# Quantum tunneling time

@article{Davies2005QuantumTT, title={Quantum tunneling time}, author={Paul C. W. Davies}, journal={American Journal of Physics}, year={2005}, volume={73}, pages={23-27} }

A simple model of a quantum clock is applied to the old and controversial problem of how long a particle takes to tunnel through a quantum barrier. The model has the advantage of yielding sensible results for energy eigenstates and does not require the use of time-dependent wave packets. Although the treatment does not forbid superluminal tunneling velocities, there is no implication of faster-than-light signaling because only the transit duration is measurable, not the absolute time of transit… Expand

#### 52 Citations

Anatomy of Quantum Tunneling

- Physics
- 2014

We use complex classical solutions to provide a simple and transparent treatment of quantum tunneling. We show that the imaginary part of the tunneling coordinate may be weakly measured, and that it… Expand

Quantum Tunneling Time: Relativistic Extensions

- Physics
- 2013

Several years ago, in quantum mechanics, Davies proposed a method to calculate particle’s traveling time with the phase difference of wave function. The method is convenient for calculating the… Expand

Aharonov-Bohm effect in the tunnelling of a quantum rotor in a linear Paul trap.

- Physics, Medicine
- Nature communications
- 2014

It is demonstrated that the charged particles in this quantum Tunnelling system are coupled to the vector potential of a magnetic field throughout the entire process, even during quantum tunnelling, as indicated by the manifestation of the Aharonov-Bohm effect in this system. Expand

Existence and nonexistence of an intrinsic tunneling time

- Physics
- 2009

Using a time operator, we define a tunneling time for a particle going through a barrier. This tunneling time is the average of the phase time introduced by other authors. In addition to the delay… Expand

Statistical Approach to Tunneling Time in Attosecond Experiments

- Physics
- 2015

Tunneling, transport of particles through classically forbidden regions, is a pure quantum phenomenon. It governs numerous phenomena ranging from single-molecule electronics to donor-acceptor… Expand

Simulations in quantum tunneling

- Physics
- 2017

We study the timing effects of nonrelativistic wave packet tunneling through a barrier using a numerical simulation readily accessible to an undergraduate audience. We demonstrate that the peak of… Expand

Smooth double barriers in quantum mechanics

- Physics
- 2010

Quantum mechanical tunneling across smooth double barrier potentials is modeled using Gaussian functions and is analyzed numerically and by using the WKB approximation. The transmission probability,… Expand

Scattering a quantum particle on the potential step: Characteristic times for transmission and reflection

- Physics
- 2013

We present a new model of scattering a quantum particle on the potential step, which reconstructs the prehistory of the subensembles of transmitted and reflected particles by their final states.… Expand

Barrier interaction time and the Salecker-Wigner quantum clock: Wave-packet approach

- Physics
- 2009

The time-of-flight measurement approach of Peres based on the Salecker-Wigner quantum clock is applied to the one-dimensional scattering of a wave packet from a rectangular barrier. By directly… Expand

Transmission time of a particle in the reflectionless Sech-squared potential: Quantum clock approach

- Physics
- 2011

Abstract We investigate the time for a particle to pass through the reflectionless Sech-squared potential. Using the Salecker–Wigner and Peres quantum clock an average transmission time of a Gaussian… Expand

#### References

SHOWING 1-10 OF 17 REFERENCES

Measurement of the single-photon tunneling time.

- Physics, Medicine
- Physical review letters
- 1993

Using a two-photon interferometer, the time delay for a photon to tunnel across a barrier consisting of a 1.1-μm-thick 1D photonic band-gap material is measured, consistent with the group delay («phase time»), but not with the semiclassical time. Expand

Properties of a quantum system during the time interval between two measurements.

- Physics, Medicine
- Physical review. A, Atomic, molecular, and optical physics
- 1990

A description of quantum systems at the time interval between two successive measurements is presented, and how this approach leads to a new concept: a weak value of an observable. Expand

How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100.

- Physics, Medicine
- Physical review letters
- 1988

We have found that the usual measuring procedure for preselected and postselected ensembles of quantum systems gives unusual results. Under some natural conditions of weakness of the measurement, its… Expand

Measurement of time by quantum clocks

- Physics
- 1980

A clock is a dynamical system which passes through a succession of states at constant time intervals. If coupled to another system, it can measure the duration of a physical process and even keep a… Expand

Barrier interaction time in tunneling

- Physics
- 1994

Over sixty years ago, it was suggested that there is a time associated with the passage of a particle under a tunneling barrier. The existence of such a time is now well accepted; in fact the time… Expand

How much time does a tunneling particle spend in the barrier region?

- Physics, Medicine
- Physical review letters
- 1995

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,… Expand

Time as an observable

- Physics
- 1999

The role of time in quantum mechanics is discussed. The differences between ordinary observables and an observable which corresponds to the time of an event is examined. In particular, the… Expand

Quantum mechanics and the equivalence principle

- Physics
- 2004

A quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum… Expand

Quantum Limitations of the Measurement of Space-Time Distances

- Physics
- 1958

This article deals with the limitations which the quantized nature of microscopic systems imposes on the possibility of measuring distances between space-time events. It is proposed to use only… Expand

Larmor precession and the traversal time for tunneling

- Physics
- 1983

Baz' and Rybachenko have proposed the use of the Larmor precession as a clock to measure the time it takes a particle to traverse a barrier. An applied magnetic field is confined to the barrier. The… Expand