Periodic ‘kicks’ Revive Quantum States, Boosting Control over Fragile Systems

Researchers investigating periodically driven quantum systems have demonstrated a novel mechanism for achieving long-lived dynamics in the paradigmatic PXP model. Francesco Perciavalle, Francesco Plastina, and Nicola Lo Gullo, all from the Dipartimento di Fisica at the Universit`a della Calabria, reveal how the interplay between spectral properties and initial states governs the emergence of dynamical revivals. Their work is significant because it establishes control over these revivals through tuning driving parameters, allowing researchers to steer dynamics and potentially circumvent Floquet thermalisation, offering new avenues for preserving quantum coherence in engineered systems.

This work focuses on the PXP model, a system relevant to interacting Rydberg atoms, and demonstrates the ability to steer long-lived dynamics through precise control of driving parameters.

Researchers have identified that for Néel-ordered initial states, revivals follow predictable trajectories determined by the Floquet spectrum, a description of the system’s evolution under periodic driving. Initial states transitioning between Néel order and full polarization exhibit hybrid dynamics, tunable by adjusting the overlap with these Floquet eigenstates via the driving parameters.
This control extends to avoiding Floquet thermalization, a process where driven quantum systems typically absorb energy and reach an infinite-temperature state. The study demonstrates that both the initial state and the driving protocol shape these long-lived dynamics in driven quantum many-body systems.

By meticulously mapping the revival behaviour across the parameter space of the drive, the research establishes a clear connection between the system’s spectral characteristics and its temporal evolution. Specifically, the team found that tuning the driving parameters allows for steering different routes for avoiding Floquet thermalization.

The investigation employed Floquet theory, a framework for analysing time-periodic systems, to understand the effective Hamiltonian governing the system at discrete time steps. Analysis of the PXP model, with open boundary conditions, revealed that the revival mechanism for the Néel state is well-defined, while the revival behaviour for interpolating initial states can be continuously tuned.

This tunability arises from differences in the projection of the initial state onto the Floquet states, offering a pathway to control distinct dynamical regimes even with a fixed initial state. The research details how the system can access qualitatively different dynamical behaviours by traversing specific regions of the driving parameter space.

Furthermore, the study assessed the tendency of the system to thermalize under periodic driving, finding that the Néel state does not exhibit thermalizing behaviour, while the fully polarized state is consistent with weak thermalization. This work provides a foundation for engineering robust and controllable quantum dynamics in many-body systems, with potential applications in quantum information processing and the development of novel quantum technologies. The findings open avenues for designing driven quantum systems with tailored dynamical properties and enhanced coherence.

Hamiltonian formulation and Floquet analysis of the driven PXP chain reveal interesting dynamical phases

A periodically driven quantum PXP model with open boundary conditions forms the basis of this work. The Hamiltonian governing the system is defined as HPXP − V(t)N, where HPXP represents the PXP interaction term and V(t)N introduces a time-dependent perturbation. Specifically, the PXP interaction term is expressed as Ω/2 multiplied by a sum of pairwise interactions between neighboring spins, incorporating open boundary conditions.

The time-dependent perturbation is introduced via a sinusoidal driving force with amplitude ‘h’ and frequency ‘ωd’, acting on all L qubits in the chain. This driving protocol modulates the system’s energy landscape over time, enabling the exploration of non-equilibrium dynamics and Floquet phenomena. Floquet theory is then employed to analyze the system’s long-time behaviour, effectively transforming the time-dependent Hamiltonian into a time-independent Floquet Hamiltonian that governs the system’s evolution at discrete time steps.

Researchers investigated the dynamics of the model by initializing it in various states, including Néel-ordered and fully polarized configurations. The evolution of revivals, which are periodic returns to the initial state, was then tracked across a parameter space defined by the driving amplitude and frequency.

For the Néel state, a dominant quasi-energy spacing in the Floquet spectrum dictates the revival trajectories. Initial states interpolating between Néel and fully polarized states exhibit hybrid dynamics, controllable by tuning their overlap with Floquet eigenstates through adjustments to the driving parameters.

This control extends to steering different routes for avoiding Floquet thermalization, demonstrating how both initial state selection and the driving protocol influence long-lived dynamics in this driven quantum many-body system. The study further examines the system’s tendency to thermalize under periodic driving, distinguishing between weak and strong thermalization scenarios and revealing mechanisms for avoiding thermalization through careful manipulation of the driving parameters and initial state.

Driving parameter dependence of revival times and long-lived dynamics is crucial for control

Initial revival times of 3, 4, 5, 6, and 7 cycles were observed, dependent on the driving parameters. These revivals follow well-defined trajectories in the parameter space of the driving, primarily determined by a dominant quasi-energy spacing in the Floquet spectrum. For initial states interpolating between Néel and fully polarized configurations, hybrid dynamics emerge, controllable by tuning their overlap with Floquet eigenstates via the driving parameters.

This control enables steering different routes for avoiding Floquet thermalization, demonstrating how both initial state choice and driving protocol shape long-lived dynamics. Specifically, the minimal revival time is obtained for conditions where J0(h/ωd) ≈1, resulting in nmin rev ≈ωd γ + α. For a driving frequency of ωd = 7, the minimal revival time was calculated to be approximately 10.3325 cycles.

Analysis of the long-time dynamics of the Y operator reveals distinct regimes dependent on the initial state and driving amplitude. For a polarized initial state, Y fluctuates weakly around the ergodic expectation value. Conversely, the Néel state exhibits more coherent oscillations, while an interpolating state, |Θ+(π/4)⟩, displays oscillations significantly deviating from the ergodic value, with a strong dependence on the driving field h.

The observed dynamics for driving amplitudes of h = 2.4, 5.7, and 9.16, with a fixed driving frequency of ωd = 5, show revival times approximately proportional to integer multiples of the period: nrev ≈8, 11, and 25 respectively. These findings, obtained with a system size of L = 12, demonstrate the ability to manipulate long-time dynamics through precise control of initial states and driving parameters.

Dynamical revival control via Floquet engineering of the PXP model offers a pathway to state preparation

Researchers have demonstrated precise control over the long-lived dynamics of a driven quantum system, specifically the periodic boundary condition PXP model. Investigations into the model’s behaviour under periodic driving have revealed how the interplay between its spectral properties and initial states governs the emergence of dynamical revivals.

These revivals, oscillatory returns to the initial state, are not merely a consequence of the driving frequency but are deeply connected to the quasi-energy structure within the Floquet spectrum, a description of the system’s long-term behaviour under periodic forcing. For initial states possessing Néel order, an alternating pattern of spins, revivals follow predictable paths determined by dominant quasi-energy spacings.

Importantly, the study extends this understanding to more complex initial states, those interpolating between Néel order and full polarization, revealing that their dynamics can be steered by tuning the driving parameters to control their overlap with specific Floquet eigenstates. This control extends to avoiding Floquet thermalization, a process where the system loses coherence and reaches equilibrium, thereby enabling the maintenance of long-lived, non-equilibrium dynamics.

The authors acknowledge that their analysis focuses on the Rydberg blockade regime, a specific condition limiting the allowed states of the system, and that extending these findings to broader parameter spaces requires further investigation. Future research directions include exploring the behaviour of the driven PXP model beyond the Rydberg blockade constraint and investigating the potential for utilising these controlled revivals in quantum information processing. The ability to manipulate long-lived dynamics through both initial state preparation and driving protocol design represents a significant step towards understanding and harnessing complex quantum systems, offering potential avenues for preserving quantum coherence and exploring non-equilibrium phenomena.