Periodic driving of optical lattices has enabled the creation of novel band structures not realizable in static lattice systems, such as topological bands for neutral particles. However, especially driven systems of interacting bosonic particles often suffer from strong heating. We have systematically studied heating in an interacting Bose-Einstein condensate in a driven one-dimensional optical lattice. We find interaction dependent heating rates that depend on both the scattering length and the driving strength and identify the underlying resonant intra- and interband scattering processes. By comparing the experimental data and theory, we find that, for driving frequencies well above the trap depth, the heating rate is dramatically reduced by the fact that resonantly scattered atoms leave the trap before dissipating their energy into the system. This mechanism of Floquet evaporative cooling offers a powerful strategy to minimize heating in Floquet engineered quantum gases.
Periodic driving of optical lattices has enabled the creation of novel band structures not realizable in static lattice systems, such as topological bands for neutral particles. However, especially driven systems of interacting bosonic particles often suffer from strong heating. We have systematically studied heating in an interacting Bose-Einstein condensate in a driven one-dimensional optical lattice. We find interaction dependent heating rates that depend on both the scattering length and the driving strength and identify the underlying resonant intra- and interband scattering processes. By comparing the experimental data and theory, we find that, for driving frequencies well above the trap depth, the heating rate is dramatically reduced by the fact that resonantly scattered atoms leave the trap before dissipating their energy into the system. This mechanism of Floquet evaporative cooling offers a powerful strategy to minimize heating in Floquet engineered quantum gases.
Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system -- leading to long-lived 'prethermal' regimes. In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model. By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude. The tunability of the lattice potentials allows us to explore one- and two-dimensional systems in a range of different interacting regimes. Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension. Our results show experimental evidence of the phenomenon of Floquet prethermalization, and provide insight into the characterization of heating for driven bosonic systems.
Abstract We investigate multi-“photon” interband excitation processes in an optical lattice that is driven periodically in time by a modulation of the lattice depth. Assuming the system to be prepared in the lowest band, we compute the excitation spectrum numerically. Moreover, we estimate the effective coupling parameters for resonant interband excitation processes analytically, employing degenerate perturbation theory in Floquet space. We find that below a threshold driving strength, interband excitations are suppressed exponentially with respect to the inverse driving frequency. For sufficiently low frequencies, this leads to a rather sudden onset of interband heating, once the driving strength reaches the threshold. We argue that this behavior is rather generic and should also be found in lattice systems that are driven by other forms of periodic forcing. Our results are relevant for Floquet engineering, where a lattice system is driven periodically in time in order to endow it with novel properties like the emergence of a strong artificial magnetic field or a topological band structure. In this context, interband excitation processes correspond to detrimental heating.
We investigate multi-photon interband excitation processes in an optical lattice that is driven periodically in time by a modulation of the lattice depth. Assuming the system to be prepared in the lowest band, we compute the excitation spectrum numerically. Moreover, we estimate the effective coupling parameters for resonant interband excitation processes analytically, employing degenerate perturbation theory in Floquet space. We find that below a threshold driving strength, interband excitations are suppressed exponentially with respect to the inverse driving frequency. For sufficiently low frequencies, this leads to a rather sudden onset of interband heating, once the driving strength reaches the threshold. We argue that this behavior is rather generic and should also be found in lattice systems that are driven by other forms of periodic forcing. Our results are relevant for Floquet engineering, where a lattice system is driven periodically in time in order to endow it with novel properties like the emergence of a strong artificial magnetic field or a topological band structure. In this context, interband excitation processes correspond to detrimental heating.
Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases.While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinitetemperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system-leading to long-lived "prethermal" regimes.In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model.By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude.The tunability of the lattice potentials allows us to explore one-and twodimensional systems in a range of different interacting regimes.Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension.Our results show experimental evidence of the phenomenon of Floquet prethermalization and provide insight into the characterization of heating for driven bosonic systems.
Periodically-driven (Floquet) quantum systems are ubiquitous in science and technology. For example, when a laser illuminates a material or an AC voltage is applied to a device, the system is well-described by a time-periodic Hamiltonian. In recent years, periodic driving has been proposed, not just as a tool to excite and probe devices, but actually as a mechanism of engineering new phases of matter, some of which have no equilibrium analog. However, with this promise comes a serious problem. Intuitively, if energy is injected into and distributed throughout a system, it is no surprise that it tends to heat up indefinitely to infinite temperature. In this thesis, we study the mechanisms of heating, i.e. the process of thermalization, in Floquet systems and propose methods to control them. Specifically, for non-interacting Floquet systems that are coupled to external bosonic and fermionic baths (e.g. laser-driven electrons in a semiconductor that interact with phonons and an external lead), we classify the relevant scattering processes that contribute to cooling/heating in the Floquet bands and suggest methods to suppress heating via bandwidth-restrictions on the baths. We find that is possible, with appropriate dissipative engineering, to stabilize a controlled incompressible nonequilibrium steady-state resembling a ground state - a state we term the "Floquet insulator." We extend this analysis to include short-range interactions that contribute additional heating processes and show, under the same framework, that heating can be controlled with dissipation. In the process, we develop a simple effective model for the Floquet band densities that captures the essence of all the Floquet scattering processes and that is useful for ballparking experimentally-relevant estimates of heating. Next, we turn our attention to strongly-interacting closed Floquet systems and study how heating emerges through a proliferation of resonances. We find a novel integrable point governing the strong-interaction limit of the Floquet system and examine the breakdown of integrability via the proliferation of resonances. We observe two distinct scaling regimes, attributed to non-thermal and thermal behavior, and discover a power-law scaling of the crossover between them as a function of system size. The lingering ergodicity-breaking effects of the conserved quantities in the vicinity (in parameter space) of the integrable point at finite size is a phenomena we term "near-integrability." These results suggest that small quantum systems, which are accessible currently in many platforms (e.g. trapped ions, cold atoms, superconducting devices), intrinsically host non-thermal states that one may be able to utilize to avoid heating. Furthermore, our results suggest a "dual" interpretation, in the thermodynamic limit, that a periodically-driven system exhibits prethermalization as a power-law in interaction strength.
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.