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Quantum Tunneling Without Transit: Near-Instantaneous Barrier Traversal as Global Structural Failure of an Extended Wave Packet

An Haizhong

Published Apr 24, 2026• 0 citations
Publisher

Abstract

The question of how long a particle takes to tunnel through a potential barrier has remained unresolved for decades. Attoclock experiments report traversal times consistent with zero, while Larmor clock measurements yield small but nonzero durations---a discrepancy recently traced to the two methods measuring fundamentally different quantities. We propose a resolution based on a discrete field-quantum network model whose continuum limit is the nonlinear Klein--Gordon equation. In this framework, a particle is not a point object localized on one side of a barrier: it is an extended structure whose electromagnetic and gravitational stress fields---carrying a significant fraction of its total energy---penetrate the barrier and extend to the far side. When a detector on the far side couples resonantly to this pre-existing stress tail, the particle's global structural integrity fails instantaneously, delivering its full energy to the detection point without any transit through the barrier. The ``tunneling time'' is near-zero not because the particle moves superluminally, but because it was already present on both sides before detection. This picture naturally explains the attoclock's null result (no transit occurs), the Larmor clock's nonzero reading (spin precession accumulates in the extended field within the barrier), and the established exponential decay of tunneling probability with barrier width (the stress-field amplitude decays exponentially in classically forbidden regions). No new parameters or modifications to quantum mechanics are introduced.

DOI
10.5281/zenodo.19718683

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The question of how long a particle takes to tunnel through a potential barrier has remained unresolved for decades. Attoclock experiments report traversal times consistent with zero, while Larmor clock measurements yield small but nonzero durations---a discrepancy recently traced to the two methods measuring fundamentally different quantities. We propose a resolution based on a discrete field-quantum network model whose continuum limit is the nonlinear Klein--Gordon equation. In this framework, a particle is not a point object localized on one side of a barrier: it is an extended structure whose electromagnetic and gravitational stress fields---carrying a significant fraction of its total energy---penetrate the barrier and extend to the far side. When a detector on the far side couples resonantly to this pre-existing stress tail, the particle's global structural integrity fails instantaneously, delivering its full energy to the detection point without any transit through the barrier. The ``tunneling time'' is near-zero not because the particle moves superluminally, but because it was already present on both sides before detection. This picture naturally explains the attoclock's null result (no transit occurs), the Larmor clock's nonzero reading (spin precession accumulates in the extended field within the barrier), and the established exponential decay of tunneling probability with barrier width (the stress-field amplitude decays exponentially in classically forbidden regions). No new parameters or modifications to quantum mechanics are introduced.
Tunnelling lies at the heart of quantum mechanics and is a fundamental process in attosecond science, molecular biology, and quantum devices. Whether tunnelling takes time and how a microscopic particle transits through a barrier have been debated since the early days of quantum mechanics. The time required for an electron to tunnel through an atomic potential barrier has been measured with attosecond angular streaking (attoclock), and a recent work on the hydrogen atom claimed that electron tunnelling is instantaneous. However, the time required for Rb atoms to tunnel through an optical potential barrier has been measured to be on the order of milliseconds with a recent Larmor clock measurement. The essence of electron and atom tunnelling is identical, but the reason for the contradictory conclusions remains unknown. Here, we demonstrate that the sub-barrier potential interaction is the root of the nonzero tunnelling delay time. We reveal that the wave-particle duality of a tunnelling electron must be fully taken into account when decoding the tunnelling delay time from the attoclock measurements. Based on energy-resolved attoclock measurements, we show that the tunnelling delay time of an electron ranges from 24 to 58 attoseconds, and the counterintuitive result that an electron with a lower energy may spend less time in the barrier is consistent with the velocity-dependent tunnelling time of atoms in Larmor clock measurements. Our results unify the tunnelling time of microscopic particles by highlighting the classically forbidden sub-barrier potential interactions of matter waves.
The analytical continuation of classical equations of motion to complex times suggests that a tunneling particle spends in the barrier an imaginary duration i|T| . Does this mean that it takes a finite time to tunnel, or should tunneling be seen as an instantaneous process? It is well known that examination of the adiabatic limit in a small additional AC field points towards |T| being the time it takes to traverse the barrier. However, this is only half the story. We probe the transmitted particle's history, and find that it very little of the field's past behavior, as if the transit time were close to zero. The ensuing contradiction suggests that the question is ill posed, and we explain why. Published by the American Physical Society 2024
Tunnelling is one of the most paradigmatic and evocative phenomena of quantum physics, underlying processes such as photosynthesis and nuclear fusion, as well as devices ranging from SQUID magnetometers to superconducting qubits for quantum computers. The question of how long a particle takes to tunnel, however, has remained controversial since the first attempts to calculate it, which relied on the group delay. It is now well understood that this delay (the arrival time of the transmitted wave packet peak at the far side of the barrier) can be smaller than the barrier thickness divided by the speed of light, without violating causality. There have been a number of experiments confirming this, and even a recent one claiming that tunnelling may take no time at all. There have also been efforts to identify another timescale, which would better describe how long a given particle spends in the barrier region. Here we present a direct measurement of such a time, studying Bose-condensed 87^{87}87Rb atoms tunnelling through a 1.3-μμμm thick optical barrier. By localizing a pseudo-magnetic field inside the barrier, we use the spin precession of the atoms as a clock to measure the time it takes them to cross the classically forbidden region. We find a traversal time of 0.62(7) ms and study its dependence on incident energy. In addition to finally shedding light on the fundamental question of the tunnelling time, this experiment lays the groundwork for addressing deep foundational questions about history in quantum mechanics: for instance, what can we learn about where a particle was at earlier times by observing where it is now?
Abstract We introduce the concept of partial-tunneling and full-tunneling processes to explain the seemingly contradictory non-zero and vanishing tunneling times often reported in the literature. Our analysis starts by considering the traversal time of a quantum particle through a potential barrier, including both above- and below-barrier traversals, using the theory of time-of-arrival operators. We then show that there are three traversal processes corresponding to non-tunneling, full tunneling, and partial tunneling. The distinction among the three depends on the support of the incident wave packet's energy distribution in relation to the shape of the barrier. Non-tunneling happens when the energy distribution of the quantum particle lies above the maximum of the potential barrier. Otherwise, full-tunneling process occurs when the energy distribution of the particle is below the minimum of the potential barrier. For this process, the obtained traversal time is interpreted as the tunneling time. Finally, the partial-tunneling process occurs when the energy distribution lies between the minimum and maximum of the potential barrier. This signifies that the quantum particle tunneled only through some portions of the potential barrier. We argue that the duration for a partial-tunneling process should not be interpreted as the tunneling time but instead as a partial traversal time to differentiate it from the full-tunneling process. We then show that a full-tunneling process is always instantaneous, while a partial-tunneling process takes a non-zero amount of time. We are then led to the hypothesis that experimentally measured non-zero and vanishing tunneling times correspond to partial- and full-tunneling processes, respectively.
We introduce the concept of partial and full tunneling processes to explain the seemingly contradictory non-zero and vanishing tunneling times often reported in the literature. Our analysis starts by considering the traversal time of a quantum particle through a potential barrier, including both above and below-barrier traversals, using the theory of time-of-arrival operators. We then show that there are three traversal processes corresponding to non-tunneling, full-tunneling, and partial tunneling. The distinction between the three depends on the support of the incident wavepackets energy distribution in relation to the shape of the barrier. Non-tunneling happens when the energy distribution of the quantum particle lies above the maximum of the potential barrier. Otherwise, full-tunneling process occurs when the energy distribution of the particle is below the minimum of the potential barrier. For this process, the obtained traversal time is interpreted as the tunneling time. Finally, the partial-tunneling process occurs when the energy distribution lies between the minimum and maximum of the potential barrier. This signifies that the quantum particle tunneled only through some portions of the potential barrier. We argue that the duration for a partial-tunneling process should not be interpreted as the tunneling time but instead as a partial traversal time to differentiate it from the full-tunneling process. We then show that a full-tunneling process is always instantaneous, while a partial-tunneling process takes a non-zero amount of time. We are then led to the hypothesis that experimentally measured non-zero and vanishing tunneling times correspond to partial and full-tunneling processes, respectively.
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.