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arXiv:1410.4756 · Physics Letters A

Photon exchange and entanglement formation during transmission through a rectangular quantum barrier

Georg Sulyok, Katharina Durstberger-Rennhofer, Johann Summhammer

Published May 7, 2015• 6 citations
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Abstract

When a quantum particle traverses a rectangular potential created by a quantum field both photon exchange and entanglement between particle and field take place. We present the full analytic solution of the Schrödinger equation of the composite particle-field system allowing investigation of these phenomena in detail and comparison to the results of a classical field treatment. Besides entanglement formation, remarkable differences also appear with respect to the symmetry between energy emission and absorption, resonance effects and if the field initially occupies the vacuum state.

DOI
10.1016/j.physleta.2015.05.010

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When a quantum particle traverses a rectangular potential created by a quantum field both photon exchange and entanglement between particle and field take place. We present the full analytic solution of the Schrödinger equation of the composite particle-field system allowing investigation of these phenomena in detail and comparison to the results of a classical field treatment. Besides entanglement formation, remarkable differences also appear with respect to the symmetry between energy emission and absorption, resonance effects and if the field initially occupies the vacuum state.
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Quantum tunneling is conventionally described using the stationary Schrödinger equation with an externally imposed potential barrier. In this work, we present a dynamical formulation of quantum tunneling in which the barrier is modeled as a structured medium possessing quantized internal modes that interact coherently with an incident electron. Using the Heisenberg operator formalism and a second-quantized representation of the barrier medium, we derive coupled dynamical equations governing the electron–barrier interaction. Under a continuum-mode and mean-field approximation, the collective response of the barrier modes generates an effective potential that reproduces the conventional rectangular barrier model and the standard tunneling transmission probability obtained from the Schrödinger equation. Within this framework, a tunneling traversal time is naturally defined from the dynamical evolution of the electron and is shown to depend on the barrier width, barrier height, and incident electron energy. Numerical simulations illustrating the transmission probability and tunneling-time behavior are presented. The results provide a complementary microscopic interpretation of tunneling processes in structured quantum media and may be relevant to nanoscale transport, photonic barriers, and coherent quantum devices.
This research paper explores the theoretical foundations of quantum tunneling, explaining how particles can pass through potential barriers despite lacking the classical energy to do so. It develops the mathematical framework using the Schrödinger equation, derives the transmission coefficient for a rectangular potential barrier, introduces the WKB approximation for more realistic barriers, and examines key applications such as alpha decay, scanning tunneling microscopy (STM), and the Josephson effect. The paper also reviews the historical development, experimental verification, and limitations of quantum tunneling, highlighting its significance as one of the most fundamental and experimentally validated predictions of quantum mechanics.
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This communication is an enquiry into the circumstances under which entropy and subentropy methods can give an answer to the question of quantum entanglement in the composite state. Using a general quantum dynamical system we obtain the analytical solution when the atom initially starts from its excited state and the field in different initial states. Different features of the entanglement are investigated when the field is initially assumed to be in a coherent state, an even coherent state (Schrodinger cate state) and a statistical mixture of coherent states. Our results show that the setting of the initial state and the Stark shift play important role in the evolution of the sub-entropies and entanglement.