Floquet engineering in quantum simulation employs externally applied high-frequency pulses to dynamically design steady-state effective Hamiltonians. Such protocols can be used to enlarge the space of Hamiltonians but approximations often limit pulse profile shapes and therefore the space of available effective Hamiltonians. We consider a nonstroboscopic high-frequency expansion formalism for Floquet engineering. We generalize the pulse profiles available by rigorously keeping all necessary terms to lowest order in inverse frequency expansions used to derive the effective Hamiltonians. Our approach allows wide tunability in application of external driving fields. We apply our method to long-range interacting XXZ spin Hamiltonians. We model an example application where we derive conditions on specific pulse shapes to engineer effective Ising models from XXZ models. Our method allows the space of continuous pulse profiles, relevant to experimental control fields, to better and more accurately explore possible effective Hamiltonians available for Floquet engineering.
Floquet engineering in quantum simulation employs externally applied high-frequency pulses to dynamically design steady-state effective Hamiltonians. Such protocols can be used to enlarge the space of Hamiltonians but approximations often limit pulse profile shapes and therefore the space of available effective Hamiltonians. We consider a nonstroboscopic high-frequency expansion formalism for Floquet engineering. We generalize the pulse profiles available by rigorously keeping all necessary terms to lowest order in inverse frequency expansions used to derive the effective Hamiltonians. Our approach allows wide tunability in application of external driving fields. We apply our method to long-range interacting XXZ spin Hamiltonians. We model an example application where we derive conditions on specific pulse shapes to engineer effective Ising models from XXZ models. Our method allows the space of continuous pulse profiles, relevant to experimental control fields, to better and more accurately explore possible effective Hamiltonians available for Floquet engineering.
Improved control and manipulation of quantum systems lies at the heart of modern quantum science and technology, with broad applications ranging from quantum metrology to quantum information science and many-body physics. In this thesis, I will introduce a novel framework for robust Hamiltonian engineering in interacting spin systems, which enables the efficient design of Floquet engineering pulse sequences for qubit and qudit systems that out-perform state-of-the-art control methods by orders of magnitude. As applications of this framework, we utilize a high density ensemble of nitrogen vacancy (NV) centers in diamond, and demonstrate significantly improved control over the disordered, interacting many-body spin system. This enabled the first solid state spin ensemble quantum sensor operating beyond the sensitivity limit imposed by interactions between sensing particles, as well as the observation and understanding of novel dynamical many-body phenomena, including discrete time crystalline order and thermalization dynamics in long-range interacting XXZ spin models.
Prethermalization, where quasisteady states are realized in the intermediate long-time regime (prethermal regime), in periodically driven (Floquet) systems is an important phenomenon since it provides a platform for nontrivial Floquet many-body physics. In this Rapid Communication, we consider Floquet systems with dual energy scales: The Hamiltonian consists of two different terms whose amplitude is either comparable to or much smaller than the frequency. As a result, when the larger-amplitude drive induces a ZN symmetry operation, we obtain the effective static Hamiltonian respecting the emergent ZN symmetry in high-frequency expansions, which describes the dynamics of such Floquet systems in the prethermal regime. As an application of our formulation, our formalism gives a general way to analyze time crystals in prethermal regimes in terms of the static effective Hamiltonian. We also provide an application to Floquet engineering, with which we can perform the simultaneous control of phases and symmetries of the systems. For example, this enables us to control symmetry protected topological phases even when the original system does not respect the symmetry.
Floquet driving uses periodic controls to tailor the behavior of quantum systems, with applications in quantum analogue simulation, sensing, and the protection of quantum information. Most approaches are designed using idealized, instantaneous pulses, even though experiments necessarily use pulses with finite duration and shape. This mismatch becomes especially challenging for interacting d-level systems, or qudits, because the number of possible controls grows rapidly with the number of levels. We develop a strong-drive Floquet theory that incorporates experimentally realizable pulse waveforms directly into the design of the effective interactions. The pulse duration, amplitude, and shape therefore become useful control parameters rather than sources of error. We show that systems with more than two levels offer capabilities unavailable in qubit systems: finite-duration driving can create new interactions that are absent from the original system and can substantially change its symmetries. We demonstrate these capabilities for interacting three-level systems. A single pulse transforms a diagonal interaction into a quantum spin-1 model dominated by nematic interactions, while pulse protocols motivated by trapped ultracold polar molecules produce models with enlarged SU(2)×U(1) and SU(3) symmetries. Numerical tests of both short-time evolution and many-body dynamics confirm the accuracy of the resulting description. Our results provide a scalable analytical framework for designing finite-duration controls in interacting qudit platforms.
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 Floquet-Magnus expansion is a widely used tool to derive effective descriptions of time-periodic quantum systems by approximating their dynamics with a time-independent Hamiltonian. However, its standard formulation is, strictly speaking, restricted to bounded Hamiltonians. In this work, we extend its definition and analysis to a broad class of time-periodic unbounded Hamiltonians. Our approach is based on an a priori distinct nonperturbative framework for the construction of effective Hamiltonians, which we show to reproduce the Floquet-Magnus expansion. A particular strength of our framework is that it allows us to prove that the resulting effective dynamics approximates the original time evolution propagators to arbitrary order in the high-frequency limit without requiring convergence of the Floquet-Magnus expansion, a condition that is already highly restrictive even in the bounded setting. We illustrate the scope of the method on representative models: the quantum Rabi Hamiltonian in the interaction picture, and the periodically driven quantum harmonic oscillator.
We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper–Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case, one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer–Wolff transformation extending the latter to driven systems.