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arXiv:quant-ph/9501015 · Physical Review Letters

How Much Time Does a Tunneling Particle Spend in the Barrier Region?

Aephraim M. Steinberg

Published Mar 27, 1995• 287 citations
arXivHTMLPDF

Abstract

The question in the title may be answered by considering the outcome of a ``weak measurement'' in the sense of Aharonov, Albert, and Vaidman. Various properties of the resulting time are discussed, including its close relation to the Larmor times. It is a universal description of a broad class of measurement interactions, and its physical implications are unambiguous.

DOI
10.1103/physrevlett.74.2405

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The question in the title may be answered by considering the outcome of a ``weak measurement'' in the sense of Aharonov, Albert, and Vaidman. Various properties of the resulting time are discussed, including its close relation to the Larmor times. It is a universal description of a broad class of measurement interactions, and its physical implications are unambiguous.
The question of how long a tunneling particle spends in the forbidden region of a barrier has been a perplexing puzzle in foundational quantum mechanics for many decades. The Larmor time, one definition of tunneling time, uses an auxiliary degree of freedom of the tunneling particles to clock the time spent inside the barrier. Recently, we made our first measurement of the Larmor time for Bose-condensed 87Rb atoms tunneling through an optical barrier.1 Here, we report on follow up measurements with improved precision in the measured times and also study the time for the reflected atomic cloud. We observe significant discrepancies between our results and a simple theory based on weak measurement. We discuss our findings, hypothesize explanations for our results, and suggest future studies.
We show that it is impossible to determine the time a tunneling particle spends under the barrier. However, it is possible to determine the asymptotic time, i.e., the time the particle spends in a large area including the barrier. We propose a model of time measurements. The model provides a procedure for calculation of the asymptotic tunneling and reflection times. The model also demonstrates the impossibility of the determination of the time the tunneling particle spends under the barrier. Examples for \ensuremath{\delta} form and rectangular barrier illustrate the obtained results.
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 Modern atto-second experiments seek to provide an insight into a long standing question: “how much time does a tunnelling particle spend in the barrier?” Traditionally, quantum theory relates this duration to the delay with which the particle emerges from the barrier. The link between these two times is self-evident in classical mechanics, but may or may not exist in the quantum case. Here we show that it does not, and give a detailed explanation why. The tunnelling process does not lend itself to classical analogies, and its duration cannot, in general, be guessed by observing the behaviour of the transmitted particle.
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.