Multi-photon resonances to high-lying energy levels represent an unavoidable source of Floquet heating in strongly driven quantum systems. In this work, we extend the recently developed two-tone approach of 'cancelling' multi-photon resonances to shaken lattices in the Hubbard regime. Our experiments show that even for strong lattice shaking the inclusion of a weak second drive leads to cancellation of multi-photon heating resonances. Surprisingly, the optimal cancelling amplitude depends on the Hubbard interaction strength $U$, in qualitative agreement with exact diagonalisation calculations. Our results call for novel analytical approaches to capture the physics of strongly-driven-strongly-interacting many-body systems.
Multi-photon resonances to high-lying energy levels represent an unavoidable source of Floquet heating in strongly driven quantum systems. In this work, we extend the recently developed two-tone approach of 'cancelling' multi-photon resonances to shaken lattices in the Hubbard regime. Our experiments show that even for strong lattice shaking the inclusion of a weak second drive leads to cancellation of multi-photon heating resonances. Surprisingly, the optimal cancelling amplitude depends on the Hubbard interaction strength U, in qualitative agreement with exact diagonalisation calculations. Our results call for novel analytical approaches to capture the physics of strongly-driven-strongly-interacting many-body 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.
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.
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.
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.
The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, the exponential suppression of heating has also been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.