Tunneling Delay Research Articles

Cost analysis of IPv6 distributed mobility management protocols in comparison with TFMIPv6.

The past decade has witnessed a significant evolution in the role of the Internet, transitioning from individual connectivity to an integral aspect of various domains. This shift has prompted a move in IP paradigms from hierarchical to distributed architectures characterized by decentralized structures. This transition empowers efficient data routing and management across diverse networks. However, traditional distributed mobility management (DMM) protocols, reliant on tunneling mechanisms, incur overheads, costs, and delays, exacerbating challenges in managing the exponential growth of mobile data traffic. This research proposes Tunnel-Free Mobility for IPv6 (TFMIPv6) as a solution to address the shortcomings of existing DMM protocols. TFMIPv6 eliminates the need for tunneling, simplifying routing processes and reducing latency. A comprehensive cost analysis and performance evaluation are conducted, comparing TFMIPv6 with traditional protocols such as MIPv6, PMIPv6, FMIPv6, and HMIPv6. The study reveals significant improvements with TFMIPv6. Signaling costs are reduced by 50%, packet delivery costs by 23%, and tunneling costs are completely eliminated (100%). Real-world network traffic datasets are used for simulation, providing statistical evidence of TFMIPv6's efficacy in supporting an uninterrupted movement of IPv6 data across networks.

Regulation of Nonadiabaticity-Induced Tunneling Delay Time

Regulation of Nonadiabaticity-Induced Tunneling Delay Time

Tunneling delay time in strong field ionization of atomic Ar

“Attoclock” provides a promising experimental scheme to explore the timing of tunnel ionization of atoms and molecules in intense laser fields. In this work, we perform a systematical investigation of tunneling delay time in strong field ionization of atomic Ar, based on the “attoclock” experimental scheme. Experimentally, the laser intensity dependence of the photoelectron momentum distributions of Ar subject to strong elliptically polarized laser fields at 800 nm has been measured. Theoretically, a dedicated semiclassical model, in which the Coulomb potential effect, the nonadiabatic effect, the Stark effect, the multielectron screening and polarization effect have been well considered, is employed to simulate the ionization dynamics of Ar. By comparing the experimental and simulated results, an upper limit of 10 attoseconds for the tunneling delay time of Ar has been derived for the laser intensity ranges explored in this work. In addition, the influence of various physical effects on the extracted tunneling delay time, in the context of semiclassical model, has been analyzed. It is demonstrated that, under otherwise identical conditions, consideration of multielectron screening effect will give rise to the least change of the extracted tunneling delay time. In contrast, consideration of nonadiabatic effect will lead to the most significant change of the extracted tunneling delay time.

Effects of time on the evolution of a wave packet in the tunneling dynamics

We investigate the time-dependent electron wave packet in a one-dimensional geometry with the potential bent by a homogeneous external field. Based on the behaviors of the wave packet over time, we observe a crossover time. After this crossover time, the temporal evolution of the wave packet comes into a new regime, where the wave packet evolves in a self-similar structure. To establish the time scale of this crossover quantitatively, we utilize the Loschmidt echo function, through which the time at which the crossover occurs can be extracted. We also find the time of the maximum ionization velocity can be comparable with the semi-classical tunneling delay time.

Newspaper Censorship in China: Evidence from Tunneling Scandals

Media dissemination plays an important role in facilitating price discovery. Political pressure that restricts media dissemination can hinder this function and affect investors’ perceptions. This paper studies the magnitude of newspaper censorship in China and its economic consequences using a setting of tunneling scandals. We find significant evidence of censorship of tunneling-related negative news at the national and local levels. We further show that news that survives censorship reduces information asymmetry and improves pricing efficiency. Censorship blocks informative tunneling news and delays incorporation of tunneling reporting into prices. This paper was accepted by Brian Bushee, accounting.

Nonadiabaticity-induced ionization time shift in strong-field tunneling ionization

Laser-induced electron tunneling is one of the most fundamental strong-field phenomena. In laser-induced electron tunneling, it is usually assumed that the highest tunneling rate appears at the peak of the laser electric field corresponding to the shortest tunneling barrier. Here we show that this fundamental assumption is broken in an orthogonally polarized two-color laser field. We find that a rapid change of the instantaneous initial momentum at the tunnel exit can lead to a distinct ionization time shift between the instant of the maximum ionization rate and the peak of the electric-field strength. This ionization time shift can be either positive or negative depending on the degree of nonadiabaticity of the electron-tunneling process, and it is mapped to a measurable momentum shift in the photoelectron momentum distribution. These findings have significant implications for resolving attosecond electron dynamics and are essential to quantify possible tunneling delay time during strong-field ionization.

Unifying Tunneling Pictures of Strong-Field Ionization with an Improved Attoclock.

We demonstrate a novel attoclock, in which we add a perturbative linearly polarized light field at 400nm to calibrate the attoclock constructed by an intense circularly polarized field at 800nm. This approach can be directly implemented to analyze the recent hot and controversial topics involving strong-field tunneling ionization. The generally accepted picture is that tunneling ionization is instantaneous and that the tunneling probability synchronizes with the laser electric field. Alternatively, recently it was described in the Wigner picture that tunneling ionization would occur with a certain of time delay. We unify the two seemingly opposite viewpoints within one theoretical framework, i.e., the strong-field approximation (SFA). We illustrate that both the instantaneous tunneling picture and the Wigner time delay picture that are derived from the SFA can interpret the measurement well. Our results show that the finite tunneling delay will accompany nonzero exit longitudinal momenta. This is not the case for the instantaneous tunneling picture, where the most probable exit longitudinal momentum would be zero.

Under-the-Tunneling-Barrier Recollisions in Strong-Field Ionization.

A new pathway of strong-laser-field-induced ionization of an atom is identified which is based on recollisions under the tunneling barrier. With an amended strong-field approximation, the interference of the direct and the under-the-barrier recolliding quantum orbits are shown to induce a measurable shift of the peak of the photoelectron momentum distribution. The scaling of the momentum shift is derived relating the momentum shift to the tunneling delay time according to the Wigner concept. This allows us to extend the Wigner concept for the quasistatic tunneling time delay into the nonadiabatic domain. The obtained corrections to photoelectron momentum distributions are also relevant for state-of-the-art accuracy of strong-field photoelectron spectrograms in general.

Superluminal and negative delay times in isotropic-anisotropic one-dimensional photonic crystal

In this work, we investigate the possibility of superluminal and negative delay times for electromagnetic wave propagation in a linear and passive periodic structure consisting of alternating isotropic and anisotropic media. This phenomenon is due to the birefringence of the anisotropic layers of the structure. By adjusting the orientations of these layers, the delay times of transmitted waves can be controlled from subluminality to superluminality and vice versa. Numerical results indicate that the apparent superluminal propagation of light occurs inside the photonic band-gaps when the principal axes of the anisotropic layers are parallel or perpendicular to the fixed axes. For other orientations of these layers, tunneling and superluminal regimes appear inside the photonic bandgaps and in the allowed bands for frequencies close to the transmission minima. The effect of the number of unit cells of the photonic crystal structure on the propagation of light with superluminal and negative delay times is also investigated. We show that the structure exhibits the Hartman effect in which the tunneling delay time of the electromagnetic wave through the photonic band-gap of the structure converges asymptotically to a finite value with increasing the number of layers. The Green's function approach has been used to derive the transmission and reflection coefficients, the density of states, and the delay times of electromagnetic waves propagating through the structure. The control of the magnitude and the sign of the delay time of light propagation represent a key point in slow and fast light technologies. The proposed structure in this study represents a new system for controlling the delay times of wave propagation without a need of active or non-linear media as well as lossy or asymmetric periodic structures.

Tunneling in attosecond optical ionization and a dynamical time operator

The conundrum parameter-operator of time in quantum mechanics (QM), as well as the time-energy uncertainty relation and the tunneling delay time, have recently been addressed in attosecond optical ioniza- tion experiments. The parameter status of time in the time dependent Schr\"odinger equation (TDSE) is supported by the well-known Pauli's ob- jection as well as by its interpretation as an emerging property of entangle- ment with a classical environment. On the other hand, the introduction of a self-adjoint dynamical time operator in Dirac's formulation of elec- tron's relativistic quantum mechanics (RQM), yields an additional system observable that represents an internal time. In the present paper the re- lation of this internal time with the parametric (laboratory) time and its relevance to the tunneling measurements in these experiments is examined within the standard framework of RQM.

Attoclock using Atomic Hydrogen

SynopsisWe present the results of attosecond angular streaking of atomic Hydrogen using elliptically polarized, 5.5 fs pulses that are centered around 770 nm, within the intensity range of 1.65 to 4 × 1014 W/cm2. We measure angular offsets in the photo-electron momentum distribution relative to the peak of the electric field of light in the polarization plane. We find a strong agreement in these results with the solutions of complete 3D-TDSE simulations. Further, we compute the contribution of coulomb effects (between the ionized electron-parent ion) to the measured angular offsets using Yukawa potential, subtracting which yields the real ‘tunneling delays’.

Strong-field ionization via a high-order Coulomb-corrected strong-field approximation

Signatures of the Coulomb corrections in the photoelectron momentum distribution during laser-induced ionization of atoms or ions in tunneling and multiphoton regimes are investigated analytically in the case of an one-dimensional problem. High-order Coulomb corrected strong-field approximation is applied, where the exact continuum state in the S-matrix is approximated by the eikonal Coulomb-Volkov state including the second-order corrections to the eikonal. Although, without high-order corrections our theory coincides with the known analytical R-matrix (ARM) theory, we propose a simplified procedure for the matrix element derivation. Rather than matching the eikonal Coulomb-Volkov wave function with the bound state as in the ARM-theory to remove the Coulomb singularity, we calculate the matrix element via the saddle-point integration method as by time as well as by coordinate, and in this way avoiding the Coulomb singularity. The momentum shift in the photoelectron momentum distribution with respect to the ARM-theory due to high-order corrections is analyzed for tunneling and multiphoton regimes. The relation of the quantum corrections to the tunneling delay time is discussed

Direct Tunneling Delay Time Measurement in an Optical Lattice

We report on the measurement of the time required for a wave packet to tunnel through the potential barriers of an optical lattice. The experiment is carried out by loading adiabatically a Bose-Einstein condensate into a 1D optical lattice. A sudden displacement of the lattice by a few tens of nanometers excites the micromotion of the dipole mode. We then directly observe in momentum space the splitting of the wave packet at the turning points and measure the delay between the reflected and the tunneled packets for various initial displacements. Using this atomic beam splitter twice, we realize a chain of coherent micron-size Mach-Zehnder interferometers at the exit of which we get essentially a wave packet with a negative momentum, a result opposite to the prediction of classical physics.

Tunneling Time and Weak Measurement in Strong Field Ionization.

Tunneling delays represent a hotly debated topic, with many conflicting definitions and little consensus on when and if such definitions accurately describe the physical observables. Here, we relate these different definitions to distinct experimental observables in strong field ionization, finding that two definitions, Larmor time and Bohmian time, are compatible with the attoclock observable and the resonance lifetime of a bound state, respectively. Both of these definitions are closely connected to the theory of weak measurement, with Larmor time being the weak measurement value of tunneling time and Bohmian trajectory corresponding to the average particle trajectory, which has been recently reconstructed using weak measurement in a two-slit experiment [S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, Science 332, 1170 (2011)]. We demonstrate a big discrepancy in strong field ionization between the Bohmian and weak measurement values of tunneling time, and we suggest this arises because the tunneling time is calculated for a small probability postselected ensemble of electrons. Our results have important implications for the interpretation of experiments in attosecond science, suggesting that tunneling is unlikely to be an instantaneous process.

Tunneling dynamics in multiphoton ionization and attoclock calibration.

The intermediate domain of strong-field ionization between the tunneling and multiphoton regimes is investigated using the strong-field approximation and the imaginary-time method. An intuitive model for the dynamics is developed which describes the ionization process within a nonadiabatic tunneling picture with a coordinate dependent electron energy during the under-the-barrier motion. The nonadiabatic effects in the elliptically polarized laser field induce a transversal momentum shift of the tunneled electron wave packet at the tunnel exit and a delayed appearance in the continuum as well as a shift of the tunneling exit towards the ionic core. The latter significantly modifies the Coulomb focusing during the electron excursion in the laser field after exiting the ionization tunnel. We show that nonadiabatic effects are especially large when the Coulomb field of the ionic core is taken into account during the under-the-barrier motion. The simple man model modified with these nonadiabatic corrections provides an intuitive background for exact theories and has direct implications for the calibration of the attoclock technique.

Ultrafast resolution of tunneling delay time

We compare the main competing theories of tunneling time against experimental measurements using the attoclock in strong laser field ionization of helium atoms. Refined attoclock measurements reveal a real and not instantaneous tunneling delay time over a large intensity regime, using two different experimental apparatus. Only two of the theoretical predictions are compatible within our experimental error: the Larmor time, and the probability distribution of tunneling times constructed using a Feynman Path Integral (FPI) formulation. The latter better matches the observed qualitative change in tunneling time over a wide intensity range, and predicts a broad tunneling time distribution with a long tail. The implication of such a probability distribution of tunneling times, as opposed to a distinct tunneling time, challenges how valence electron dynamics are currently reconstructed in attosecond science. It means that one must account for a significant uncertainty as to when the hole dynamics begin to evolve.

Simulating Quantum-Mechanical Barrier Tunneling Phenomena with a Nematic-Liquid-Crystal-Filled Double-Prism Structure

We present an electrically-controlled nematic-liquid-crystal-filled double-prism structure that can be used to simulate quantum-mechanical tunneling through a barrier of variable height. Measurements of time delay in reflection from this structure, taken with femtosecond resolution using entangled photon pairs in a Hong-Ou-Mandel interferometer, are compared to theoretical predictions. We show that the Goos-Hänchen contribution to the tunneling delay is unmeasurable in this geometry. Our research contributes to the understanding of quantum-mechanical barrier tunneling times, and can lead to the fabrication of optical analogues to the tunnel junction and other photonic devices.

Only Above Barrier Energy Components Contribute to Barrier Traversal Time

A time of arrival operator across a square potential barrier is constructed. The expectation value of the barrier time of arrival operator for a sufficiently localized incident wave packet is compared with the expectation value of the free particle time of arrival operator for the same wave packet. The comparison yields an expression for the expected traversal time across the barrier. It is shown that only the above barrier components of the momentum distribution of the incident wave packet contribute to the barrier traversal time, implying that below the barrier components are transmitted without delay. This is consistent with the recent experiment in attosecond ionization in helium indicating that there is no real tunneling delay time [P. Eckle et al., Science 322, 1525 (2008)].

Tunneling delays in frustrated total internal reflection

We demonstrate a direct relationship between tunneling delays in a one-dimensional potential barrier and the delays observed in frustrated total internal reflection. Expressions relating the group delays in these two cases have been formulated in the past [A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994)], but only for certain limits of the normalized particle energy $E/{V}_{0}$. Here, we derive a single expression relating these two group delays that is valid for arbitrary particle energy by decomposing the group delay into dwell-time and self-interference components. This decomposition also explains why the predicted delay differs in the limiting cases observed by Steinberg and Chiao.

Recent attoclock measurements of strong field ionization

The attoclock is a powerful, new, and unconventional experimental tool to study fundamental attosecond dynamics on an atomic scale. We have demonstrated the first attoclock with the goal to measure the tunneling delay time in laser-induced ionization of helium and argon atoms, with surprising results. It was found that the time delay in tunneling is zero for helium and argon atoms within the experimental uncertainties of a few 10’s of attoseconds. Furthermore we showed that the single active electron approximation is not sufficient even for atoms such as argon and the parent-ion interaction is much more complex than normally assumed. For double ionization of argon we found again surprising results because the ionization time of the first electron is in good agreement with the predictions, whereas the ionization of the second electron occurs significantly earlier than predicted and the two electrons exhibit some unexpected correlation.