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Journal of Physics Conference Series

Tunneling dynamics of a two-atom system

G. A. Muradyan, H. R. Hakobyan, A. Zh. Muradyan

Published Jan 20, 2016• 0 citations
Publisher

Abstract

We discuss the quantum tunneling of a diatomic molecule, concentrating on the transmission differences corresponding to different internal states. The evolution picture is constructed basing on introduction of notion of effective potential, the form of which is dependent on interatomic separation. To fully treat the tunneling problem analytically, we slightly modify the effective potential for each internal state. Clear splitting of these resonances enables us to suggest a scheme of molecular interferometer working as a Earth gravity sensor.

DOI
10.1088/1742-6596/672/1/012013

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We discuss the quantum tunneling of a diatomic molecule, concentrating on the transmission differences corresponding to different internal states. The evolution picture is constructed basing on introduction of notion of effective potential, the form of which is dependent on interatomic separation. To fully treat the tunneling problem analytically, we slightly modify the effective potential for each internal state. Clear splitting of these resonances enables us to suggest a scheme of molecular interferometer working as a Earth gravity sensor.
We study a diatomic homonuclear molecule incident upon a potential barrier. We allow transitions between binding energy states of the molecule during the process of tunneling and consider both single and double barriers. By applying an elegant method to solve this system we show that transmission resonances do occur in both cases and that expressions for the locations of the resonances can be found. Moreover, we find that the addition of binding energy levels tends to decrease the probability of tunneling. We also show that by relaxing rigor and treating the length of the molecule as though it is fixed we can obtain exact analytical expressions for the transmission probability that capture important features of the full solution.
Abstract This article examines resonant tunnelling of multi-atomic systems, extending the body of work on resonant tunnelling in this area beyond diatomic homo-nuclear systems. We consider diatomic molecules with distinct atoms having different masses, and linear triatomic molecules with indistinguishable atoms. The molecule is incident in the bound state upon a step potential with an energy increase of V 0 for each atom. We calculate the probabilities of reflection p R and transmission p T in the bound state and the dependence on the energy of the molecule. We find that, as was the case for the homo-nuclear molecule, resonant transmission for diatomic molecules with distinguishable atoms occurs for arbitrarily weak binding, and p T is close to one for finite binding energy. We also find resonant transmission for linear triatomic molecules. We show results for the time-dependent Schrödinger equation which agree with resonant transmission. We also consider the transmission of an N -atom one-dimensional molecule.
We summarize our study of a diatomic homonuclear molecule incident upon a potential barrier in one dimension [G.L. Goodvin and M.R.A. Shegelski. Phys. Rev. A, 71, 032719 (2005).]. We study various initial states for the molecule and allow transitions between vibrational states of the molecule during the process of tunneling. By applying an elegant method to solve this problem, we show that transmission resonances occur in several cases and that adding more binding energy levels for the molecule can tend to decrease the probability of tunneling. We also discuss the extension of our results to more realistic three-dimensional and experimental systems.PACS Nos.: 34.20.Cf, 03.65.Xp, 34.20.Gj, 34.50.Pi
We study the effects of multiple bound states on the probability of tunneling of a homonuclear diatomic molecule incident upon a potential barrier in one dimension. We obtain additional bound states by several means: by varying individual features of the binding potential as well as increasing the mass of the two atoms. We find that the tunneling behavior of a molecule with a large number of bound states $(\ensuremath{\sim}30)$ is drastically different from that for a molecule with a small number of states $(\ensuremath{\lesssim}5)$. Further, we find that the effect of multiple bound states on the proabability of tunneling is largely dependent upon the separation between the bound-state energies. It is also found that intermediary transitions between many bound states results in significantly larger reductions in the probability of tunneling. Finally, we investigate molecules of different masses and observe common qualitative features. We focus on molecules incident upon a $\ensuremath{\delta}$ barrier but we also consider Gaussian barriers.
We investigate, in one spatial dimension, the quantum mechanical tunnelling of a diatomic, homogeneous molecule with a single bound state incident upon an external barrier. Both time-independent and time-dependent tunnelling are investigated, using analytical and numerical methods. In the time-independent case, we first derive a formal solution for the molecule's wave function. Then, using the method of variable reflection and transmission amplitudes, we find that the probabilities of reflection and transmission in the bound state decrease with decreased binding strength, while the probabilities of refection and transmission in an unbound state increase with decreased binding energy. In the time-dependent case, we consider a molecule with discrete unbound states. The molecular wave function is modeled as a Gaussian wave packet, and its propagation is calculated numerically using Crank-Nicholson integration. It is found that, in addition to reflecting and transmitting, the molecule may also straddle the potential barrier in an unbound state.
We study a diatomic homonuclear molecule incident upon a potential barrier in three dimensions. We study various initial states for the molecule and allow transitions between rotational states of the molecule during the process of tunneling. By applying an elegant method to solve this problem we show that transmission resonances occur in several cases and that adding more binding energy levels for the molecule can tend to decrease the probability of tunneling. We also find that the probability of transmission can be enhanced by the addition of a second potential barrier. These results are in qualitative agreement with those found for the tunneling of a molecule in a one-dimensional model studied previously.