We derive an effective trapped atom--cavity model in which a constant gravitational acceleration shifts the oscillator equilibrium and changes the local standing-wave coupling, thereby encoding the acceleration in the Jaynes Cummings exchange frequencies. With the atom and motion initially in their ground states and the cavity field initially coherent, we solve the closed-system carrier dynamics exactly and derive the displaced-frame quantum Fisher information (QFI) of the joint atom-cavity state. This QFI is proportional to the square of the local coupling slope, grows quadratically with interrogation time, and scales linearly with mean photon number. At the node, phase-referenced Ramsey detection gives a sign-sensitive estimate of axial acceleration and locally saturates the joint QFI. Away from the node, photon counting and phase-optimized homodyne detection provide cavity readouts when the cavity state carries more QFI than the atomic state. At the off-node operating point studied, Lindblad simulations show that cavity loss produces a finite-time QFI optimum. Lamb Dicke and sideband-suppression conditions control the carrier approximation. In the closed-system benchmark, the carrier-model QFI agrees with the atom-cavity QFI obtained from the unexpanded model after tracing out motion.
We derive an effective trapped atom--cavity model in which a constant gravitational acceleration shifts the oscillator equilibrium and changes the local standing-wave coupling, thereby encoding the acceleration in the Jaynes Cummings exchange frequencies. With the atom and motion initially in their ground states and the cavity field initially coherent, we solve the closed-system carrier dynamics exactly and derive the displaced-frame quantum Fisher information (QFI) of the joint atom-cavity state. This QFI is proportional to the square of the local coupling slope, grows quadratically with interrogation time, and scales linearly with mean photon number. At the node, phase-referenced Ramsey detection gives a sign-sensitive estimate of axial acceleration and locally saturates the joint QFI. Away from the node, photon counting and phase-optimized homodyne detection provide cavity readouts when the cavity state carries more QFI than the atomic state. At the off-node operating point studied, Lindblad simulations show that cavity loss produces a finite-time QFI optimum. Lamb Dicke and sideband-suppression conditions control the carrier approximation. In the closed-system benchmark, the carrier-model QFI agrees with the atom-cavity QFI obtained from the unexpanded model after tracing out motion.
We study quantum gravimetry when the interrogation time carries intrinsic uncertainty, motivated by a fundamental limit on temporal resolution associated with the energy--time uncertainty relation. For linearly gravity-coupled gravimeters, we obtain the effective gravity information by profiling the interrogation time from the two-parameter quantum Fisher information (QFI) matrix. In this class, the time-information block is quadratic in the gravitational parameter, and for quadratic background dynamics, the gravity--time cross term becomes affine in g. These properties yield a normalized expression for the fraction of standard single-parameter gravity QFI that remains once interrogation time is treated as a nuisance parameter, with an affine numerator and a Lorentzian denominator. We work out these results in three benchmark models: a freely falling Gaussian wavepacket, the Kasevich--Chu light-pulse atom interferometer, and an idealized closed-unitary optomechanical model. The Gaussian free-fall benchmark yields an exact closed-form expression for the effective gravity information and shows explicitly how nuisance-time profiling suppresses the momentum-spread-dependent part of the standard single-parameter gravity QFI. In the Kasevich--Chu interferometer, internal state population readout gives a rank-deficient measured two-parameter geometry unless independent timing information is supplied, whereas full access to the final motional and internal states restores a full-rank geometry with retention controlled by the competition between initial velocity spread and gravitationally accumulated motion. In atom-interferometric benchmarks, the framework yields explicit conditions for minimizing nuisance-time information loss, together with corresponding constraints on momentum spread, spatial localization, and long-interrogation-time operation.
We analyze the time-dependent physical spectrum of a driven Jaynes-Cummings model in which both the two-level system and the quantized cavity mode are subject to coherent classical driving. The time-dependent Hamiltonian is mapped, via well-defined unitary transformations, onto an effective stationary Jaynes-Cummings form. Within this framework, we derive closed-form expressions for the two-time correlation functions of both the atomic and field operators. These correlation functions are subsequently used to evaluate the time-dependent physical spectrum according to the Eberly-Wódkiewicz definition, which properly accounts for finite spectral resolution and transient emission dynamics. We show that the external driving leads to substantial modifications of the atomic spectral response, including controllable frequency shifts and asymmetric line shapes. Importantly, we identify a regime in which the driving parameters are chosen such that the coherent displacement induced in the cavity field exactly cancels out the initial coherent amplitude. In this limit, the system dynamics reduce to that of an effectively vacuum-initialized Jaynes-Cummings model, and the standard vacuum Rabi splitting is recovered. This behavior provides a clear and physically transparent interpretation of the spectral features as arising from coherent field displacement rather than from modifications of the underlying atom-cavity coupling.
In an open quantum system, we study the evolution of a two-level atom as a detector which interacts with given environments. For a uniformly accelerated two-level atom coupled to a massless scalar field in the Minkowski vacuum, when it evolves for a certain time, we find that there exists a peak value for the quantum Fisher information (QFI) of acceleration, which indicates that the optimal precision of estimation is achieved when choosing an appropriate acceleration a. QFI has different behaviors for different initial state parameters $\ensuremath{\theta}$ of the atom, displaying periodicity. However, the periodicity fades away with the evolution of time, which means that the initial state cannot affect the later stable quantum state. Furthermore, adding a boundary, we observe that the peak value of QFI increases when the atom is close to the boundary, which shows that QFI is protected by the boundary. Here, QFI fluctuates, and there may exist two peak values with a certain moment, which expands the detection range of the acceleration. Therefore, we can enhance the estimation precision of acceleration by choosing an appropriate position and acceleration a. The periodicity of QFI with respect to the initial state parameter $\ensuremath{\theta}$ lasts a longer time than the previous unbounded case, which indicates that the initial state is protected by the boundary. Finally, for a thermal bath with a boundary, QFI of temperature has no more than one peak value with a certain moment, which is different from QFI of acceleration with a boundary. The periodicity also lasts a longer time than unbounded case, which shows the initial quantum state of the atom is protected by the boundary for two cases.
Abstract We investigate how phase information initially stored in a diamond four-level atom is redistributed when the atom interacts with a quantized cavity field and a mechanical mode. The phase ϕ is encoded in the atomic superposition (∣1⟩+eiϕ∣2⟩)/2, while the optical and mechanical subsystems start in Fock states. The dynamics are generated by a coarse-grained optomechanical Hamiltonian together with normalized non-Hermitian no-jump evolution. A central point of the analysis is that the induced ∣2⟩↔∣3⟩ channel contains the distinct photon operators a†kak and aka†k; they cannot be merged without changing the dynamics. The numerical study is deliberately restricted to the stationary, single-photon case k=1, for which the calculation is reproducible and the Hilbert-space truncation can be checked directly. We track the reduced-atomic quantum Fisher information (QFI), von Neumann entropy, purity, and total l1 coherence. In the parameter range considered, increasing the optomechanical coupling G reduces the maximum conditioned atom--rest entropy from about 1.676 to 0.374 bits and raises the minimum atomic purity from about 0.356 to 0.876. At the same time, the time-averaged local QFI decreases from about 0.450 to 0.336, while the mean total coherence changes only weakly and non-monotonically. Thus stronger optomechanical coupling does not improve all quantum resources simultaneously: it keeps the conditioned atomic state purer and less entangled with the rest, but it also reduces the amount of phase information locally accessible from the atom. To expose this contrast more clearly, the time-dependent observables are plotted for two complementary combinations of G values, and the full nine-point coupling scan is summarized separately.
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.
We find the optimal initial states of a linearized cavity-optomechanical system for estimating the single-photon coupling by quantum Fisher information. In the red-detuned (beam-splitter) regime the interaction exchanges excitations between the two modes, and for pure inputs the Fisher information is four times the variance of the excitation-exchange operator, reducing the optimization to variance maximization with a closed-form solution. With the mechanical mode in a Fock state the probe is degenerate: any state saturating the photon-number constraint is optimal, and a Fock reference with many phonons enhances the per-photon sensitivity linearly. For an arbitrary fixed mechanical reference it becomes a phase-matched squeezed vacuum, from an exact bound on that coherence obtained by a Lagrange-dual argument. Jointly optimizing both modes at fixed total excitation number, the quantum Fisher information obeys a Heisenberg bound quadratic in the energy, saturated by equal superpositions of the two extremal eigenstates of the generator, equivalently a two-mode NOON state after a balanced beam splitter; balanced product Fock states reach only a linear enhancement. Exact diagonalization in truncated Fock spaces confirms all the results, the familiar single-photon input being the simplest saturating case. Three extensions are worked out: the blue sideband has an unbounded two-mode-squeezing spectrum, so the entangled optimum becomes impossible and the balanced product Fock state is exactly optimal at definite energy; under cavity loss the information accumulation turns linear on the cavity-lifetime timescale, at a renewal-optimal duration of about two and a half lifetimes; and for a state-of-the-art quantum-coherent coupling experiment the per-hour relative precision lies between one part in a million and ten parts in a million, number and thermal references being the most robust.