We propose a stroboscopic Floquet protocol that applies periodic coherent displacement kicks to a cavity–Bose–Einstein condensate system operating in the normal phase near the Dicke superradiant critical point. The kicks leave the Hamiltonian and dissipation rates unchanged, yet generate a period-dependent stroboscopic steady state whose Fisher information exhibits a clear bounded maximum at an optimal strobe period T*. In the linearized Gaussian regime, enhancement arises from stroboscopic resonance at T* ≈ 2π/ω₀. In the full Lindblad treatment, non-commutativity between the free Liouvillian and the kick generator produces Baker–Campbell–Hausdorff corrections that renormalize the effective gap. Numerical fits support the local form μ(T) ≈ μ₀ + a/T² + c T² (a < 0, c > 0) in the intermediate-period regime, leading to an optimal sensing window via competition between gap-closing virtual transitions and restoring interaction effects. Exact diagonalization on truncated Fock–Dicke spaces (N = 3–5) with displacement kicks yields Fisher information gains of ×4.5–5.0 relative to the static case. A higher-truncation benchmark (N = 11) with a squeezing kick shows no enhancement, underscoring strong sensitivity to kick symmetry. Convergence in the thermodynamic limit remains open. The protocol offers a practical route to quantum sensing enhancement near a phase transition without crossing criticality or requiring feedback control. It highlights both the promise and current practical limits of Floquet Liouvillian engineering for metrology
We propose a stroboscopic Floquet protocol that applies periodic coherent displacement kicks to a cavity–Bose–Einstein condensate system operating in the normal phase near the Dicke superradiant critical point. The kicks leave the Hamiltonian and dissipation rates unchanged, yet generate a period-dependent stroboscopic steady state whose Fisher information exhibits a clear bounded maximum at an optimal strobe period T*. In the linearized Gaussian regime, enhancement arises from stroboscopic resonance at T* ≈ 2π/ω₀. In the full Lindblad treatment, non-commutativity between the free Liouvillian and the kick generator produces Baker–Campbell–Hausdorff corrections that renormalize the effective gap. Numerical fits support the local form μ(T) ≈ μ₀ + a/T² + c T² (a < 0, c > 0) in the intermediate-period regime, leading to an optimal sensing window via competition between gap-closing virtual transitions and restoring interaction effects. Exact diagonalization on truncated Fock–Dicke spaces (N = 3–5) with displacement kicks yields Fisher information gains of ×4.5–5.0 relative to the static case. A higher-truncation benchmark (N = 11) with a squeezing kick shows no enhancement, underscoring strong sensitivity to kick symmetry. Convergence in the thermodynamic limit remains open. The protocol offers a practical route to quantum sensing enhancement near a phase transition without crossing criticality or requiring feedback control. It highlights both the promise and current practical limits of Floquet Liouvillian engineering for metrology
We propose a stroboscopic Floquet sensing protocol that applies periodic coherent displacement kicks to a cavity–Bose-Einstein condensate system operated in the normal phase near the Dicke superradiant critical point. The kicks do not alter the underlying Hamiltonian or dissipation rates, yet they produce a stroboscopic steady state with a period-dependent Fisher information that exhibits a bounded maximum at an optimal strobe period (T^*).Two complementary theoretical pictures are developed. In the linearized Gaussian model, the enhancement arises from stroboscopic resonance at (T^* \approx 2\pi/\omega_0). In the full Lindblad treatment, noncommutativity between the Liouvillian and the kick generator generates Baker-Campbell-Hausdorff corrections. After projection onto the slow mode, these corrections renormalize the effective gap in the intermediate-period regime. Numerical fits support the local behavior[\mu(T) \approx \mu_0 + \frac{a}{T^2} + cT^2,\qquad a<0,;c>0.]This produces an optimal sensing period determined by competition between the two terms.Numerical simulations at moderate truncation levels ((N=3\text{–}5)) with a displacement kick yield a Fisher information gain of (\times4.5\text{–}5.0) relative to the static case. However, a higher-truncation benchmark at (N=11) using a squeezing kick shows no detectable enhancement. That benchmark simultaneously changes the kick type, the coupling (g/\kappa), and the kick strength (\epsilon) relative to the (N\leq5) runs, and therefore does not isolate a truncation effect.As shown in Sec. 4.3, the squeezing null is instead a first-moment sector effect that does not depend on truncation: the enhancement resides entirely in the stroboscopic mean[R^*(T)=\left(I-e^{AT}\right)^{-1}d](Appendix A). A squeezing kick contributes no affine displacement ((d=0)), so the corresponding homodyne Fisher information vanishes identically.The displacement-kick gains are shown to be exactly truncation-converged (Sec. 4.4) and therefore represent robust finite-(N) enhancements. In the thermodynamic limit (N\rightarrow\infty) at fixed (g/\sqrt{N}), the enhancement decays as a power law. The protocol is therefore best understood as a finite-size resonance rather than a thermodynamic-limit divergence.The protocol offers a route to sensing enhancement without operating at the critical point or requiring feedback. Its performance is highly sensitive to the choice of kick operator, highlighting both the promise and the practical limits of Floquet control for quantum metrology.
We demonstrate the emergence of a non-equilibrium superradiant phase in the dissipative Rabi-Dicke model. This phase is characterized by a photonic steady state that oscillates with a frequency close to the cavity frequency, in contrast to the constant photonic steady state of the equilibrium superradiant phase in the Dicke model. We relate this superradiant phase to the population inversion of Floquet states by introducing a Schwinger representation of the driven two-level systems in the cavity. This inversion is depleted near Floquet energies that are resonant with the cavity frequency to sustain a coherent light-field. In particular, our model applies to solids within a two-band approximation, in which the electrons act as Schwinger fermions. We propose to use this Floquet-assisted superradiant phase to obtain controllable optical gain for a laser-like operation.
Floquet dynamics of a quantum system subject to periodic modulations of system parameters provides a powerful tool for engineering new quantum matter with exotic properties. While system dynamics is significantly altered, the periodic modulation itself is usually induced externally and independent of Floquet dynamics. Here we propose a new type of Floquet physics for a Bose-Einstein condensate (BEC) subject to a shaken lattice generated inside a cavity, where the shaken lattice and atomic Floquet bands are mutually dependent, resulting in self-adapted Floquet dynamics. In particular, the shaken lattice induces Floquet quasienergy bands for the BEC, whose backaction leads to a self-adapted dynamical normal-superradiant phase transition for the shaken lattice. Such self-adapted Floquet dynamics shows two surprising and unique features: (i) The normal-superradiant phase transition possesses a hysteresis even without atom interactions. (ii) The dynamical atom-cavity steady state could exist at free energy maxima. The atom interactions strongly affect the phase transition of the BEC from zero to finite momenta. Our results provide a powerful platform for exploring self-adapted Floquet physics, which may open an avenue for engineering novel quantum materials.
Abstract We investigate the non-equilibrium dynamics and quantum metrological potential of an ensemble of four-level atoms interacting with a dissipative optical cavity. By deriving an effective master equation for the atomic degrees of freedom, we identify first-order dissipative phase transitions driven by the competition between coherent driving and collective decay. Focusing on a specific parametric trajectory, we employ Liouvillian spectral projections in the thermodynamic limit to rigorously delineate the basins of attraction corresponding to the multistable phases. Furthermore, the mean-field superradiance potential reveals that the dissipative phase transition manifests as a saddle-node bifurcation where a metastable trapping potential vanishes. In the vicinity of the critical point, the system exhibits critical slowing down, leading to a vanishing Liouvillian spectral gap. Utilizing the matrix product state formalism, we demonstrate that due to this dissipative phase transition, the system possesses the potential to achieve Heisenberg-limited precision in continuous sensing. Our results confirm that the driven four-level superradiant model serves as a robust platform for exploiting critical dynamics to enhance metrological performance.
In this work, we investigate the dissipative generation of metrologically useful steady states in a generalized atom-cavity system that incorporates two-photon exchange, diamagnetic interactions, and auxiliary nonlinearities inherent to superconducting circuits. By quantifying the normalized Quantum Fisher Information (QFI), we demonstrate that the interplay between coherent driving and Kerr–Stark anharmonicity allows for the autonomous preparation of states that surpass the Standard Quantum Limit (SQL). Our results reveal that unlike simple Gaussian squeezing, the introduction of realistic nonlinearities induces non-Gaussian phase-space distortions, accompanied by small but finite Wigner negativity, that maximise the information content for photon-number encoding while maintaining a mean photon number below unity throughout. The Mandel Q M parameter is found to exceed the thermal-state reference 〈 n ^ 〉 across all dynamical regimes and coupling strengths, providing a stringent quantitative demonstration that the observed super-Poissonian statistics originate from non-classical correlations rather than thermal fluctuations. Crucially, a rigorous spectral decomposition of the Liouvillian superoperator confirms that these high-sensitivity regimes are protected by a finite spectral gap, precluding critical slowing down and ensuring that state preparation occurs on timescales significantly shorter than typical qubit decoherence times. These findings establish a viable blueprint for engineering always-on quantum sensors that are both metrologically superior and dynamically robust.
We introduce a self-adaptive Floquet system based on a quantum kicked rotor, in which the kicking strength itself becomes a dynamical variable generated self-consistently through cavity-mediated feedback. A superradiant transition gives rise to cavity-mediated kicking and two competing instability channels, symmetric and antisymmetric, which provide a unified organizing principle for the nonequilibrium Floquet phases. For resonant kicking, their competition produces double-kick dynamics that support resonant ballistic transport and an emergent antiresonance with period-quadrupled rotor evolution, arising from a balance between the two instability channels. Remarkably, for incommensurate kicking, the antisymmetric instability stabilizes a robust period-doubled localized phase with persistent subharmonic dynamics despite the underlying incommensurate driving, revealing localized temporal order absent in conventional kicked rotors. As the feedback strength increases, correlated temporal fluctuations progressively suppress quantum interference, driving crossovers from period-doubled localization to irregular localization and eventually to subdiffusive transport. Our results establish a general framework for self-adaptive quantum-chaotic dynamics and demonstrate how dynamical feedback can fundamentally reshape transport, localization, and temporal order in driven quantum systems.