In this work we present a theoretical model supported with a physical reasoning leading to a relation which performs an excellent estimation for the tunneling time in attosecond and strong field experiments, where we address the important case of the He-atom \cite{Eckle:2008s,Eckle:2008}. Our tunneling time estimation is found by utilizing the time-energy uncertainty relation and represents a quantum clock. The tunneling time is also featured as the time of passage (at the exit of the tunnel) similarly to the Einstein's {\it photon box Gedanken experiment}. Our work tackles an important study case for the theory of time in quantum mechanics and is very promising for the search for a (general) time operator in quantum mechanics. The work can be seen as a new fundamental step in dealing with the tunneling time in strong field and ultra-fast science, and is appealing for more elaborate treatments using quantum wave packet dynamics and especially for complex atoms and molecules.
The measurement of the tunneling time (T-time) in today's attosecond and strong field (low-frequency) experiments, despite its controversial discussion, offers a fruitful opportunity to understand time measurement and the time in quantum mechanics. In addition, as we will see in this work, a related controversial issue is the particulate nature of the radiation. Different models used to calculate the T-time will be discussed in this work in relation to my model of real T-time, Phys. Rev. {\bf 92}, 052118 (2015), where an intriguing similarity to the Bohr-Einstein photon box Gedanken experiment…
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 Schrödinger 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 mech…
Tunneling, transport of particles through classically forbidden regions, is a pure quantum phenomenon. It governs numerous phenomena ranging from single-molecule electronics to donor-acceptor transition reactions. The main problem is the absence of a universal method to compute tunneling time. This problem has been attacked in various ways in the literature. Here, in the present work, we show that a statistical approach to the problem, motivated by the imaginary nature of time in the forbidden regions, lead to a novel tunneling time formula which is real and subluminal (in contrast to various …
A quantum simulator based on ultracold optically trapped atoms for simulating the physics of atoms and molecules in ultrashort intense laser fields is introduced. The slowing down by about 13 orders of magnitude allows to watch in slow motion the tunneling and recollision processes that form the heart of attosecond science. The extreme flexibility of the simulator promises a deeper understanding of strong-field physics, especially for many-body systems beyond the reach of classical computers. The quantum simulator can experimentally straightforwardly be realized and is shown to recover the ion…
We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of times for the scattering of a particle through a static rectangular barrier and for the tunneling decay of an initially bound state after the sudden deformation of the potential, the latter case being relevant to understand tunneling times in recent attosecond experiments involving strong field ionization.
Beginners studying quantum mechanics are often baffled with electron tunneling.Hence an easy approach for comprehension of the topic is presented here on the basis of uncertainty principle.An estimate of the tunneling time is also derived from the same method.
Does the Heisenberg uncertainty principle (HUP) apply along the time dimension in the same way it applies along the three space dimensions? Relativity says it should; current practice says no. With recent advances in measurement at the attosecond scale it is now possible to decide this question experimentally. The most direct test is to measure the time-of-arrival of a quantum particle: if the HUP applies in time, then the dispersion in the time-of-arrival will be measurably increased. We develop an appropriate metric of time-of-arrival in the standard case; extend this to include the case whe…
The position-momentum uncertainty relations containing the dependence of their quantum bounds on state purity parameter $μ$ are discussed in context of possibilities to influence on the potential barrier transparency by means of decoherence processes. The behavior of barrier transparency $D$ is shown to satisfy the condition $μ^{-1}\ln D=const$. The particular case of thermal state with temperature $T$ where the purity parameter is a function of temperature is considered. For large temperature the condition for the barrier transparency is shown to be $T\ln D=const$.
The time taken by a wave packet to cross through a finite layered $PT$-symmetric system is calculated by stationary phase method. We consider the $PT$- symmetric system of fix spatial length $L$ consisting of $N$ units of the potential system `$+iV$' and `$-iV$' of equal width `$b$' such that $L=2Nb$. In the limit of large `$b$', the tunneling time is found to be independent of $L$ and therefore the layered $PT$-symmetric system display the Hartman effect. The interesting limit of $N \rightarrow \infty$ such that $L$ remains finite is investigated analytically. In this limit the tunneling 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…
There remains the old question of how long a quantum particle takes to tunnel through a potential barrier higher than its incident kinetic energy. In this article a solution of the question is proposed on the basis of a realistic explanation of quantum mechanics. The explanation implies that the tunneling particle has a certain chance to borrow enough energy from self-interference to high-jump over the barrier. The root-mean-square velocity and the effective tunneling time of an electron tunneling through a rectangular barrier are numerically calculated. No superluminal effect (Hartman effect)…
The fundamental sources of noise in a vacuum-tunneling probe used as an electromechanical transducer to monitor the location of a test mass are examined using a first-quantization formalism. We show that a tunneling transducer enforces the Heisenberg uncertainty principle for the position and momentum of a test mass monitored by the transducer through the presence of two sources of noise: the shot noise of the tunneling current and the momentum fluctuations transferred by the tunneling electrons to the test mass. We analyze a number of cases including symmetric and asymmetric rectangular poten…
Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of this system are obtained through a variation-induced exact diagonalization procedure. The information entropy-based uncertainty relation is shown to be a better measure than conventional uncertainty product in interpreting purely quantum mechanical phenomena, such as, tunneling and quantum confinement in this case. Additionally, the phase-space description …
We have studied dynamical properties and quantum tunneling in asymmetric double-well (DW) systems, by solving Schrödinger equation with the use of two kinds of spectral methods for initially squeezed Gaussian wavepackets. Time dependences of wavefunction, averages of position and momentum, the auto-correlation function, an uncertainty product and the tunneling probability have been calculated. Our calculations have shown that (i) the tunneling probability is considerably reduced by a potential asymmetry $ΔU$, (ii) a resonant tunneling with $|ΔU| \simeq κ\:\hbar ω$ is realized for motion starti…
We show by a statistical analysis of high-resolution scanning tunneling microscopy (STM) experiments, that the interpretation of the density of electron charge as a statistical quantity leads to a conflict with the Heisenberg uncertainty principle. Given the precision in these experiments we find that the uncertainty principle would be violated by close to two orders of magnitude, if this interpretation were correct. We are thus forced to conclude that the density of electron charge is a physically real, i.e., in principle precisely measurable quantity.
The measurement of the tunneling time in attosecond experiments, termed attoclock, triggered a hot debate about the tunneling time, the role of time in quantum mechanics, where the interaction with the laser pulse involves two regimes of a different character, the multiphoton and the tunneling (field-) ionization. In the adiabatic field calibration, one of us (O. K.) developed in earlier works a real tunneling time model and showed that the model fits well to the experimental data of Landsmann et al. (Optica {\bf 1}, 343 2014). In the present work, it is shown that the model explains the exper…
We theoretically study the tunneling time by investigating a wave packet of Bose-condensed atoms passing through a square barrier. We find that the tunneling time exhibits different scaling laws in different energy regimes. For negative incident energy of the wave packet, counterintuitively, the tunneling time decreases very rapidly with decreasing incident velocity. In contrast, for positive incident energy smaller than the barrier height, the tunneling time increases slowly and then reaches a maximum, which is in agreement with the Larmor clock experiments. The effect of the barrier width re…
In a previous paper [Blado G, Owens C, and Meyers V 2014 Quantum Wells and the Generalized Uncertainty Principle Eur. J. Phys. 35 065011], we showed that quantum gravity effects can be discussed with only a background in non-relativistic quantum mechanics at the undergraduate level by looking at the effect of the generalized uncertainty principle (GUP) on the finite and infinite square wells. In this paper, we derive the GUP corrections to the tunneling probability of simple quantum mechanical systems which are accessible to undergraduates (alpha decay, simple models of quantum cosmogenesis an…
We analyze the tunneling time problem via the presence time formalism. With this method we reproduce previous results for very long wavepackets and we are able to calculate the tunneling time for general wavepackets of arbitrary shape and length. The tunneling time for a general wavepacket is equal to the average over the energy components of the standard phase time. With this approach we can also calculate the time uncertainty. We have checked that the results obtained with this approach agree extremely well with numerical simulations of the wavepacket evolution.
Tunneling of a particle through a potential barrier remains one of the most remarkable quantum phenomena. Owing to advances in laser technology, electric fields comparable to those electrons experience in atoms are readily generated and open opportunities to dynamically investigate the process of electron tunneling through the potential barrier formed by the superposition of both laser and atomic fields. Attosecond-time and angstrom-space resolution of the strong laser-field technique allow to address fundamental questions related to tunneling, which are still open and debated: Which time is s…
The refinement and specifications of time-energy uncertainty relations have shown that the experimentally observed phenomena of superluminal signaling are describable by such their form: $ΔEΔτ\geqπ\hbar$, where both standard deviations are negative. When $Δτ<0$, these evanescent photons would be instantly tunneling from one light cone into another on the distance $c| Δτ| $. (This assertion, previously proved via dispersion relations, is described here by the temporal parameters of process.) Special forms of these relations describe the transmutation of particles into their partners of bigger m…
Dynamics of a particle is formulated from classical principles that are amended by the uncertainty principle. Two best known quantum effects: interference and tunneling are discussed from these principles. It is shown that identical to quantum results are obtained by solving only classical equations of motion. Within the context of interference Aharonov-Bohm effect is solved as a local action of magnetic force on the particle. On the example of tunneling it is demonstrated how uncertainty principle amends traditional classical mechanics: it allows the momentum of the particle to change without…
This paper revisited quantum tunneling dynamics through a square double-barrier potential. We emphasized the similarity of tunneling dynamics through double-barrier and that of optical Fabry--P$\acute{e}$rot (FP) interferometer. Based on this similarity, we showed that the well-known resonant tunneling can also be interpreted as a result of matter multi-wave interference, analogous to that of FP interferometer. From this analogy, we also got an analytical finesse formula of double-barrier. Compared with that obtained numerically for a specific barrier configuration, we found that this formula …
Using a time operator, we define a tunneling time for a particle going through a barrier. This tunneling time is the average of the phase time introduced by other authors. In addition to the delay time caused by the resonances over the barrier, the present tunneling time is also affected by the branch point at the edge of the energy continuum. We find that when the particle energy is near the branch point, the tunneling time becomes strongly dependent on the width of the incoming wave packet, which implies that there is no intrinsic tunneling time. This effect is related to the quantum uncerta…
In quantum mechanics the time dimension is treated as a parameter, while the three space dimensions are treated as observables. This assumption is both untested and inconsistent with relativity. From dimensional analysis, we expect quantum effects along the time axis to be of order an attosecond. Such effects are not ruled out by current experiments. But they are large enough to be detected with current technology, if sufficiently specific predictions can be made. To supply such we use path integrals. The only change required is to generalize the usual three dimensional paths to four. We predi…
Quantum Kinetic Uncertainty Relations in Mesoscopic Conductors at Strong Coupling
University of Geneva（日内瓦大学）；Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB)（交叉物理与复杂系统研究所 IFISC (CSIC-UIB)）；ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；Department of Metal and Semiconductor Physics, NTU “Kharkiv Polytechnic Institute”（哈尔科夫理工学院金属与半导体物理系）
Quantum coherence between electronic states of a photoionized molecule and the resulting process of ultrafast electron-hole migration have been put forward as a possible quantum mechanism of charge-directed reactivity governing the photoionization-induced molecular decomposition. Attosecond experiments based on the indirect (fragment ion-based) characterization of the proposed electronic phenomena suggest that the photoionization-induced electronic coherence can survive for tens of femtoseconds, while some theoretical studies predict much faster decay of the coherence due to the quantum uncert…
In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be described in terms of classical physics without invoking violations of the energy conservation law at any time instance. A formula is presented that generates a wide class of potential barrier shapes with the desirable reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schrödinger…
