve a weak parabolic trapping potential which merely serves to confine the atoms, but otherwise remains negligible. In contrast, we suggest a different class of experiments in which the presence of a stronger trap is an essential part of the set-up. Because the trap-modified on-site energies exhibit a slowly varying level spacing, similar to that of an anharmonic oscillator, an additional time-periodic trap modulation with judiciously chosen parameters creates nonlinear resonances which enable efficient Floquet engineering. We employ a Mathieu approximation for constructing the near-resonant Floquet states in an accurate manner and demonstrate the emergence of effective ground states from the resonant trap eigenstates. Moreover, we show that the population of the Floquet states is strongly affected by the phase of a sudden turn-on of the trap modulation, which leads to significantly modified and rich dynamics. As a guideline for further studies, we argue that the deliberate population of only the resonance-induced effective ground states will allow one to realize Floquet condensates which follow classical periodic orbits, thus providing challenging future perspectives for the investigation of the quantum-classical correspondence.

arXiv:2405.02125•May 3, 2024•0 citations

Quantum chaos for cold atoms in an optical lattice with a tilted harmonic trap

T. M. Fromhold, Christopher R. Tench, Sylwia Bujkiewicz +2 more

We show how ultracold (sub-µK temperature) atoms in a one-dimensional periodic optical potential with a harmonic trap can provide a new quantum chaotic system that is accessible to experiment. Provided that the harmonic potential varies slowly over a lattice period, the optical lattice has well defined energy bands. The energy-wavevector dispersion curves define an effective Hamiltonian that can be used to calculate classical orbits for atoms confined to a single band. We show that tilting the harmonic trap relative to the optical lattice induces a controllable transition from stable regular motion to classical chaos. The onset of chaos strongly delocalizes the atom orbits and should be manifest in both the classical and quantum properties of the trapped atoms. We also consider how the transition to chaos might affect the collective time-dependent dynamics of interacting atoms in Bose-Einstein condensates.

Journal of Optics B Quantum and Semiclassical Optics•Oct 1, 2000•11 citations

Floquet engineering of tight-binding Hamiltonians in momentum space lattices

Dominique Ronco, Floriane Arrouas, Nicolas Ombredane +4 more

Quantum simulation with ultracold atoms provides a versatile platform to emulate condensed-matter models. In particular, momentum-space lattices enable the realization of programmable tight-binding Hamiltonians. Here, we generalize this approach by exploiting quantum resonances of a periodically driven (shaken) rotor within the Floquet framework. Using first-order time-dependent perturbation theory, we derive analytical relations between the lattice modulation and the effective tight-binding parameters, and identify explicit solutions for several resonances. We further apply optimal-control techniques to enhance the multi-period Floquet fidelity and extend the accessible parameter regimes. Experimentally, we implement this scheme with a Bose-Einstein condensate of rubidium-87 atoms in a dynamically modulated optical lattice. We demonstrate the simulation of the Rice-Mele model, including band-structure measurements and topological edge states, as well as momentum Bloch oscillations, and superlattice configurations with controlled periodicity. Our results establish quantum resonances as a powerful resource for Floquet engineering of tight-binding models in momentum space.

arXiv:2604.24722•Apr 27, 2026•0 citations

Many-Body Floquet Engineering in Periodically Driven Optical Lattices

Christoph Sträter

The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically.

•Jul 26, 2017•0 citations

Significantly stable mode of the ultracold atomic wave packet in amplitude-modulated parabolic optical lattices

Tomotake Yamakoshi, Farhan Saif, Shinichi Watanabe

We show that a conspicuous wave packet of ultracold noninteracting bosonic atoms emerges in a one-dimensional parabolic optical lattice as in the setup of the Aarhus experiment [P. L. Pedersen, M. Gajdacz, N. Winter, A. J. Hilliard, J. F. Sherson, and J. Arlt, Phys. Rev. A 88, 023620 (2013)], given the lattice height is harmonically modulated with a particular amplitude at a resonant frequency. We show that this four-band periodic wave packet (4B PWP) executes stable timewise periodic motion for an infinitely long time. We apply the Floquet theory to analyze the parameter dependence of the 4B PWP in detail. Our analysis shows that it consists mainly of two principal Floquet eigenstates of the periodically driven Hamiltonian. The informative Husimi representation yields temporal slices of the phase space of the 4B PWP, visually identifying moments where the interband transitions take place. The provided data should aid the experiment in locating the 4B PWP.

arXiv:1709.10268•Physical Review A•Feb 13, 2018•6 citations

Floquet engineering of optical nonlinearities: a quantum many-body approach

Nathan Goldman

Subjecting a physical system to a time-periodic drive can substantially modify its properties and applications. This Floquet-engineering approach has been extensively applied to a wide range of classical and quantum settings in view of designing synthetic systems with exotic properties. Considering a general class of two-mode nonlinear optical devices, we show that effective optical nonlinearities can be created by subjecting the light field to a repeated pulse sequence, which couples the two modes in a fast and time-periodic manner. The strength of these drive-induced optical nonlinearities, which include an emerging four-wave mixing, can be varied by simply adjusting the pulse sequence. This leads to topological changes in the system's phase space, which can be detected through light intensity and phase measurements. Our proposal builds on an effective-Hamiltonian approach, which derives from a parent quantum many-body Hamiltonian describing driven interacting bosons. As a corollary, our results equally apply to Bose-Einstein condensates in driven double-well potentials, where pair tunneling effectively arises from the periodic pulse sequence. Our scheme offers a practical route to engineer and finely tune exotic nonlinearities and interactions in photonics and ultracold quantum gases.

arXiv:2203.05554•Mar 10, 2022•3 citations
Abstract Experiments with ultracold atoms in optical lattices usually involve a weak parabolic trapping potential which merely serves to confine the atoms, but otherwise remains negligible. In contrast, we suggest a different class of experiments in which the presence of a stronger trap is an essential part of the set-up. Because the trap-modified on-site energies exhibit a slowly varying level spacing, similar to that of an anharmonic oscillator, an additional time-periodic trap modulation with judiciously chosen parameters creates nonlinear resonances which enable efficient Floquet engineering. We employ a Mathieu approximation for constructing the near-resonant Floquet states in an accurate manner and demonstrate the emergence of effective ground states from the resonant trap eigenstates. Moreover, we show that the population of the Floquet states is strongly affected by the phase of a sudden turn-on of the trap modulation, which leads to significantly modified and rich dynamics. As a guideline for further studies, we argue that the deliberate population of only the resonance-induced effective ground states will allow one to realize Floquet condensates which follow classical periodic orbits, thus providing challenging future perspectives for the investigation of the quantum–classical correspondence.
Experiments with ultracold atoms in optical lattices usually involve a weak parabolic trapping potential which merely serves to confine the atoms, but otherwise remains negligible. In contrast, we suggest a different class of experiments in which the presence of a stronger trap is an essential part of the set-up. Because the trap-modified on-site energies exhibit a slowly varying level spacing, similar to that of an anharmonic oscillator, an additional time-periodic trap modulation with judiciously chosen parameters creates nonlinear resonances which enable efficient Floquet engineering. We employ a Mathieu approximation for constructing the near-resonant Floquet states in an accurate manner and demonstrate the emergence of effective ground states from the resonant trap eigenstates. Moreover, we show that the population of the Floquet states is strongly affected by the phase of a sudden turn-on of the trap modulation, which leads to significantly modified and rich dynamics. As a guideline for further studies, we argue that the deliberate population of only the resonance-induced effective ground states will allow one to realize Floquet condensates which follow classical periodic orbits, thus providing challenging future perspectives for the investigation of the quantum-classical correspondence.
We show how ultracold (sub-µK temperature) atoms in a one-dimensional periodic optical potential with a harmonic trap can provide a new quantum chaotic system that is accessible to experiment. Provided that the harmonic potential varies slowly over a lattice period, the optical lattice has well defined energy bands. The energy-wavevector dispersion curves define an effective Hamiltonian that can be used to calculate classical orbits for atoms confined to a single band. We show that tilting the harmonic trap relative to the optical lattice induces a controllable transition from stable regular motion to classical chaos. The onset of chaos strongly delocalizes the atom orbits and should be manifest in both the classical and quantum properties of the trapped atoms. We also consider how the transition to chaos might affect the collective time-dependent dynamics of interacting atoms in Bose-Einstein condensates.
Quantum simulation with ultracold atoms provides a versatile platform to emulate condensed-matter models. In particular, momentum-space lattices enable the realization of programmable tight-binding Hamiltonians. Here, we generalize this approach by exploiting quantum resonances of a periodically driven (shaken) rotor within the Floquet framework. Using first-order time-dependent perturbation theory, we derive analytical relations between the lattice modulation and the effective tight-binding parameters, and identify explicit solutions for several resonances. We further apply optimal-control techniques to enhance the multi-period Floquet fidelity and extend the accessible parameter regimes. Experimentally, we implement this scheme with a Bose-Einstein condensate of rubidium-87 atoms in a dynamically modulated optical lattice. We demonstrate the simulation of the Rice-Mele model, including band-structure measurements and topological edge states, as well as momentum Bloch oscillations, and superlattice configurations with controlled periodicity. Our results establish quantum resonances as a powerful resource for Floquet engineering of tight-binding models in momentum space.
The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically.
We show that a conspicuous wave packet of ultracold noninteracting bosonic atoms emerges in a one-dimensional parabolic optical lattice as in the setup of the Aarhus experiment [P. L. Pedersen, M. Gajdacz, N. Winter, A. J. Hilliard, J. F. Sherson, and J. Arlt, Phys. Rev. A 88, 023620 (2013)], given the lattice height is harmonically modulated with a particular amplitude at a resonant frequency. We show that this four-band periodic wave packet (4B PWP) executes stable timewise periodic motion for an infinitely long time. We apply the Floquet theory to analyze the parameter dependence of the 4B PWP in detail. Our analysis shows that it consists mainly of two principal Floquet eigenstates of the periodically driven Hamiltonian. The informative Husimi representation yields temporal slices of the phase space of the 4B PWP, visually identifying moments where the interband transitions take place. The provided data should aid the experiment in locating the 4B PWP.
Subjecting a physical system to a time-periodic drive can substantially modify its properties and applications. This Floquet-engineering approach has been extensively applied to a wide range of classical and quantum settings in view of designing synthetic systems with exotic properties. Considering a general class of two-mode nonlinear optical devices, we show that effective optical nonlinearities can be created by subjecting the light field to a repeated pulse sequence, which couples the two modes in a fast and time-periodic manner. The strength of these drive-induced optical nonlinearities, which include an emerging four-wave mixing, can be varied by simply adjusting the pulse sequence. This leads to topological changes in the system's phase space, which can be detected through light intensity and phase measurements. Our proposal builds on an effective-Hamiltonian approach, which derives from a parent quantum many-body Hamiltonian describing driven interacting bosons. As a corollary, our results equally apply to Bose-Einstein condensates in driven double-well potentials, where pair tunneling effectively arises from the periodic pulse sequence. Our scheme offers a practical route to engineer and finely tune exotic nonlinearities and interactions in photonics and ultracold quantum gases.