Periodically driven quantum systems offer remarkable flexibility in tailoring effective Hamiltonians and synthetic band structures. However, such driving also induces heating and dynamical instabilities that limit the coherence and lifetime of many-body states. Here, we demonstrate that these instabilities can be suppressed by employing multi-tone driving schemes. Using a Bose-Einstein condensate of cesium atoms in an optical lattice, we experimentally explore two approaches: pulsed driving composed of odd harmonics and two-tone driving with tunable amplitude and relative phase. We show that both methods allow independent control of the effective tunneling amplitude and Peierls phase factor, while significantly reducing phonon excitation and the resulting rapid decay of the condensate. Numerical simulations and theoretical modeling based on Bogoliubov-de Gennes equations confirm the suppression of unstable modes under optimized driving conditions. Our results establish multifrequency drives as powerful tools for stabilizing driven many-body systems and pave the way toward robust Floquet engineering with interactions.
Periodically driven quantum systems offer remarkable flexibility in tailoring effective Hamiltonians and synthetic band structures. However, such driving also induces heating and dynamical instabilities that limit the coherence and lifetime of many-body states. Here, we demonstrate that these instabilities can be suppressed by employing multi-tone driving schemes. Using a Bose-Einstein condensate of cesium atoms in an optical lattice, we experimentally explore two approaches: pulsed driving composed of odd harmonics and two-tone driving with tunable amplitude and relative phase. We show that both methods allow independent control of the effective tunneling amplitude and Peierls phase factor, while significantly reducing phonon excitation and the resulting rapid decay of the condensate. Numerical simulations and theoretical modeling based on Bogoliubov-de Gennes equations confirm the suppression of unstable modes under optimized driving conditions. Our results establish multifrequency drives as powerful tools for stabilizing driven many-body systems and pave the way toward robust Floquet engineering with interactions.
Periodically driven quantum systems are currently explored in view of realizing novel many-body phases of matter. This approach is particularly promising in gases of ultracold atoms, where sophisticated shaking protocols can be realized and interparticle interactions are well controlled. The combination of interactions and time-periodic driving, however, often leads to uncontrollable heating and instabilities, potentially preventing practical applications of Floquet engineering in large many-body quantum systems. In this work, we experimentally identify the existence of parametric instabilities in weakly interacting Bose-Einstein condensates in strongly driven optical lattices through momentum-resolved measurements, in line with theoretical predictions. Parametric instabilities can trigger the destruction of weakly interacting Bose-Einstein condensates through the rapid growth of collective excitations, in particular in systems with weak harmonic confinement transverse to the lattice axis. Understanding the onset of parametric instabilities in driven quantum matter is crucial for determining optimal conditions for the engineering of modulation-induced many-body systems.
We experimentally investigate the stability of a quantum gas with repulsive interactions in an optical one-dimensional lattice subjected to periodic driving. Excitations of the gas in the lowest lattice band are analyzed across the complete stability diagram, from slow to fast driving frequencies and from weak to strong driving strengths. To interpret our results, we expand the established analysis based on parametric instabilities to include modulational instabilities. Extending the concept of modulational instabilities from static to periodically driven systems provides a convenient mapping of the stability in a static system to the cases of slow and fast driving. At intermediate driving frequencies, we observe an interesting competition between modulational and parametric instabilities. We experimentally confirm the existence of both types of instabilities in driven systems and probe their properties. Our results allow us to predict stable and unstable parameter regions for the minimization of heating in future applications of Floquet driving.
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.
The concept of "Floquet engineering" relies on an external periodic drive to realize novel, effectively static Hamiltonians.This technique is being explored in experimental platforms across physics, including ultracold atoms, laser-driven electron systems, nuclear magnetic resonance, and trapped ions.The key challenge in Floquet engineering is to avoid the uncontrolled absorption of photons from the drive, especially in interacting systems in which the excitation spectrum becomes effectively dense.The resulting dissipative coupling to higher-lying modes, such as the excited bands of an optical lattice, has been explored in recent experimental and theoretical works, but the demonstration of a broadly applicable method to mitigate this effect is lacking.Here, we show how two-path quantum interference applied to strongly correlated fermions in a driven optical lattice suppresses dissipative coupling to higher bands and increases the lifetime of double occupancies and spin correlations by 2 to 3 orders of magnitude.Interference is achieved by introducing a weak second modulation at twice the fundamental driving frequency with a definite relative phase.This technique is shown to suppress dissipation in both weakly and strongly interacting regimes of an offresonantly driven Hubbard system, opening an avenue to realizing low-temperature phases of matter in interacting Floquet systems.
The concept of “Floquet engineering” relies on an external periodic drive to realize novel, effectively static Hamiltonians. This technique is being explored in experimental platforms across physics, including ultracold atoms, laser-driven electron systems, nuclear magnetic resonance, and trapped ions. The key challenge in Floquet engineering is to avoid the uncontrolled absorption of photons from the drive, especially in interacting systems in which the excitation spectrum becomes effectively dense. The resulting dissipative coupling to higher-lying modes, such as the excited bands of an optical lattice, has been explored in recent experimental and theoretical works, but the demonstration of a broadly applicable method to mitigate this effect is lacking. Here, we show how two-path quantum interference applied to strongly correlated fermions in a driven optical lattice suppresses dissipative coupling to higher bands and increases the lifetime of double occupancies and spin correlations by 2 to 3 orders of magnitude. Interference is achieved by introducing a weak second modulation at twice the fundamental driving frequency with a definite relative phase. This technique is shown to suppress dissipation in both weakly and strongly interacting regimes of an offresonantly driven Hubbard system, opening an avenue to realizing low-temperature phases of matter in interacting Floquet systems.
Abstract We demonstrate the existence of exact Floquet flat bands in a class of non-integrable quantum many-body Hamiltonians leading to strong violation of the eigenstate thermalization hypothesis in the presence of a two-tone drive characterized by frequencies Ω1 and Ω 2 = ν Ω 1 , where ν is an integer. We provide the exact analytic condition for this phenomenon to occur for a generic protocol. A small departure from the flat band conditions leads to suppression of heating over a long prethermal timescale in an otherwise ergodic many-body system away from integrable or perturbative regimes; we elucidate the central role of the flat band behind such heating suppression. Our analysis indicates the existence of a perturbative Floquet Hamiltonian, away from high drive frequency/amplitude limit, which controls the dynamics of the driven system near such flat bands. We demonstrate this phenomenon by exact numerical studies of Floquet bandwidth, spectral form factor, entanglement and Shannon entropies, heat absorption, and correlation functions of a driven Rydberg chain. We also study the corresponding micromotion which exhibits coherent reversal of excitations reminiscent of echoes; in addition, it harbors an exact reflection symmetry about t = T 1 / 2 , where T 1 = 2 π / Ω 1 , which we elucidate. We discuss experiments which can test our theory.