Abstract We study phase-sensitive quantum dynamics in a hybrid cavity system consisting of a mov-ing four-level ladder atom, a quantized optical mode, and a mechanical oscillator. The atomicTransitions interact with the cavity field through a motion-dependent Jaynes-Cummings coupling.while radiation pressure couples the intracavity photons to the mechanical mode. A Kerr mediumprovides photon-number-dependent phase shifts, and an external magnetic field generates Zeeman-shifted atomic sublevels. The quantum Fisher information and the von Neumann entropy of thereduced atomic states are used to follow the redistribution of phase information and the generationof atomenvironment correlations. The results show that stronger hybrid coupling generally trans-fers locally accessible phase information away from the atom while increasing the mixedness of theatomic subsystem. Since the full state evolves unitarily, the reduced atomic entropy also quantifiesthe entanglement between the atom and the combined field mechanics sector. Kerr nonlinearityreorganizes this information flow and can produce delayed loss of phase sensitivity or partial recoveryseries at selected times. The work highlights why quantum Fisher information and von NeumannEntropy must be interpreted together when metrological usefulness and entanglement are studied.in hybrid light-matter systems.
Abstract We study phase-sensitive quantum dynamics in a hybrid cavity system consisting of a mov-ing four-level ladder atom, a quantized optical mode, and a mechanical oscillator. The atomicTransitions interact with the cavity field through a motion-dependent Jaynes-Cummings coupling.while radiation pressure couples the intracavity photons to the mechanical mode. A Kerr mediumprovides photon-number-dependent phase shifts, and an external magnetic field generates Zeeman-shifted atomic sublevels. The quantum Fisher information and the von Neumann entropy of thereduced atomic states are used to follow the redistribution of phase information and the generationof atomenvironment correlations. The results show that stronger hybrid coupling generally trans-fers locally accessible phase information away from the atom while increasing the mixedness of theatomic subsystem. Since the full state evolves unitarily, the reduced atomic entropy also quantifiesthe entanglement between the atom and the combined field mechanics sector. Kerr nonlinearityreorganizes this information flow and can produce delayed loss of phase sensitivity or partial recoveryseries at selected times. The work highlights why quantum Fisher information and von NeumannEntropy must be interpreted together when metrological usefulness and entanglement are studied.in hybrid light-matter systems.
Abstract In science and technology, precision measurement of physical quantities is crucial, and the quantum Fisher information (QFI) plays a significant role in the study of quantum systems. In this work, we explore the dynamics of QFI in a hybrid optomechanical system, which consists of a ♢-type four-level atom interacting with a single-mode quantized field via a multi-photon process. We account for various sources of dissipation, including the decay rates of the atom, the cavity and the mechanical modes. Using an effective Hamiltonian, we analytically derive the explicit form of the state vector of the entire system via the time-dependent Schrödinger equation. We then investigate the atomic QFI for the estimation precision of the decay rate of the mechanical oscillator. Furthermore, we examine how optomechanical and atom-field coupling strengths, dissipation parameters and multi-photon transition influence the dynamics of atomic QFI. Our numerical results suggest that the estimation precision of the decay rate of the mechanical oscillator can be controlled by these parameters.
Abstract We present a finite-time study of energy exchange, quantum correlations, work capacity, and phase sensitivity in a driven hybrid system composed of a five-level atom, a Kerr nonlinear optical mode, and a mechanical oscillator. The atom--field interaction is modulated periodically, while four local Lindblad channels describe two selected atomic transitions together with optical and mechanical damping. Rather than treating the dynamics as a completed heat-engine cycle, we analyze the system as a transient open quantum process and keep the different energetic and information-theoretic quantities clearly separated. The initial optical and mechanical states are taken to be displaced squeezed thermal states, and the atomic subsystem is prepared in a coherent superposition carrying a relative phase. We follow the total energy, reservoir-associated currents, signed driving work, total and reduced entropies, atom--rest negativity, local mechanical ergotropy, and the quantum Fisher information associated with the initial atomic phase. Four parameter sets are considered in order to identify how the Kerr-plus-shift term, atom--field coupling strength, and atomic temperature bias influence the finite-time response. The calculations also track the first-law residual and include selected solver, time-step, and Hilbert-space checks to assess numerical sensitivity without claiming uniform convergence for every parameter set. The results show that stronger atom--field coupling produces the largest sampled atom--rest negativity, but this increase in correlation does not lead to a comparable preservation of the reduced atomic phase quantum Fisher information. Within the employed finite truncation, removing the Kerr-plus-shift term changes the energy balance sufficiently to produce a small positive end-of-window signed work, whereas the other cases give negative final signed work. Because the zero-χ Hamiltonian has a formal high-occupation instability in the untruncated model and no dedicated enlarged-cutoff test was completed for that case, this small positive value is treated as a result conditional on the adopted finite truncation rather than as a converged engine-performance claim. The mechanical ergotropy remains a local state property and should not be identified with the work exchanged through the external modulation. Taken together, the results show that entanglement, metrological sensitivity, ergotropy, reservoir currents, and driving work respond differently to the same parameter changes. The conclusions therefore apply to the specified phenomenological finite-time model and should not be interpreted as evidence of a completed thermodynamic cycle or of a particular experimental implementation.
We explore the dynamics of Quantum Fisher Information (QFI) and Von Neumann Entropy (VNE) in three-level stationary and moving Stark-shifted atomic systems influenced by a Nonlinear Kerr Medium (NLKM). QFI, which measures coherence and sensitivity to parameter changes, decreases over time due to decoherence, with slower decay at higher nonlinearity values. VNE, an indicator of quantum entanglement, increases over time, with stronger growth observed at lower nonlinearity valueThe Stark effect, caused by an external electric field, introduces energy level shifts that result in oscillatory behavior in both QFI and VNE. Stronger electric fields amplify these oscillations, enhancing sensitivity and entanglement dynamics. The system's phase significantly impacts its behavior, with symmetric patterns emerging at zero phase and more complex dynamics occurring at other phase values. In moving systems, atomic motion interacts with NLKM and Stark effects to produce periodic modulations in QFI and VNE. Lower nonlinearity values lead to pronounced oscillations, reflecting stronger quantum interactions, while higher values stabilize coherence. Peaks in QFI often align with dips in VNE, indicating a trade-off between precision and entanglement. Transient spikes in VNE highlight moments of enhanced quantum entanglement, while high QFI values signify robust coherence, critical for precision measurements. This study demonstrates the tunability of quantum systems through external field strength, nonlinearity, and phase, providing a framework for optimizing quantum sensing and exploring the fundamental dynamics of coherence and entanglement in quantum systems.
We investigated numerically the dynamics of quantum Fisher information (QFI) and entanglement for three- and four-level atomic systems interacting with a coherent field under the effect of Stark shift and Kerr medium. It was observed that the Stark shift and Kerr-like medium play a prominent role during the time evolution of the quantum systems. The non-linear Kerr medium has a stronger effect on the dynamics of QFI as compared to the quantum entanglement (QE). QFI is heavily suppressed by increasing the value of Kerr parameter. This behavior was found comparable in the cases of three- and four-level atomic systems coupled with a non-linear Kerr medium. However, QFI and quantum entanglement (QE) maintain their periodic nature under atomic motion. On the other hand, the local maximum value of QFI and von Neumann entropy (VNE) decrease gradually under the Stark effect. Moreover, no prominent difference in the behavior of QFI and QE was observed for three- and four-level atoms while increasing the value of Stark parameter. However, three- and four-level atomic systems were found equally prone to the non-linear Kerr medium and Stark effect. Furthermore, three- and four-level atomic systems were found fully prone to the Kerr-like medium and Stark effect.
This study investigates the quantum dynamics of three-level Stark-shifted atomic systems under the influence of a Nonlinear Kerr Medium (NLKM), focusing on the interplay between Quantum Fisher Information (QFI), Von Neumann Entropy (VNE), and photon-mediated interactions. By analyzing the temporal evolution of QFI (quantifying parameter estimation precision) and VNE (measuring quantum entanglement (QE), we demonstrate how Kerr nonlinearity (χ), Stark shifts (β), phase (ϕ), and photon numbers govern system behavior. Key findings reveal that lower χ values (e.g., [Formula: see text]) induce oscillatory QFI decay and rapid VNE growth, driven by atomic motion and NLKM interactions, with QFI peaks inversely correlated to VNE dips. Higher [Formula: see text] stabilizes both metrics, suppressing decoherence and entanglement fluctuations. Elevated photon numbers enhance stability by strengthening field-atom correlations, reducing oscillation amplitudes (particularly at low χ), and mitigating quantum fluctuations. The Stark effect (SE) amplifies energy-level shifts, while phase adjustments introduce asymmetries in quantum interference. These results highlight the system's tunability via [Formula: see text], and photon density. They position it as a versatile platform for quantum metrology and information processing, where precision, entanglement stability, and photon-mediated coherence are critical. Kerr interactions suppress long-time coherence and entanglement, while when [Formula: see text], Stark shifts can induce mild, transient quantum correlations. These dynamics are essential for controlling entanglement in cavity QED systems, especially when precise metrological performance is desired.
We have investigated numerically the dynamics of quantum Fisher information (QFI) and quantum entanglement (QE) of a two moving two-level atomic systems interacting with a coherent and thermal field in the presence of intrinsic decoherence (ID) and Kerr (non-linear medium) and Stark effects. The state of the entire system interacting with coherent and thermal fields is evaluated numerically under the influence of ID and Kerr (nonlinear) and Stark effects. QFI and von Neumann entropy (VNE) decrease in the presence of ID when the atomic motion is neglected. QFI and QE show an opposite response during its time evolution in the presence of a thermal environment. QFI is found to be more susceptible to ID as compared to QE in the presence of a thermal environment. The decay of QE is further damped at greater time-scales, which confirms the fact that ID heavily influences the system’s dynamics in a thermal environment. However, a periodic behavior of entanglement is observed due to atomic motion, which becomes modest under environmental effects. It is found that a non-linear Kerr medium has a prominent effect on the VNE but not on the QFI. Furthermore, it has been observed that QFI and QE decay soon under the influence of the Stark effect in the absence of atomic motion. The periodic response of QFI and VNE is observed for both the non-linear Kerr medium and the Stark effect in the presence of atomic motion. It is observed that the Stark, Kerr, ID, and thermal environment have significant effects during the time evolution of the quantum system.