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arXiv:2611.01325

Floquet engineering of quantum relaxation

Kang Xu, Dionisio Cendoya, Nazar Delegan, Daniela Pagliero, Lisandro Buljubasich, Carlos A. Meriles

quant-phSubmitted Oct 31, 2026• Announced Nov 3, 2026
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Abstract

Dynamical decoupling suppresses decoherence by averaging selected interactions between a quantum system and its environment. Here, we extend this notion through a general Floquet formalism that maps periodic control onto relaxation and dephasing channels. Environmental fluctuations are decomposed into Floquet components that sample the noise spectrum at distinct frequencies, with coupling strengths determined by control-induced Floquet coefficients. We experimentally investigate this approach using a single nitrogen-vacancy center in diamond under multi-pulse control. By tuning the drive and detuning, we reshape the coupling to environmental fluctuations and create isolated operating points where the dominant decoherence channel vanishes, strongly suppressing Floquet dephasing. The resulting coherence enhancement follows the predicted Floquet coupling coefficients and can be shifted by modifying the control sequence. These results establish Floquet driving as a general framework for engineering transverse and longitudinal relaxation through the design of quantum control protocols.

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Dynamical decoupling suppresses decoherence by averaging selected interactions between a quantum system and its environment. Here, we extend this notion through a general Floquet formalism that maps periodic control onto relaxation and dephasing channels. Environmental fluctuations are decomposed into Floquet components that sample the noise spectrum at distinct frequencies, with coupling strengths determined by control-induced Floquet coefficients. We experimentally investigate this approach using a single nitrogen-vacancy center in diamond under multi-pulse control. By tuning the drive and detuning, we reshape the coupling to environmental fluctuations and create isolated operating points where the dominant decoherence channel vanishes, strongly suppressing Floquet dephasing. The resulting coherence enhancement follows the predicted Floquet coupling coefficients and can be shifted by modifying the control sequence. These results establish Floquet driving as a general framework for engineering transverse and longitudinal relaxation through the design of quantum control protocols.
Controlling the decoherence induced by the interaction of quantum system with its environment is a fundamental challenge in quantum technology. Utilizing Floquet theory, we explore the constructive role of temporal periodic driving in suppressing decoherence of a spin-1/2 particle coupled to a spin bath. It is revealed that, accompanying the formation of a Floquet bound state in the quasienergy spectrum of the whole system including the system and its environment, the dissipation of the spin system can be inhibited and the system tends to coherently synchronize with the driving. It can be seen as an analog to the decoherence suppression induced by the structured environment in spatially periodic photonic crystal setting. Comparing with other decoherence control schemes, our protocol is robust against the fluctuation of control parameters and easy to realize in practice. It suggests a promising perspective of periodic driving in decoherence control.
Non-equilibrium steady states are created when a periodically driven quantum system is also incoherently interacting with an environment - as it is the case in most realistic situations. The notion of Floquet engineering refers to the manipulation of the properties of systems under periodic perturbations. Although it more frequently refers to the coherent states of isolated systems (or to the transient phase for states that are weakly coupled to the environment), it may sometimes be of more interest to consider the final steady states that are reached after decoherence and dissipation take place. In this work, we demonstrate how those final states can be optimally tuned with respect to a given predefined metric, such as for example the maximization of the temporal average value of some observable, by using multicolor periodic perturbations. We show a computational framework that can be used for that purpose, and exemplify the concept using a simple model for the nitrogen-vacancy center in diamond: the goal in this case is to find the driving periodic magnetic field that maximizes a time-averaged spin component. We show that, for example, this technique permits to prepare states whose spin values are forbidden in thermal equilibrium at any temperature.
Quantum technology resorts to efficient utilization of quantum resources to realize technique innovation. The systems are controlled such that their states follow the desired manners to realize different quantum protocols. However, the decoherence caused by the system-environment interactions causes the states deviating from the desired manners. How to protect quantum resources under the coexistence of active control and passive decoherence is of significance. Recent studies have revealed that the decoherence is determined by the feature of the system-environment energy spectrum: Accompanying the formation of bound states in the energy spectrum, the decoherence can be suppressed. It supplies a guideline to control decoherence. Such idea can be generalized to systems under periodic driving. By virtue of manipulating Floquet bound states in the quasienergy spectrum, coherent control via periodic driving dubbed as Floquet engineering has become a versatile tool not only in controlling decoherence, but also in artificially synthesizing exotic topological phases. We will review the progress on quantum control in open and periodically driven systems. Special attention will be paid to the distinguished role played by the bound states and their controllability via periodic driving in suppressing decoherence and generating novel topological phases.
Quantum sensing is typically based on phase accumulation and is therefore fundamentally tied to the coherence time of the sensing system. Here we introduce an alternative sensing paradigm based on programmable Floquet locking in periodically driven two-level systems. We show that periodic control generates an effective Floquet locking field whose orientation and amplitude depend on global offset, allowing information to be encoded in the driven population relaxation dynamics, not in the integrated phase. By controlling transfer between distinct Floquet locking manifolds, external perturbations can be mapped onto engineered relaxation responses whose characteristics are programmable through the driving sequence. We numerically demonstrate this approach for both DC and frequency-selective AC sensing, and show that temporal encoding of the response can provide enhanced precision in the presence of slow instrumental fluctuations. These results illustrate the potential of programmable Floquet responses and open the way to exploring new sensing strategies in driven quantum systems.
Dynamical decoupling as a quantum control strategy aims at suppressing quantum decoherence adopting the popular philosophy that the disorder in the unitary evolution of the open quantum system caused by environmental noises should be neutralized by a sequence of ordered or well-designed external operations acting on the system. This work studies the solution of quantum-state-diffusion equations by mixing two channels of environmental noises, i.e., relaxation (dissipation) and dephasing. It is interesting to find in two-level and three-level atomic systems that a non-Markovian relaxation or dissipation process can be suppressed by a Markovian dephasing noise. The discovery results in an anomalous control strategy by coordinating relaxation and dephasing processes. Our approach opens an avenue of noise control strategy with no artificial manipulation over the open quantum systems.
Periodic driving underlies many forms of quantum control, including spin-based quantum sensing. However, in an ensemble sensor, one waveform must act on spins with different detunings, drive amplitudes, hyperfine environments, and local fields. Existing robust-control approaches to such disorder are usually framed in terms of coherence, effective Hamiltonians, filter functions, or refocusing. Here we identify a complementary geometric requirement for collective ensemble Floquet control: disorder realizations must share a common Floquet eigenframe. When this condition is met, initialization, protection, signal coupling, and readout are defined in one dressed basis, so the ensemble responds as a collective Floquet sensor rather than as an average over inequivalent driven members. We make this condition measurable with an eigenvector-based synchronization order parameter and a complementary fragmentation metric that quantify the alignment and spread of Floquet quantization axes across the ensemble. As one realization of this framework, we use a continuous counterdiabatic Floquet drive to derive synchronization criteria and predict resonance-governed breakdown at the first two low-order commensurabilities between the engineered Floquet gap and the drive modulation, with detuning and amplitude disorder producing distinct breakdown channels. Experiments on a nitrogen-vacancy (NV) ensemble in diamond verify the synchronized regime through long-lived collective oscillations, a two-dimensional disorder-robustness map, and breakdown resonances that shift with the modulation rate. Finally, we demonstrate a harmonic-free continuous-drive AC magnetometry protocol whose collective single-tone response is enabled by the synchronized Floquet eigenframe. These results establish Floquet eigenframe synchronization as a measurable condition for disorder-resilient collective control and quantum sensing.