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.
Highlights
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 “weak values” themselves are the subject of an ongoing discussion, and in the following we will rely on the analysis of their meaning, given in ref
Is the WS delay a kind “weak value”, ? And if so, what could it mean for one’s hope to find the elusive duration governing a tunnelling process? In the following we focus on the simpler case of a wave packet impinged on a potential barrier, with the expectation that any fundamental difficulties encountered in our analysis, would be likely to persist in the more complex cases, such as strong field ionisation reviewed in ref. 6
Summary
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. In a “tunnelling time” discussion, it is not unusual to expect that the sought time might be revealed by a suitable experimental procedure, without stating clearly which theoretical concept should be used to define the said time[6] This position is sustainable in classical physics, where a particle moves along a predictable classical trajectory. In what follows we approach the problem from the opposite perspective, and provide a detailed theory of the WS delay, in order to analyse both its meaning and usefulness
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