Tunneling Time Research Articles

Does the Hartman effect exist in triangular barriers

We study the phase, Larmor and dwell times of a particle scattered off triangular barriers (TBs). It is interesting that the dependences of dwell, reflective phase and Larmor times on the wave number, barrier width and height for a pair of mirror-symmetric (MS) exact triangular barriers (ETBs) are quite different, as the two ETBs have quite distinct scattering surfaces. In comparison, the dependence of the transmitted phase or Larmor times is exactly the same, since the transmitted amplitudes are the same for a pair of MS TBs. We further study the Hartman effect by defining the phase and Larmor velocities associated with the phase and Larmor times. We find no barrier width saturation effect for the transmitted and reflected times. This is indicated by the fact that all the velocities approach finite constants that are much smaller than the speed of light in vacuum for TBs with positive-slope impact faces. As for ETBs with vertical left edges, the naive velocities seem to also indicate the absence of the Hartman effect. These are quite distinct from rectangular barriers and may shed new light on the clarification of the tunneling time issues.

First Detection and Tunneling Time of a Quantum Walk.

We consider the first detection problem for a one-dimensional quantum walk with repeated local measurements. Employing the stroboscopic projective measurement protocol and the renewal equation, we study the effect of tunneling on the detection time. Specifically, we study the continuous-time quantum walk on an infinite tight-binding lattice for two typical situations with physical reality. The first is the case of a quantum walk in the absence of tunneling with a Gaussian initial state. The second is the case where a barrier is added to the system. It is shown that the transition of the decay behavior of the first detection probability can be observed by modifying the initial condition, and in the presence of a tunneling barrier, the particle can be detected earlier than the impurity-free lattice. This suggests that the evolution of the walker is expedited when it tunnels through the barrier under repeated measurement. The first detection tunneling time is introduced to investigate the tunneling time of the quantum walk. In addition, we analyze the critical transitive point by deriving an asymptotic formula.

Erratum: Relation between quantum tunneling times for relativistic particles [Phys. Rev. A 70, 052112 (2004)

Erratum: Relation between quantum tunneling times for relativistic particles [Phys. Rev. A 70, 052112 (2004)

Spectral Analysis of Discrete Metastable Diffusions

We consider a discrete Schrödinger operator H_varepsilon = -varepsilon ^2Delta _varepsilon + V_varepsilon on ell ^2(varepsilon mathbb {Z}^d), where varepsilon >0 is a small parameter and the potential V_varepsilon is defined in terms of a multiwell energy landscape f on mathbb {R}^d. This operator can be seen as a discrete analog of the semiclassical Witten Laplacian of mathbb {R}^d. It is unitarily equivalent to the generator of a diffusion on varepsilon mathbb {Z}^d, satisfying the detailed balance condition with respect to the Boltzmann weight exp {(-f/varepsilon )}. These type of diffusions exhibit metastable behavior and arise in the context of disordered mean field models in Statistical Mechanics. We analyze the bottom of the spectrum of H_varepsilon in the semiclassical regime varepsilon ll 1 and show that there is a one-to-one correspondence between exponentially small eigenvalues and local minima of f. Then we analyze in more detail the bistable case and compute the precise asymptotic splitting between the two exponentially small eigenvalues. Through this purely spectral-theoretical analysis of the discrete Witten Laplacian we recover in a self-contained way the Eyring–Kramers formula for the metastable tunneling time of the underlying stochastic process.

Effect of the Rashba interaction on the tunneling time and Hartman effect in an 8-Pmmn borophene superlattice

The spin-dependent group delay time and Hartman effect as well as the valley/spin polarization in an 8-Pmmn borophene superlattice under Rashba interaction are investigated theoretically, by using the stationary phase and the transfer matrix approaches. The group delay time depends on the spin degree of freedoms, and can be effectively controlled by changing the direction of superlattice, incident electron angle and Rashba strength. Both the valley and spin polarization reveal a strong dependence on the number of the superlattice barriers. Furthermore, group delay time oscillates as the width of the potential barriers increases, but in special conditions, the dependence on the width of the potential barriers will disappear. Interestingly, by increasing the angle of the direction of the superlattice the Hartman effect can be observed for most electron incidence angles. Our study show that, the 8-Pmmn borophene superlattice can be useful for future electronics and spintronics applications.

Injected coherence and phase control in the tunneling of ultra slow three-level atoms

Our research aims to investigate the impact of injecting atomic coherence on the phase tunneling time of ultra slow cascade three-level atoms traversing through high-quality cavities. Prior to interacting with the cavity in the Fock state, the atoms are initially prepared in a superposition of the two upper levels. Our study has demonstrated that the coherence of the injected atoms can be tuned to control the phase time. Specifically, we have observed that the injected coherence can regulate the peak values and sub-superclassical nature of the traversal time. Moreover, we have investigated how the number of superclassical peaks and resonances in the tunneling time curve can be influenced by the cavity length and de Broglie waves of the atom. Additionally, we have discovered that the phase time behavior is not only affected by the center-of-mass (CM) motion but also by the atom–field detuning and the final internal state of the transmitted atoms. These findings have potential implications for developing and controlling ultracold atom-based technologies, such as quantum sensors, quantum information processing, and quantum simulation.

RETRACTED: Non-Hermiticity of tunneling time in a spacetime-symmetric extension of nonrelativistic quantum mechanics

Time continues to be an intriguing physical property in the modern era. On the one hand, we have the classical and relativistic notions of time, where space and time have the same hierarchy, which is essential in describing events in spacetime. On the other hand, in quantum mechanics time appears as a classical parameter, meaning that it does not have an uncertainty relation with its canonical conjugate. In this work, we use a recent spacetime-symmetric proposal [Phys. Rev. A 95, 032133 (2017)] that tries to solve the unbalance in nonrelativistic quantum mechanics by extending the usual Hilbert space, having the time parameter $t$ and the position operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}$ in one subspace and the position parameter $x$ and time operator $\mathbb{T}$ in the other subspace. Time as an operator is better suitable for describing tunneling processes. We then solve the $1/2$-fractional integrodifferential equation for a particle subjected to strong and weak potential limits and obtain an analytical expression for the tunneling time through a rectangular barrier. Using a Gaussian energy distribution, we demonstrate that, for wavepackets well resolved in time, the expectation value of the operator $\mathbb{T}$ is the energy average of the classical time ${T}_{\text{class}}=\ensuremath{\partial}S/\ensuremath{\partial}E$, where $S$ is the classical action, which can be real or imaginary. For wavepackets not well resolved in time, the contribution of ${T}_{\text{class}}$ consistently vanishes, and solely properties of the energy distribution contribute to $\mathbb{T}$. We show that the time of travel for nontunneling particles is purely real. When tunneling is involved, complex arrival times emerge, becoming a signature of tunneling. Furthermore, we apply our results to a constant energy distribution, obtaining pure imaginary times for energies below the barrier while obtaining complex times for particles with a wavepacket spreading energies below and above the barrier, and show a comparison to previous works.

Superluminal tunneling times without superluminal signaling: Fading of the MacColl-Hartman effect at early times

A curious feature of quantum tunneling known as the MacColl-Hartman effect results in the numerical observation that particles can traverse a barrier with effective superluminal speed. However, because tunneling is never certain, any attempt to use this effect to send a signal faster than light would require sending many particles. In this work, we consider sending---in parallel, without interactions between particles---sufficiently many particles to ensure at the least one of them tunnels. In this case, in spite of the time advance of the mean time for a single tunneling particle, the mean time to send one bit of information is larger for tunneling particles than for the same number of free photons. This removes any possibility of superluminal signaling. We show that the mean time to send one bit using $N$ particles is determined by the early-time tail of the distribution of tunneling times for one particle and that, when this early-time tail is highly accurately modeled using steepest descent, the MacColl-Hartman effect is seen to fade away.

Magnonic Klein and acausal tunneling enabled by breaking the anti parity-time symmetry in antiferromagnets

Klein tunneling associated with particle-antiparticle pair productions across a potential barrier is a key prediction of quantum-field theory for relativistic particles. Yet, a direct experimental realization is hampered by the particles large rest mass resulting in high potential barrier. Here, for non-Hermitian antiferromagnets, at the verge of the anti-parity-time symmetry transition, chiral magnons are demonstrated to offer a bosonic platform to access Klein tunneling at meV energies in experimentally feasible settings. Our analytical and numerical simulations evidence that magnetic damping renders a low energy mechanism for the breakdown of the magnonic vacuum and for creating particle-antiparticle pairs in strong magnetic fields. Adopting Feynman’s picture for antiparticles, the tunneling time of an incident magnon wave packet across a supercritical barrier is found to be negative. The uncovered aspects point to the potential of chiral magnons for addressing fundamental physics in a conceptually simple setup with the potential for use in chirality-dependent magnonic computing.

Sub-barrier recollisions and the three classes of tunneling time delays in strong-field ionization

Tunneling ionization is characterized by a negative time delay, observed asymptotically as a specific shift of the photoelectron momentum distribution, which is caused by the interference of the sub-barrier recolliding and direct ionization paths. In contrast, a \textit{Gedankenexperiment} following the peak of the wavefunction shows a positive tunneling time delay at the tunnel exit, considering only the direct ionization path. In this paper, we investigate the effects of sub-barrier recollisions on the time delay pattern at the tunnel exit. We conclude that the interference of the direct and recolliding trajectories decreases the tunneling time delay at the exit by the value equal to the asymptotic time delay maintaining, however, its sizeable positive value. Finally, we discuss the recent experiment [Light: Science \& Applications 11, 1 (2022)] addressing the tunneling time in a modified two-color attoclock setup. The analysis of the experimental findings with our theoretical model indicates the physical necessity to introduce a new time characteristic for tunneling ionization -- the time delay describing the initiation of the tunneling wave packet.

Quantized relativistic time-of-arrival operators for spin-0 particles and the quantum tunneling time problem

We provide a full account of our recent report (Flores and Galapon in EPL 141:10001, 2023) which constructed a quantized relativistic time-of-arrival operator for spin-0 particles using a modified Weyl-ordering rule to calculate the traversal time across a square barrier. It was shown that the tunneling time of a relativistic spin-0 particle is instantaneous under the condition that the barrier height $$V_o$$ is less than the rest mass energy. This implies that instantaneous tunneling is an inherent quantum effect in the context of arrival times.

Numerical quantum clock simulations for measuring tunneling times

We numerically study two methods of measuring tunneling times using a quantum clock. In the conventional method using the Larmor clock, we show that the Larmor tunneling time can be shorter for higher tunneling barriers. In the second method, we study the probability of a spin-flip of a particle when it is transmitted through a potential barrier including a spatially rotating field interacting with its spin. According to the adiabatic theorem, the probability depends on the velocity of the particle inside the barrier. It is numerically observed that the probability increases for higher barriers, which is consistent with the result obtained by the Larmor clock. By comparing outcomes for different initial spin states, we suggest that one of the main causes of the apparent decrease in the tunneling time can be the filtering effect occurring at the end of the barrier.

Effect of strain on tunneling time in graphene magnetic barrier

We solve the Dirac equation in three regions of graphene to get the solutions of the energy spectrum in connection to the strain, energy gap, and magnetic field. The Goos-H\"anchen shifts and group delay time will be obtained by applying the stationary phase approximation after the wave functions at the interfaces have been matched. Our results suggest that the group delay time is influenced by the presence of strain along the armchair and zigzag directions. We show that the gate voltage and strain have the ability to change the group delay from subluminality to superluminality. This may have significant uses in high-speed graphene-based nanoelectronics.

A study of tunneling in triangular resonant tunnel diodes: Effect of barrier width, barrier height, pressure, temperature, and heterostructure strain

Using the transfer matrix, the transmission coefficient of electrons is examined in the triangular double-barrier semiconductor heterostructure. GaAs-based heterostructure is considered to study the role of barrier width, barrier height, pressure and temperature. The geometrical parameters of the heterostructures (barrier width and barrier height) and the external perturbation (pressure and temperature) influence the tunneling properties. The tunneling time of the electrons is also studied using Heisenberg's uncertainty principle. The account of the heterostructure strain is also discussed.

Tunneling time in PT -symmetric systems

In the present work, we propose a generalization of tunneling time in parity and time $(\mathcal{P}\mathcal{T})$-symmetric systems. The properties of tunneling time in $\mathcal{P}\mathcal{T}$-symmetric systems are studied with a simple contact interaction periodic finite-size diatomic $\mathcal{P}\mathcal{T}$-symmetric model. The physical meaning of negative tunneling time in $\mathcal{P}\mathcal{T}$-symmetric systems and its relation to spectral singularities is discussed.

Gate reflectometry in dense quantum dot arrays

Silicon quantum devices are maturing from academic single- and two-qubit devices to industrially-fabricated dense quantum-dot (QD) arrays, increasing operational complexity and the need for better pulsed-gate and readout techniques. We perform gate-voltage pulsing and gate-based reflectometry measurements on a dense 2 × 2 array of silicon QDs fabricated in a 300 mm-wafer foundry. Utilizing the strong capacitive couplings within the array, it is sufficient to monitor only one gate electrode via high-frequency reflectometry to establish single-electron occupation in each of the four dots and to detect single-electron movements with high bandwidth. A global top-gate electrode adjusts the overall tunneling times, while linear combinations of side-gate voltages yield detailed charge stability diagrams. To test for spin physics and Pauli spin blockade at finite magnetic fields, we implement symmetric gate-voltage pulses that directly reveal bidirectional interdot charge relaxation as a function of the detuning between two dots. Charge sensing within the array can be established without the involvement of adjacent electron reservoirs, important for scaling such split-gate devices towards longer 2 × N arrays. Our techniques may find use in the scaling of few-dot spin-qubit devices to large-scale quantum processors.

Spin-dependent tunnelling time in phosphorene superlattice

ABSTRACT We study theoretically the Hartman effect and spin-dependent group delay time in a strained phosphorene superlattice in the presence of Rashba spin–orbit interaction (RSOI). It is found that the total group delay time depends on the spin degree of freedom. Thus, spin filtering can be obtained in the time domain by means of the phosphorene superlattice. The total group delay time can be efficiently controlled by the angles of incidence of electrons, strength of RSOI and number of superlattice barriers. Particularly, the magnitude of the total group delay time can be tuned via the direction and strength of strain. Therefore, in phosphorene superlattice the total group delay time can be efficiently adjusted mechanically. Moreover, in a strained phosphorene superlattice the superluminal tunnelling or Hartman effect can be observed even for a normal incident.

Ultrahigh Rectification Ratio in an Asymmetric Metal/Semiconductor/Metal Nanoscale Tunneling Junction: Implications for High-Frequency Rectifiers

The ultrafast quantum-based electron-transport mechanism with a typical tunneling time of femtoseconds is appealing to fabricate high-frequency rectifier diode devices for applications such as solar energy harvesting, THz mixers, and infrared detectors. Here, we demonstrate an ultrahigh rectification of more than 104 and a large forward current density of 13.8 A/cm2 at −2 V in the structure of a metal/semiconductor/metal (MSM, Pt/ZnO/TiN) nanoscale tunneling junction. Technology computer-aided design (TCAD) simulations demonstrate that high rectification originates from the switching of the electron-transport mechanism between direct tunneling (DT) and Fowler–Nordheim tunneling (FNT) under positive and negative voltage biases, respectively. The quantum-based FNT mechanism gives very slight temperature dependence of currents in a wide temperature range of 100–400 K. This work opens an avenue for high-frequency rectifier diodes based on MSM nanoscale tunneling junctions.

Numerical study of flow establishment process of engine in a shock tunnel

In this paper, an unsteady numerical simulation of the full-scale flow field establishment process of a scramjet in shock tunnel is carried out. The simulation covers from the driving process of the shock tube to the flow field establishment of nozzle and engine, and combines the chemical reaction of air. The feasibility of the calculation method is verified by comparing the pressure from simulation results and the experimental ones that measured in the shock tube. The results show that in the shock tube, the total pressure at the nozzle inlet is formed by the incident shock wave, the shock wave reflected by the diaphragm and the shock wave train caused by the nozzle high pressure. After the nozzle flow field is established, the Mach number of the core flow reaches the design value of 9.0, and the total pressure of the core flow reaches 30 MPa. By comparing the results of flow fields, wall pressure distributions and drag coefficients with the steady case, we show that the flow in test section approaches steady state in 16 ms, which includes the shock tunnel and nozzle starting time. The non-dimensional characteristic establishment time of the engine is about 4 and it is closed to that of the flat plate case.

Quantum tunneling time delay investigation of [Formula: see text] ion in human telomeric G-quadruplex systems.

Guanine-rich quadruplex DNA (G-quadruplex) is of interest both in cell biology and nanotechnology. Its biological functions necessitate a G-quadruplex to be stabilized against escape of the monovalent metal cations. The potassium ion ([Formula: see text]) is particularly important as it experiences a potential energy barrier while it enters and exits the G-quadruplex systems which are normally found in human telomere. In the present work, we analyzed the time it takes for the [Formula: see text] cations to get in and out of the G-quadruplex. Our time estimate is based on entropic tunneling time-a time formula which gave biologically relevant results for DNA point mutation by proton tunneling. The potential energy barrier experienced by [Formula: see text] ions is determined from a quantum mechanical simulation study, Schrodinger equation is solved using MATLAB, and the computed eigenfunctions and eigenenergies are used in the entropic tunneling time formula to compute the time delay and charge accumulation rate during the tunneling of [Formula: see text] in G-quadruplex. The computations have shown that ion tunneling takes picosecond times. In addition, average [Formula: see text] accumulation rate is found to be in the picoampere range. Our results show that time delay during the [Formula: see text] ion tunneling is in the ballpark of the conformational transition times in biological systems, and it could be an important parameter for understanding its biological role in human DNA as well as for the possible applications in biotechnology. To our knowledge, for the first time in the literature, time delay during the ion tunneling from and into G-quadruplexes is computed.