The dynamics of resonant tunneling via a spatially oscillating narrow well is investigated. The well generates a quasiresonance state, which can trap the incoming particles. Four spectral regimes are found: (1) the adiabatic regime, when the vibrations' frequency is lower than the spectral width of the resonance. In this regime, the mean current is independent of the vibration's frequency, and the current decreases as a function of the vibration's amplitude. (2) When the frequency of the vibration is higher than the spectral width of the resonance, the particle is partially trapped to the moving well and the dependence of the current on the vibrations' amplitude is more moderate. (3) However, and this is the main result of this paper, beyond a certain frequency the kinetic energy of the trapped particle exceeds the spectral width of the resonance, in which case particles cannot be trapped in the moving well and the current is abruptly suppressed. (4) When the energy quanta of the vibrations are higher than the energy gap between the resonance energy and the barrier's potential height, a single phonon can be absorbed by the particle only when the final energy agrees with the resonances of the barrier, in which case current suppression is selective and occurs only for specifics frequencies. The model is solved exactly numerically, and analytical approximations are presented for the different regimes. The analytical solutions show high agreement with the numerical ones. This effect can be implemented in extremely sensitive accelerometers. Moreover, it may explain the odor receptor's sensitivity to molecular vibrations.
The dynamics of resonant tunneling via a spatially oscillating narrow well is investigated. The well generates a quasiresonance state, which can trap the incoming particles. Four spectral regimes are found: (1) the adiabatic regime, when the vibrations' frequency is lower than the spectral width of the resonance. In this regime, the mean current is independent of the vibration's frequency, and the current decreases as a function of the vibration's amplitude. (2) When the frequency of the vibration is higher than the spectral width of the resonance, the particle is partially trapped to the moving well and the dependence of the current on the vibrations' amplitude is more moderate. (3) However, and this is the main result of this paper, beyond a certain frequency the kinetic energy of the trapped particle exceeds the spectral width of the resonance, in which case particles cannot be trapped in the moving well and the current is abruptly suppressed. (4) When the energy quanta of the vibrations are higher than the energy gap between the resonance energy and the barrier's potential height, a single phonon can be absorbed by the particle only when the final energy agrees with the resonances of the barrier, in which case current suppression is selective and occurs only for specifics frequencies. The model is solved exactly numerically, and analytical approximations are presented for the different regimes. The analytical solutions show high agreement with the numerical ones. This effect can be implemented in extremely sensitive accelerometers. Moreover, it may explain the odor receptor's sensitivity to molecular vibrations.
The physics of dynamic resonant tunneling is investigated.First, the resonant tunneling effect through an opaque barrier via a delta-function well is illustrated.Then, it is shown that, even in the adiabatic regime, where the dynamics can be governed by an analytic solution, the particle can be activated to higher energies.If the well varies quickly enough that the particle cannot escape from the well during the energetic elevation, the activation can be enhanced, as was anticipated by Azbel.However, and this is the main result of this work, the quasi-bound state of the well can even "reduce" the activation.In fact, because the resonant energy of the well matches twice the incoming particle's energy, and if the contribution to the wave function from both parts destructively interferes, then the particle cannot dwell in the well and activation is suppressed.This effect can be utilized in frequency-controlled transistors, and it is even speculated that it may explain the reason that humans can distinguish between tens of thousands of different odors with merely few hundreds of odor receptors.Lastly, the short time dynamics of a very fast perturbative well is also discussed.
The quantum tunneling current via an opaque barrier with an oscillating well reveals a wealth of physical phenomena: eigenstate-assisted activation, the elevator effect, coherent destruction of tunneling, suppression of activation, and the Sisyphus effect are a few examples. In this paper, we investigate these effects from a different perspective---transmission via a quasibound super state (QBSS). It is shown that an oscillating well supports a QBSS, which consists of numerous quasibound substates. Each one of these substates has a finite spectral width, which corresponds to the escape probability. However, they construct a unique spectrum, which consists of activated and suppressed quasi substates all of which are simultaneously excited. Thus, when the oscillating well is integrated into an opaque barrier, one can borrow an analogy from stationary resonant tunneling (RT). In the stationary RT scenario, current flows via a quasibound state. In the oscillating RT scenario, current flows via a QBSS. This analogy can easily explain many of the system's complex behaviors: the symmetry between the current's sensitivity to the incoming energy and the outgoing one, and even why some frequencies induce activation while others suppress it. This analogy can be applied to improve the sensitivity of the system when used for a frequency-controlled transistor for it predicts that when the incoming energy is shifted from the central resonance of the QBSS, the device's current becomes exponentially sensitive to the applied frequency. While the oscillations' frequency mainly determines the spectral distance between substates, the oscillations' amplitude determines the spectral width and center of the QBSS. Furthermore, it is suggested that this analogy can be applied to investigate microbiological systems (the olfactory system) and optical devices.
The existence of Fano resonances in dynamic resonant tunneling (RT) systems has been investigated. Fano resonances are characterized by the appearance of a 100% reflection coefficient in proximity to a high transmission coefficient. For a Fano resonance to appear, a bound state must exist. On the other hand, a resonant tunneling process is characterized by a high transmission and the existence of a quasi-bound state (QBS) instead of a bound one. It has been shown that, by narrowing the width of the barrier, the resonance energy of the QBS gradually decreases and eventually turns into a bound state. Consequently, in a dynamic RT process, there are two scenarios: either a bound state exists, in which case, Fano resonances exist for any barrier width, or a QBS exists, and the barrier should be narrow enough for the Fano resonance to appear. In both cases, the incoming particle’s frequency must be lower than the oscillating well’s frequency. In this work, these resonances are investigated in detail, and both exactly numerically and approximated analytical expressions are derived for both the weak and strong oscillating amplitude regimes. One of the conclusions is that, when the oscillating frequency is low enough, multiple Fano resonances can appear by varying the barrier’s width. Since these resonances are very sharp and zero transmission can easily be detected, this property can be used as a very accurate method for measuring the barrier’s width, even when the particle’s de-Broglie wavelength is much larger than the barrier’s width.
We analyze the periodic tunneling of a Bose-Einstein condensate in a double-well potential which has an oscillating energy barrier. We show that the dynamics of the Bose condensate critically depends on the frequency ω of the oscillating energy barrier. In the regime of periodic macroscopic quantum tunneling (PMQT) with frequency ωJ, the population imbalance of the condensate in the two wells can be enhanced under the condition of parametric resonance ω=2ωJ. Instead, in the regime of macroscopic quantum self-trapping (MQST), we find that MQST can be reduced or suppressed under the condition of parametric resonance between the frequency ω of the energy barrier and the frequency ωST of oscillation through the barrier of the very small fraction of particles which remain untrapped during MQST.
The extremely small probability of tunneling through an almost classical potential barrier may become not small under the action of the specially adapted nonstationary signal which selects the certain particle energy ER. For particle energies close to this value, the tunneling rate is not small during a finite interval of time and has a very sharp peak at the energy ER. After entering inside the barrier, the particle emits electromagnetic quanta and exits the barrier with a lower energy. The signal amplitude can be much less compared to the field of the static barrier. This phenomenon can be called the Euclidean resonance since the under-barrier motion occurs in imaginary time. The resonance may stimulate chemical and biochemical reactions in a selective way by adapting the signal to a certain particular chemical bond. The resonance may be used in search of the soft-\ensuremath{\alpha}-particle decay for which a conventional observation is impossible due to an extremely small decay rate.
The resonant tunneling of a wave packet is studied, for a one-dimensional double barrier, by solving the time-dependent Schrödinger equation. The transmission is determined as a function of the spatial width of the incident wave packet. It is shown that if the double barrier acts as an energy filter, then the spatial width of the transmitted wave packet is increased, due to the trapping of the particle between the two barriers for a time, ℏ/Γ, where Γ is the width of the resonance. The reflected wave packet consists of two components: one corresponding to reflection from the first barrier and the other due to the particle being trapped between the barriers for a time ℏ/Γ.