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.
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 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.
Frequency estimation, a cornerstone of quantum metrology, has been significantly enhanced by advanced quantum sensing strategies. However, most protocols rely either on static or time-independent encoding mechanisms, inherently limiting their achievable precision scaling, or on control strategies requiring changing the Hamiltonian and/or implementing feedback mechanisms. To overcome this, we investigate a simpler dynamical encoding protocol where the quantum oscillator is driven by a general continuous temporal frequency modulation Ω(t)=ω0f(t). We analytically demonstrate that for a given modulation profile f(t) and its corresponding time-integral F(t), the quantum Fisher information (QFI) scales as O(F(t)2). This enhancement stems from the fact that temporal encoding fundamentally alters the mechanism of dynamical phase accumulation. Crucially, when evaluated under the energy and evolution-time constraints, this framework reveals a genuine precision enhancement over the conventional time-independent baseline. By analyzing explicit polynomial and exponential modulations, we establish that arbitrary precision scaling can be deterministically engineered, with ultimate bounds that are asymptotically saturable via optimal homodyne detection. Our framework provides a universal paradigm for exploiting time-dependent quantum control in next-generation sensors.
Periodically driven quantum systems have emerged as one of the most versatile tools for quantum simulation, enabling the engineering of effective Hamiltonians, topological phases, and inherently nonequilibrium phenomena such as discrete time crystals. Yet fundamental challenges persist: from a spectral ambiguity that precludes a unique Floquet ground state to an inability to manipulate Floquet eigenstates beyond the adiabatic regime. This thesis demonstrates that counterdiabatic driving—a technique from adiabatic quantum control—provides a unifying framework to address these challenges. We first show that the periodic lab-frame Hamiltonian generates counterdiabatic driving for the Floquet eigenstates, revealing Floquet theory as an inverse counterdiabatic driving problem. Exploiting this equivalence, we develop geometric Floquet theory: a reformulation based on the parallel-transport gauge, which uniquely decomposes Floquet dynamics into a geometric contribution, encoded in Berry phases, and a dynamical contribution, generated by the average-energy operator. The average-energy operator provides an unambiguous sorting of the quasienergy spectrum, identifies a unique Floquet ground state at all drive frequencies, and serves as a sensitive diagnostic for heating and symmetry-breaking transitions. Inherently nonequilibrium phenomena—the 𝜋-quasienergy splitting of discrete time crystals and the anomalous edge modes of Floquet topological insulators—are traced to geometric phases. On the practical side, we exploit the intrinsic robustness of prethermal discrete time crystals for a highly frequency-selective DTC-based AC magnetic field sensing scheme and demonstrate it experimentally on a nuclear spin quantum simulator. We then generalize counterdiabatic driving to periodically driven systems. In particular, we derive a non-perturbative variational principle for the Floquet adiabatic gauge potential; this yields local, experimentally feasible control protocols for transitionless manipulation of Floquet states. We demonstrate this formalism on Floquet state preparation in an ultracold atom quantum simulator and many-body state transfer across a quantum phase transition, with significant improvements over unassisted protocols in both cases.
Periodic driving plays a central role in quantum control, but its application in interacting spin systems is often restricted to near-resonant conditions, where standard averaging techniques remain valid. Here we investigate how detuning from resonance can be used to dynamically spin-lock a dipolar-coupled ensemble. We show that the combination of offset and pulse structure generates an effective Rabi field with sharply structured amplitude and tilt. This behavior - supported by a semi-analytical framework, numerical simulations and experiment - enables new approaches to many-body system control, here exemplified via offset-induced reversible interconversion of Zeeman and dipolar order, and heterospin polarization transfer away from rf-field matching conditions. Further, we leverage artificial-intelligence-assisted sequence design to explore regimes with long control cycles - where average Hamiltonian theory breaks down, but effective locking persists - opening pathways to rich offset-dependent responses. These findings position offset-enabled dynamic locking as a promising tool for quantum sensing, energy transfer, and spin-order manipulation beyond traditional approaches.
We propose a Floquet-engineered framework for the coherent control of the light-matter interaction in a two-level system (TLS) located in a time-modulated cavity. Strictly phase-preserving operation of the TLS-cavity interaction is demonstrated, allowing the interrupt and retrieval of coherent Rabi oscillations without the loss of quantum information. By introducing a phonon reservoir, it is proved that the frequency instability induced from non-Markovian processes does not produce significant phase decoherence during Floquet modulation. Our results provide new insights into the fundamental physics of a driven quantum system and establish Floquet engineering as a powerful tool for coherent quantum information processing.
Periodically driven quantum systems can function as highly selective parameter filters. We demonstrate this capability in a finite-size, three-qubit system described by the transverse-field Floquet Ising model. In this system, we identify a period-doubling (PD) dynamical phase that exhibits a stark asymmetry in metrological sensitivity to the magnetic field applied on the qubits and to the coupling strength between the qubits. The PD phase originates from π-pairing, where the initial state exhibits strong overlap with π-paired Floquet eigenstates, leading to robust period-doubled dynamics and enhanced metrological sensitivity. The analysis of quantum Fisher information reveals that the PD regime significantly enhances precision for estimating the Ising interaction strength while simultaneously suppressing sensitivity to the transverse magnetic field. Conversely, non-PD regimes are optimal for sensing the transverse field. This filtering effect is robust for larger system sizes and is quantifiable using experimentally accessible observables, such as magnetization and two-qubit correlations, via the classical Fisher information. Our work shows that distinct dynamical regimes in finite-size Floquet systems can be harnessed for targeted quantum sensing.