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Europhysics Letters (EPL)

Barrier Traversal Time in the Quantum Potential Picture

Timothy P. Spiller, Terrence D. Clark, Robert J. Prance, Helen Prance

Published May 1, 1990• 41 citations
Publisher

Abstract

We discuss the time taken for a particle to pass through a classically forbidden barrier in the quantum potential approach to quantum mechanics.
DOI
10.1209/0295-5075/12/1/001

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How long does a quantum particle take to traverse a classically forbidden energy barrier? In other words, what is the correct expression for quantum tunneling time? This seemingly simple question has inspired widespread debate in the physics literature. By drawing an analogy with the double-slit experiment, I argue that we should not even expect the standard interpretation of quantum mechanics to provide an expression for quantum tunneling time. I explain how this conclusion connects to time’s special status in quantum mechanics, the meaningfulness of classically inspired concepts in different interpretations of quantum mechanics, and the prospect of constructing experimental tests to distinguish between different interpretations.
Introduction In classical physics it is meaningful to ask the question, ‘How much time does a particle take to pass through a given region?’ The interesting question in quantum mechanics is: does a particle take a definite time to tunnel through a classically forbidden region? The question has been debated ever since the idea that there was such a time in quantum theory was first put forward by MacColl way back in 1932 [253]. A plethora of times has since then been proposed, and the answer seems to depend on the interpretation of quantum mechanics one uses. A reliable answer is clearly of great importance for the design of high-frequency quantum devices, tunnelling phenomena (as, for example, in scanning tunneling microscopy), nuclear and chemical reactions and, of course, for purely conceptual reasons. Most of the controversies centre around simple and intuitive notions in idealized one-dimensional models in a scattering configuration in which a particle (usually represented by a wave packet) is incident on a potential barrier localized in the interval [ a, b ]. Three kinds of time have been defined in this context. One, called the transmission time τ T ( a, b ), is the average time spent within the barrier region by the particles that are eventually transmitted. Similarly, the reflection time τ R ( a, b ) is the average time spent within the barrier region by the particles that are eventually reflected.
Abstract How long does a quantum particle take to traverse a classically forbidden energy barrier? In other words, what is the correct expression for quantum tunnelling time? This seemingly simple question has inspired widespread debate in the physics literature. I argue that we should not expect the orthodox interpretation of quantum mechanics to provide a unique correct expression for quantum tunnelling time, because to do so it would have to provide a unique correct answer to a question whose assumptions are in tension with its core interpretational commitments. I explain how this conclusion connects to time’s special status in quantum mechanics, the meaningfulness of classically inspired concepts in different interpretations of quantum mechanics, the prospect of constructing experimental tests to distinguish between different interpretations, and the status of weak measurement in resolving questions about the histories of subensembles.
Quantum particles interacting with potential barriers are ubiquitous in physics, and the question of how much time they spend inside classically forbidden regions has attracted interest for many decades. Recent developments of new experimental techniques revived the issue and ignited a debate with often contradictory results. This motivates the present study of an exactly solvable model for quantum tunneling induced by a strong field. We show that the tunneling dynamics can depart significantly from the scenario in which the barrier-traversal time is zero or very small. However, our findings do not support the idea of a well-defined tunneling time either. Our numerically exact results should help in finding a consensus about this fundamental problem.