Synopsis High-order nonlinear multiphoton dynamics of closed and open periodically driven quantum systems are studied within the semiclassical Floquet formalism. Multiphoton up/down frequency conversion in a super-conducting circuit is realized and faithfully reproduced with calculations. The absorption spectra are suppressed at sharp avoided crossings of the Floquet states. We include the effect of coupling to cavity by time evolving the master equation. The characteristics of the time-averaged absorption spectra are investigated by probing details near and around the exceptional points where suppression occurs.
We investigate Floquet dynamics of a particle held in a three-well system driven by a two-frequency field and identify integer and fractional photon resonances due to the dual-frequency driving. It is found that pairs of photon-assisted tunneling near the resonance originate from avoided level crossings in the Floquet spectra which, in essence, are quantum features of the hybridization between different quantum states. In particular, we establish a close connection between fractional-order resonances and Floquet mode properties under two-frequency driving conditions and illustrate their dependence on driving parameters. These results provide us a possibility to realize coherent control of quantum states with the assistance of classical external driving fields.
We characterize the avoided crossings in a two-parameter, time-periodic system which has been the basis for a wide variety of experiments. By studying these avoided crossings in the near-integrable regime, we are able to determine scaling laws for the dependence of their characteristic features on the nonintegrability parameter. As an application of these results, the influence of avoided crossings on dynamical tunneling is described and applied to the recent realization of multiple-state tunneling in an experimental system.
Non-equilibrium dynamics of strongly and rapidly driven quantum many-body systems is poorly understood beyond periodic driving, where heating is exponentially slow in the drive frequency (Floquet Prethermalization). In contrast, non-periodic drives were found to exhibit widely different heating scalings with no unifying principle. This work identifies a resonance-suppression principle governing slow heating up to a prethermal lifetime
τ∗: When the drive's spectral arithmetic structure restricts multiphoton resonances,
τ∗ is controlled by low-frequency spectral suppression. The principle distinguishes (i) Single-photon suppression, quantified by a low-frequency suppression law
f(Ω) for the drive's Fourier Transform weight near
Ω=0, from (ii) Multi-photon suppression, where nested commutators remain controlled if exceptional arithmetic structure satisfies a subadditive property. Remarkably, if multi-photon suppression holds,
τ∗ scaling with drive speed
λ is governed by
f(Ω). This law of
τ∗ is found through a small-divisor mechanism in this work's iterative rotating frame scheme. Multi-photon suppression breakdown separates
λ-scaling of
τ∗ in linear response and non-perturbative theory, shown by a case study of Quasi-Floquet driving. The principle is applied to (i) Resolve inconsistencies in literature on non-periodic driving, and (ii) Provide design principles for engineering prethermal phases of matter in programmable quantum simulators, exemplified by new non-periodic `Factorial' drives with tunable
τ∗.
We show how to create maximally entangled dressed states of a weakly interacting multi-partite quantum system by suitably tuning an external, periodic driving field. Floquet theory allows us to relate, in a transparent manner, the occurrence of entanglement resonances to avoided crossings in the spectrum of quasi-energies, tantamount of well-defined conditions for the controlled, resonant interaction of particles. We demonstrate the universality of the phenomenon for periodically driven, weakly interacting two-level systems, by considering different interaction mechanisms and driving profiles. In particular, we show that entanglement resonances are a generic feature of driven, multi-partite systems, widely independent of the details of the interaction mechanism. Our results are therefore particularly relevant for experiments on interacting two-level systems, in which the microscopic realization of the inter-particle coupling is unknown.
In the linear response theory, it is well known that the response of a quantum system to an external perturbation described by the susceptibility is formulated in the Schrödinger picture. The theory might apply to open quantum systems (or Floquet systems); however, it has ignored the non-Markovian effect in almost all works so far. In this Letter, we propose a new method to address those issues by introducing Heisenberg operators to derive an exact susceptibility for the non-Markovian Floquet periodic driving system. The susceptibility includes all the influences of the environment on the Floquet system. We will show that the susceptibility connects closely to the structure of the Floquet energy spectrum of the whole system (system plus environment). Moreover, we can read out Floquet bound states in the first Brillouin zone of the whole system from the susceptibility. The presented results may find applications in quantum engineering with open systems following modulated periodic evolution in quantum optics.