Measurement Of Tunneling Time Research Articles

Time Operator, Real Tunneling Time in Strong Field Interaction and the Attoclock

Attosecond science, beyond its importance from application point of view, is of a fundamental interest in physics. The measurement of tunneling time in attosecond experiments offers a fruitful opportunity to understand the role of time in quantum mechanics. In the present work, we show that our real T-time relation derived in earlier works can be derived from an observable or a time operator, which obeys an ordinary commutation relation. Moreover, we show that our real T-time can also be constructed, inter alia, from the well-known Aharonov–Bohm time operator. This shows that the specific form of the time operator is not decisive, and dynamical time operators relate identically to the intrinsic time of the system. It contrasts the famous Pauli theorem, and confirms the fact that time is an observable, i.e., the existence of time operator and that the time is not a parameter in quantum mechanics. Furthermore, we discuss the relations with different types of tunneling times, such as Eisenbud–Wigner time, dwell time, and the statistically or probabilistic defined tunneling time. We conclude with the hotly debated interpretation of the attoclock measurement and the advantage of the real T-time picture versus the imaginary one.

Statistical approach to tunneling time in attosecond experiments

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 known time definitions implying superluminal tunneling). In addition to this, we show explicitly that the entropic time formula is in good agreement with the tunneling time measurements in laser-driven He ionization. Moreover, it sets an accurate range for long-range electron transfer reactions. The entropic time formula is general enough to extend to the photon and phonon tunneling phenomena.

Measurement of superluminal optical tunneling times in double-barrier photonic band gaps.

Tunneling of optical pulses at 1.5 microm wavelength through double-barrier periodic fiber Bragg gratings is experimentally investigated in this paper. Tunneling time measurements as a function of the barrier distance show that, far from resonances of the structure, the transit time is paradoxically short--implying superluminal propagation--and almost independent of the barrier distance. This result is in agreement with theoretical predictions based on phase-time analysis and provides, in the optical context, an experimental evidence of the analogous phenomenon in quantum mechanics of nonresonant superluminal tunneling of particles across two successive potential barriers.

Inelastic processes in time dependent tunneling in a scanning tunneling microscope junction

Experiments on frequency mixing and tunneling time measurements have stirred renewed interest in the problem of tunneling through time dependent barriers in a vacuum diode configuration such as the scanning tunneling microscope (STM) junction. In the present work we have formulated a theory of photoassisted emission for a planar bimetallic junction with both a static dc voltage and a time dependent bias of angular frequency ω. An expression for the current is derived using kinetic theory and the transfer Hamiltonian method. The wave functions are determined from time dependent perturbation theory and are calculated recursively to infinite order. Although the current is initially calculated within the free-electron model, this kinetic formalism allows for the inclusion of band-structure effects through the density of states factors. The photoassisted inelastic tunneling current was calculated as a function of frequency, fields, barrier parameters, and material asymmetry. The results are applied to an analysis of the tunneling time experiments of Nguyen et al. [H. Q. Nguyen et al., IEEE Trans. Electron Devices 36, 2671 (1989)]. The conclusions impose some constraints but do not limit the experimental procedure used for extracting tunneling times in an irradiated STM junction.