Wave-packet revival in a Floquet engineering quadratic potential system

The study investigates how periodic driving can engineer novel quantum dynamics in one-dimensional tight-binding lattices, revealing that specific driving frequencies can induce coherent wave-packet revivals even in non-Hermitian systems.

How it works

The research focuses on a one-dimensional tight-binding lattice driven by a spatially quadratic and time-periodic potential, analyzing both Hermitian and non-Hermitian hopping regimes. The core methodology involves mapping the time-dependent problem onto an effective static Floquet Hamiltonian in Sambe space to study how the quasienergy spectra evolve as a function of the driving frequency ω. This framework allows for a detailed investigation of the quasi-energy spectrum and its relation to dynamical properties.

The analysis reveals several key aspects of this system's behavior across different driving regimes:

1. At high drive frequencies, the system is well described by the time-averaged Hamiltonian and supports extended Bloch-like states.

2. In the limit of vanishing frequency (ω → 0), the static quadratic confinement dominates, and eigenstates are strongly localized, forming harmonic-oscillatorlike and Wannier-Stark-like families.

3. For non-Hermitian systems, the periodic drive can dynamically stabilize an almost real, uniformly spaced quasi-energy ladder, which enables Hermitian-like revivals even when the underlying static Hamiltonian lacks Hermiticity.

Gauge Transformation and Critical Frequencies

To analytically determine the optimal driving frequency ωc for spectral regularity, a gauge transformation is employed. This transformation removes the explicit on-site drive by defining a time-dependent phase factor φ(t) related to the quadratic potential. The transformed Hamiltonian, Hg(t), simplifies significantly, becoming equivalent to a hopping problem with bond-dependent periodic Peierls phases described by Bessel functions of the first kind, Jm(αl).

The critical frequency ωc is identified as the point where the first pronounced optimal ladder structure should be controlled by the single-photon process on the outermost bonds. This occurs when the modulation index αedge reaches a value αc determined by maximizing J1(α), which leads to an analytical estimate: ωc ≈ (2L − 1)F0αc. This frequency marks where the coupling between neighboring Floquet sectors is maximized most efficiently, resulting in the best approximate ladder structure after zone folding.

Dynamical Consequences and Revivals

The emergence of nearly equidistant quasi-energy ladders directly implies periodic dynamics with well-defined revival times, leading to Bloch-oscillation–like behavior. An initial wave packet supported on this ladder subspace exhibits periodic return at times tc = 2π/∆E, where ∆E is the ladder spacing. This leads to highcontrast revival behavior in both Hermitian and non-Hermitian regimes.

In the non-Hermitian case, the analysis demonstrates that the periodic drive can dynamically stabilize an almost real, uniformly spaced quasi-energy ladder, i.e., a nearHermitian subsector. This stabilization enables Hermitian-like revivals even when the underlying static Hamiltonian lacks Hermiticity, confirming that Floquet engineering can create and protect useful dynamical behavior.

Robustness Against Disorder

To assess experimental relevance, the study investigates the effect of quenched disorder in hopping amplitudes, replacing uniform hoppings with site-dependent values J(l). The numerical results show that the Floquet-induced revival dynamics are robust against moderate amounts of static disorder. The maximum fidelity peak associated with periodic revivals persists up to a finite disorder window. Beyond this characteristic scale, the ladder structure becomes progressively distorted due to disorder-induced broadening and fragmentation of the ladder subspace, leading to the suppression of coherent revivals.

Summary and Outlook

The work establishes a unifying mechanism for forming equidistant quasi-energy structures in both Hermitian and non-Hermitian tight-binding lattices under quadratic periodic driving, providing clear spectroscopic (minimum in normalized variance ∆(ω)) and dynamical signatures (Bloch-like revivals) for this phenomenon. The findings demonstrate that Floquet engineering of quasi-harmonic ladders is a practical and disorder-tolerant route for controlling coherent dynamics in driven lattice systems. The ability to dynamically stabilize nearreal spectra even in the presence of nonreciprocity highlights new possibilities for realizing controllable, long-lived dynamical states in driven quantum platforms.

The gist: Critical driving frequencies induce nearly equidistant quasi-energy ladders that lead to robust Bloch-like revivals and can dynamically stabilize nearreal spectra even in non-Hermitian systems.

Key Findings Enumerated:

(1) The emergence of the Floquet ladder structure is numerically identified by a pronounced minimum in the normalized variance ∆(ω) of nearest-neighbor quasi-energy spacings.

**(2) The condition for this structure is analytically obtained through a gauge transformation, leading to the analytical estimate ωc ≈ (2L − 1)F0αc.

As a fastidious and diligent researcher, I have analyzed this paper on wave-packet revival in Floquet engineering quadratic potential systems, focusing on Hermitian and non-Hermitian tight-binding lattices driven by spatially quadratic potentials.

The core scientific contribution lies in demonstrating how periodic driving can induce nearly equidistant quasi-energy ladders (Floquet structures) and robust Bloch-like revivals, even when the underlying static system is non-Hermitian or asymmetric.

Here are the specific improvements that can be made to AI systems, categorized by application area:

The improved AI system will possess a sophisticated understanding of time-periodic, driven quantum dynamics in engineered lattices. It can perform high-fidelity simulations and predictive modeling in domains where standard static models fail due to time-dependent driving or gain/loss mechanisms.

1. The improved AI system can accurately predict the long-time coherent dynamics (revivals) of a quantum state subjected to a spatially quadratic, time-periodic drive, even in non-Hermitian settings.

2. It can identify and characterize optimal driving frequencies that maximize the coherence and regularity of quasi-energy spectra (i.e., finding the critical frequency windows, e.g., the analytically derived resonance condition).

3. It can model and predict robust Bloch-like oscillations in non-Hermitian systems, which are typically suppressed by gain/loss mechanisms, by leveraging the dynamical stabilization mechanism described in Section V.

4. The system can quantify the robustness of engineered quantum features (like quasi-energy ladders) against realistic spatial disorder, determining the characteristic disorder scale beyond which coherence is lost.

5. It can perform spectral diagnostics on driven systems by calculating metrics like the normalized variance of level spacings, allowing for automated identification of Floquet ladder formation in complex parameter spaces.

Specific applications and capabilities:

• AI could be used to design novel quantum control protocols for cold atom or photonic systems, specifically targeting regimes where long-lived coherent states (revivals) are desired despite the inherent open/driven nature of the platforms.

• It can serve as a high-fidelity simulator for designing Floquet topological phases by navigating the parameter space (hopping asymmetry, driving frequency) to achieve desired spectral structures.

• The system can be deployed in materials science to predict how engineered time-periodic potentials affect transport properties in nonreciprocal materials or active metamaterials.

• It can accelerate the discovery of new dynamical control schemes by efficiently searching for the optimal drive frequencies that maximize spectral regularity, reducing reliance on computationally expensive brute-force numerical sweeps.