Review of F. Lindner et al, Attosecond Double-Slit Experiment, PRL 95, 040401 (2005)

Updated 9-20-22

Summary:

This is a very interesting paper with results that appear to have significant bearing on the measurement problem. The authors utilize intense multiphoton ionization at 760 nm that ionizes argon. The input beam has a Gaussian envelope with only a few cycles. The electrons can be ejected either to a detector that is to the right of the argon or to a detector that is to the left of the argon. The velocity of the electron is proportional to the vector potential $A$ of the field. An electric field that is of the form of a Gaussian envelope $-\sin \omega t$ will have a vector potential that is $A(t)\propto -\cos\omega t$ . As the direction of emission can be found from the sign of the velocity, the direction of emission for this case is to the right if the vector potential is positive and to the left if the vector potential is negative. Hence for a Gaussian envelope that allows primarily only three half cycles of $A(t)\propto-\cos\omega t$ , it can be seen that at time $t_{0}=0$ there is a single negative vector potential that can cause ionization and the electron emitted toward the left detector. On the other hand, at either time $t_{0}=\frac{\pi}{2\omega}$ or $t_{0}=-\frac{\pi}{2\omega}$ there can be emission towards the right detector.

The electron wavefunction is such that if the time of emission were to occur in superposition, that is if the time of emission process were unitary and not a measurement process, the two electron wavefunctions in superposition at both times $t_{0}=\frac{\pi}{2\omega}$ and $t_{0}=-\frac{\pi}{2\omega}$ are predicted to exhibit interference. Lindner et al refer to this as two-slit interference in-time. On the other hand, if ionization was truly a bonafide measurement event that localized the electron to a given half-cycle upon measurement, then no interference would be expected. Hence the experimental results are of importance to the theory of measurement.

Strengths:

It was found in this paper that significant interference was seen in the case when there are two-slits in-time, for the parameters of the setup. This indicates that the time of emission that was investigated in this experiment obeys unitary or Schrödinger evolution in the sense that the electron is not localized in time-of-emission to one of the two half-cycles shown . The experiment does not appear to be particularly easy to conduct as ionization is occurring on the order of attoseconds. The paper is well-written and the ideas are communicated well.

Weaknesses:

The precise understanding of the mechanics of the electron emission and the formation of the superposition is not very clear from reading the paper. This may be because of the page limitation imposed on PRL papers. We found that the exposition given in [1] Figs. 15-19 and the related discussion significantly aided in understanding the more detailed mechanics of the electron superposition.

Implications:

This experiment indicates that ionization is not a sufficient condition for a measurement to localize the electron emission time within the parameters that were utilized in this experiment. One must be careful not to overgeneralize to conclude that all ionization processes are unitary processes for all possible selections of parameters. Also, the process utilized was multiple photon ionization which is non-linear.

This experimental result is rather significant regarding the theory of measurement and we were not aware of it when we wrote our first edition of the QMP. However, we plan on including in future editions this result as well as other significant work that we become aware of.

[1] F. Krausz, M. Ivanov, Attosecond physics, Reviews of Modern Physics, Vol 81, p. 163-234, 2009