Time-dependent Coupling Research Articles

Properties of Pancharatnam Phase and Entanglement of a Five-Level Atom Interacting with a Squeezed Field

We introduce a quantum scheme where a single five-level atom interacts with a single-mode cavity field by a time-dependent coupling. During the interaction, the temporal behavior of the quantum entropy in the atomic basis is compared with that of the Mandel parameter used to quantify the nonclassical properties of the field. With the field prepared in a squeezed coherent state, the atomic quantum entropy is then used to quantify the entanglement or the nonlocal correlation of the five-level atom (5 LA) – field system. The influence of one- and two-photon transitions and the atomic motion on the degree of entanglement and the Pancharatnam phase is analyzed. The analysis emphasizes that both the time dependence and photon multiplicity play an important role in the evolution of the degree of entanglement, the Pancharatnam phase, and nonclassical properties. This insight may be very useful in various applications in quantum physics and quantum optics.

Ultrastrong time-dependent light-matter interactions are gauge relative

The authors show that the assumption of a time-dependent light-matter coupling function is physically different in each different gauge, resulting in non-equivalent models with different final predictions for fast and strong interactions.

Multi-body dynamics modeling and transient characteristics analysis for a folding wing

The investigation of modeling the time evolution of a folding wing during the morphing process and the dynamic characteristics analysis is carried out. The governing equations with uniform form are developed from the integration of floating frame method in multi-body dynamics and component mode synthesis in structural dynamics. The time-dependent aerodynamic force is taken into the governing equations. The equation achieves the time-dependent coupling between structure and aerodynamics and avoids the data transmission and low efficiency, which holds true for the multi-segmented folding wing. The relative parameters in constraint equations are easily modified to be applied to both slow and fast-varying processes for a folding wing. Also, the influence of the velocity and attack angle on transient responses can be investigated. Transient response analysis shows that slower morphing means more stable transient responses. The flexibility of the folding wing has the significant influence on transient responses. To some extent, the aerodynamic force can be beneficial to the morphing process.

Real-time steering of curved sound beams in a feedback-based topological acoustic metamaterial

We present the concept of a feedback-based topological acoustic metamaterial as a tool for realizing autonomous and active guiding of sound beams along arbitrary curved paths in free two-dimensional space. The metamaterial building blocks are acoustic transducers, embedded in a slab waveguide. The transducers generate a desired dispersion profile in closed-loop by processing real-time pressure field measurements through preprogrammed controllers. In particular, the metamaterial can be programmed to exhibit analogies of quantum topological wave phenomena, which enables unconventional and exceptionally robust sound beam guiding. As an example, we realize the quantum valley Hall effect by creating, using a collocated pressure feedback, an alternating acoustic impedance pattern across the waveguide. The pattern is traversed by artificial trajectories of different shapes, which are reconfigurable in real-time. Due to topological protection, the sound waves between the plates remain localized on the trajectories, and do not back-scatter by the sharp corners or imperfections in the design. The feedback-based design can be used to realize arbitrary physical interactions in the metamaterial, including non-local, nonlinear, time-dependent, or non-reciprocal couplings, paving the way to unconventional acoustic wave guiding on the same reprogrammable platform. We then present a non-collocated control algorithm, which mimics another quantum effect, rendering the sound beams uni-directional.

Quantum correlation and statistical properties in semiconductor microcavities with time-varying coupling effect

In this manuscript, we show how the photon-exciton entanglement and distribution of photons depend on the main parameters of the physical model in the semiconductor microcavities without and with of the time-dependent coupling effect (TDCE). We examine the dynamics of the quantum entanglement and photon statistics by considering the time variation of the coupling between the excitons and photons in weak excitation regime of quantum well confined in a semiconductor microcavity. We show that the manipulation and control of the degree of the entanglement and statistical distribution of photons in the presence of the TDCE can be benefited by a convenient choice of the strength field and the rate of the excitonic spontaneous emission.

The Second Law of Thermodynamics from Concave Energy in Classical Mechanics

A recently proposed quantum mechanical criterion `concavity of energy' for the second law of thermodynamics is studied also for classical particle systems confined in a bounded region by a potential with a time-dependent coupling constant. It is shown that the time average of work done by particles in a quench process cannot exceed that in the corresponding quasi-static process, if the energy is a concave function of the coupling constant. It is proven that the energy is indeed concave for a general confining potential with certain properties. This result implies that the system satisfies the principle of maximum work in the adiabatic environment as an expression of the second law of thermodynamics.

Dark D-brane cosmology: From background evolution to cosmological perturbations

We study the cosmological predictions of the dark D-brane model, in which dark matter resides on a D-brane moving in a higher-dimensional space. By construction, dark matter interacts only gravitationally with the standard model sector in this framework. The dark energy scalar field is associated with the position of the D-brane, and its dynamics is encoded in a Dirac-Born-Infeld action. On the other hand, dark matter is identified with matter on the D-brane, that naturally couples to dark energy \textit{via} a disformal coupling. We analyse the numerical evolution of the cosmological background, highlighting the fact that there are two regimes of interest: one, in which the coupling is positive throughout; and another, in which the coupling is negative at the present. In the latter, there is the enticing possibility of having scenarios in which the coupling is positive for a significant part of the evolution, before decreasing towards negative values. In both cases, the coupling is very small at early times, and only starts to grow during the late matter dominated era. We also derive the equations for the linear cosmological perturbations, an expression for the effective time-dependent gravitational coupling between dark matter particles and present the numerical results for the CMB anisotropy and matter power spectra. This allows for a direct comparison of the predictions for the growth of large scale structure with other disformal quintessence models.

On the Interaction Between a Time-Dependent Field and a Two-Level Atom: Path Integral Treatment

We use the coherent state path integral and a Schwinger model for the spin to solve the generalized Jaynes-Cummings model with a time-dependent coupling parameter of the photons-field. The propagators are given explicitly as perturbation series. These are summed up exactly. The wave functions are deduced.

Sigma models with local couplings: a new integrability-RG flow connection

We consider several classes of σ-models (on groups and symmetric spaces, η-models, ⋋-models) with local couplings that may depend on the 2d coordinates, e.g. on time τ . We observe that (i) starting with a classically integrable 2d σ-model, (ii) formally promoting its couplings hα to functions hα(τ ) of 2d time, and (iii) demanding that the resulting time-dependent model also admits a Lax connection implies that hα(τ ) must solve the 1-loop RG equations of the original theory with τ interpreted as RG time. This provides a novel example of an ‘integrability-RG flow’ connection. The existence of a Lax connection suggests that these time-dependent σ-models may themselves be understood as integrable. We investigate this question by studying the possibility of constructing non-local and local conserved charges. Such σ-models with D-dimensional target space and time-dependent couplings subject to the RG flow naturally appear in string theory upon fixing the light-cone gauge in a (D + 2)-dimensional conformal σ-model with a metric admitting a covariantly constant null Killing vector and a dilaton linear in the null coordinate.

The Second Law of Thermodynamics from Concavity of Energy Eigenvalues

Quantum dynamics controlled by a time-dependent coupling constant are studied. It is proven that an energy eigenstate expectation value of work done by the system in a quench process cannot exceed the work in the corresponding quasi-static process, if and only if the energy eigenvalue is a concave function of the coupling constant. We propose this concavity of energy eigenvalues as a new universal criterion for quantum dynamical systems to satisfy the second law of thermodynamics. We argue simple universal conditions on quantum systems for the concavity, and show that every energy eigenvalue is indeed concave in some specific quantum systems. These results agree with the maximal work principle for adiabatic quench and quasi-static processes as an expression of the second law of thermodynamics. Our result gives a simple example of an integrable system satisfying an analogue to the strong eigenstate thermalization hypothesis (ETH) with respect to the principle of maximum work.

Combined Molecular Dynamics Simulation and Rouse Model Analysis of Static and Dynamic Properties of Unentangled Polymer Melts with Different Chain Architectures

Chain architecture effect on static and dynamic properties of unentangled polymers is explored by molecular dynamics simulation and Rouse mode analysis based on graph theory. For open chains, although they generally obey ideal scaling in chain dimensions, local structure exhibits nonideal behavior due to the incomplete excluded volume (EV) screening, the reduced mean square internal distance (MSID) can be well described by Wittmer’ theory for linear chains and the resulting chain swelling is architecture dependent, i.e., the more branches a bit stronger swelling. For rings, unlike open chains they are compact in term of global sizes. Due to EV effect and nonconcatenated constraints their local structure exhibits a quite different non-Gaussian behavior from open chains, i.e., reduced MSID curves do not collapse to a single master curve and fail to converge to a chain-length-independent constant, which makes the direct application of Wittmer’s theory to rings quite questionable. Deviation from ideality is further evidenced by limited applicability of Rouse prediction to mode amplitude and relaxation time at high modes as well as the non-constant and mode-dependent scaled Rouse mode amplitudes, while the latter is architecture-dependent and even molecular weight dependent for rings. The chain relaxation time is architecture-dependent, but the same scaling dependence on chain dimensions does hold for all studied architectures. Despite mode orthogonality at static state, the role of cross-correlation in orientation relaxation increases with time and the time-dependent coupling parameter rises faster for rings than open chains even at short time scales it is lower for rings.

Controlling spin without magnetic fields: The Bloch-Rashba rotator

We consider the dynamics of a quantum particle held in a lattice potential, and subjected to a time-dependent spin-orbit coupling. Tilting the lattice causes the particle to perform Bloch oscillations, and by suitably changing the Rashba interaction during its motion, the spin of the particle can be gradually rotated. Even if the Rashba coupling can only be altered by a small amount, large spin-rotations can be obtained by accumulating the rotation from successive oscillations. We show how the time-dependence of the spin-orbit coupling can be chosen to maximize the rotation per cycle, and thus how this method can be used to produce a precise and controllable spin-rotator, the Bloch-Rashba rotator, without requiring an applied magnetic field.

Experimental and numerical investigation on temperature field and tailored mechanical properties distribution of 22MnB5 steel in spray quenching process

Abstract Functional gradient high-strength steel structures on the basis of a novel tailored spray quenching process can achieve an excellent crashworthiness and weight reduction, which own a promising future in advanced automotive and mechanical engineering. This paper focuses on the temperature distributions and mechanical properties characteristics of high strength 22MnB5 steel under complex spray jetting conditions. A spray density-based physical modeling method is simplified to describe the spray flow field and the water film evolution on the hot 22MnB5 surface during the spray quenching process. Fluid characteristics of spray jetting with single/twin nozzles and corresponding heat transfer intensity are systematically investigated by self-developed experimental scenarios. The results reveal that the fluid-solid heat transfer coefficient (IHTC) is dependent on the spray-quenching temperature distribution, which owns an intense correlation between post-quenched mechanical property and the jetting parameters involving the spray jetting pressure (SJP), the spray jetting height (SJH), the nozzle distance (ND), and initial quenching temperature (IQT). The average cooling rate under the single/twin nozzles jetting conditions can reached as 28.5–170.5 °C/s and 36.84–137.42 °C/s, corresponding to the peak IHTCs are 10.11–49.47 kW/(m2 K) and 9.69–44.76 kW/(m2 K), respectively. The hardness firstly increases and then decreases from the central point/zone to the edge along the radial direction after the spray quenching process. The largest radial hardness after the single/double nozzles spray quenching can be up to 50.21 % and 31.58 % larger than the lowest value, respectively. Moreover, the in-plane temperature field and corresponding post-quenched mechanical properties are further numerically predicted by introducing into the time-dependent IHTC and coupling with the CFD and Johnson-Mehl-Avrami (JMA) modeling. Finally, a validation work of U-type specimen was conducted to show the spray quenching technology owns a prospective future for gaining more complex-shaped parts with tailored mechanical properties.

Dynamical dark sectors and neutrino masses and abundances

We investigate generalized interacting dark matter-dark energy scenarios with a time-dependent coupling parameter, allowing also for freedom in the neutrino sector. The models are tested in the phantom and quintessence regimes, characterized by an equation of state $w_x<-1$ and $w_x>-1$, respectively. Our analyses show that for some of the scenarios the existing tensions on the Hubble constant $H_0$ and on the clustering parameter $S_8$ can be significantly alleviated. The relief is either due to \textit{(a)} a dark energy component which lies within the phantom region; or \textit{(b)} the presence of a dynamical coupling in quintessence scenarios. The inclusion of massive neutrinos into the interaction schemes does not affect neither the constraints on the cosmological parameters nor the bounds on the total number or relativistic degrees of freedom $N_{\rm eff}$, which are found to be extremely robust and, in general, strongly consistent with the canonical prediction $N_{\rm eff}=3.045$. The most stringent bound on the total neutrino mass $M_{\nu}$ is $M_{\nu}<0.116$ eV and it is obtained within a quintessence scenario in which the matter mass-energy density is only mildly affected by the presence of a dynamical dark sector coupling.

Novel scheme for anti-dynamical Casimir effect using nonperiodic ultrastrong modulation

Dynamical Casimir effect (DCE) denotes a plethora of phenomena characterized by generation of quanta (usually photons) from vacuum due to modulation of parameters of some neutral system. Its counterpart, or Anti-DCE, can be defined as a process in which photons, as well as overall system excitations, are annihilated from the thermal state of the field due to variation of system parameters. In this paper is proposed a new fast scheme for Anti-DCE based on coupling a single-mode cavity to a qubit with time-dependent coupling strength g=εsin⁡ηt, where the modulation frequency η is a linear or quadratic function of time and ε lies in the ultrastrong coupling regime. Numeric solutions of time-dependent Rabi Hamiltonian illustrate some convenient forms of η that reduce the average number of system excitations for initial thermal and Poissonian mixed states, and modification of the photon statistics is discussed.

Quantum correlations and quantum Fisher information of two qubits in the presence of the time-dependent coupling effect

In this paper, we consider two separate Jaynes–Cummings (JC) nodes with a nonidentical qubit-field system in the presence of dissipation terms. We reveal the influence of the time variation of the coupling terms on some important measures when the qubits are immersed in a vacuum. The density matrix for the two qubits initially in Bell states are obtained. The dynamical behavior of the quantum discord (QD), classical correlation (CC), qubit-qubit entanglement, and quantum Fisher information (QFI) is investigated. We explore the relationship among QD, CC, qubit-qubit entanglement, and QFI in the absence and presence of the dissipation effect during the time evolution. Furthermore, we show the main optimal conditions for obtaining a high level of correlation and coherence between the two qubits.

Entanglement and photon statistics of two dipole–dipole coupled superconducting qubits with Kerr-like nonlinearities

The engineering of Kerr and time-dependent coupling interactions is of great attention for treating quantum information in quantum systems and for investigating the collective behavior of large numbers of interacting particles in a cavity-qubit network. In this manuscript, we investigate the time evolution of the entanglement and some nonclassical properties of two superconducting qubits interacting with a single-mode field in the presence of a Kerr-like medium and dipole–dipole interaction without and with time-dependent coupling effect. We show that a slight alteration in the interaction, detuning, and Kerr parameters might cause a change in the entanglement of subsystem states during the evolution. By taking into account the influence of the different physical parameters, we show the statistical distributions produced in the photons of the single mode field through the calculation of the Mandel’s parameter. Finally, we find that the time-dependent Mandel’s parameter not only provide the statistical properties of the field, but also include the information of quantum entanglement for the subsystem states.

Time-evolution of nonlinear optomechanical systems: interplay of mechanical squeezing and non-Gaussianity

We solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical displacement, mechanical single-mode squeezing and a time-dependent optomechanical coupling up to the solution of two second-order differential equations. The solution is based on identifying a minimal and finite Lie algebra that generates the time-evolution of the system. This reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. To demonstrate the applicability of our method, we compute the degree of non-Gaussianity of the time-evolved state of the system by means of a measure based on the relative entropy of the non-Gaussian state and its closest Gaussian reference state. We find that the addition of a constant mechanical squeezing term to the standard optomechanical Hamiltonian generally decreases the overall non-Gaussian character of the state. For sinusoidally modulated squeezing, the two second-order differential equations mentioned above take the form of the Mathieu equation. We derive perturbative solutions for a small squeezing amplitude at parametric resonance and show that they correspond to the rotating-wave approximation at times larger than the scale set by the mechanical frequency. We find that the non-Gaussianity of the state increases with both time and the squeezing parameter in this specific regime.

Nonadiabatic Dynamics in a Laser Field: Using Floquet Fewest Switches Surface Hopping To Calculate Electronic Populations for Slow Nuclear Velocities.

We investigate two well-known approaches for extending the fewest switches surface hopping (FSSH) algorithm to periodic time-dependent couplings. The first formalism acts as if the instantaneous adiabatic electronic states were standard adiabatic states, which just happen to evolve in time. The second formalism replaces the role of the usual adiabatic states by the time-independent adiabatic Floquet states. For a set of modified Tully model problems, the Floquet FSSH (F-FSSH) formalism gives a better estimate for both transmission and reflection probabilities than the instantaneous adiabatic FSSH (IA-FSSH) formalism, especially for slow nuclear velocities. More importantly, only F-FSSH predicts the correct final scattering momentum. Finally, in order to use Floquet theory accurately, we find that it is crucial to account for the interference between wavepackets on different Floquet states. Our results should be of interest to all those interested in laser-induced molecular dynamics.

Short-time behavior of continuous-time quantum walks on graphs

Dynamical evolution of systems with sparse Hamiltonians can always be recognized as continuous time quantum walks (CTQWs) on graphs. In this paper, we analyze the short time asymptotics of CTQWs. In recent studies, it was shown that for the classical diffusion process the short time asymptotics of the transition probabilities follows power laws whose exponents are given by the usual combinatorial distances of the nodes. Inspired by this result, we perform a similar analysis for CTQWs both in closed and open systems, including time-dependent couplings. For time-reversal symmetric coherent quantum evolutions, the short time asymptotics of the transition probabilities is completely determined by the topology of the underlying graph analogously to the classical case, but with a doubled power-law exponent. Moreover, this result is robust against the introduction of on-site potential terms. However, we show that time-reversal symmetry breaking terms and non-coherent effects can significantly alter the short time asymptotics. The analytical formulas are checked against numerics, and excellent agreement is found. Furthermore, we discuss in detail the relevance of our results for quantum evolutions on particular network topologies.