Tunneling time
Post date: Sep 10, 2013 12:25:06 AM
The question of time in quantum mechanics has always been a vexing one. While one often hears about "time-energy uncertainty", one rarely sees a discussion of time-Hamiltonian commutation relations, the operator equivalent to the Heisenberg uncertainty principle. This is because such a time operator does not exist! The simplest definition of such an object was shown to be impossible by Pauli. However, this does not mean time is just a parameter in quantum mechanics. One kind of operator that does have a well defined meaning is a dwell time operator, which is a measure of time differences. This is just the thing you need to speak about how long a particle spends in a certain region of space, for example. A fascinating (and old) question in quantum mechanics is how long a particle spends in a classically forbidden region. Many physicists have thought about and worked on this problem. The only difficulty is that there are too many answers - each different from the one before! In our recent paper on the subject, Yunjin Choi and I link this problem with my group's recent work on how to define a post-selected average in a principled and self-consistent way. The post-selection here is quite natural: only particles that successfully tunnel count for the tunneling time! We show how to indirectly measure the tunneling time, based on measurements on an auxiliary degree of freedom - the precession of the particle's spin in an external magnetic field that exists only in the tunneling region. This physics set-up is not new - it is called the "Larmor clock". However, we view the precession of the spin not as a clock, in and of itself, but as inputs to create the generalized time eigenvalues for the dwell time operator. It turns out that in the simplest case of a square barrier, the time we find is indeed just the precession of the spin in the plane perpendicular to the magnetic field. However, our method gives a general approach for an arbitrary shaped barrier.
An operational approach to indirectly measuring tunneling time
Comments: 16 pages, 3 figures
Subjects: Quantum Physics (quant-ph)
