Momentum Kicks in Imperfect Which-Way Measurement

TL;DR

This paper investigates the concept of momentum kicks in a double-slit experiment with imperfect which-way detection, revealing that such kicks occur with a fixed magnitude regardless of detection quality, and establishing a relation between kick frequency and interference visibility.

Contribution

It demonstrates that momentum kicks of fixed magnitude occur regardless of detection imperfection and quantifies how detection quality affects kick frequency and interference loss.

Findings

Momentum kicks have a magnitude of h/2d regardless of detection quality.

The frequency of momentum kicks decreases with increasing detection imperfection.

A precise relation links kick frequency to the visibility of interference.

Abstract

There has been an intense debate on the question as to whether a quanton, passing through a double-slit, experiences a 'momentum kick' due to the act of which-way detection. There have been conflicting points of view on this issue over many decades. This issue is addressed here in the general setting where the which-way detection may be imperfect. It is shown here that the loss of interference may still be interpreted as arising out of tiny momentum kicks which the quanton appears to receive, irrespective of the nature of the which-way detector. Interestingly, the magnitude of the random momentum kicks is always h/2d, d being the slit separation, irrespective of how perfect or imperfect the which-way detection is. This is contrary to what has been suggested in the earlier literature. The imperfection of which-way detection decides how frequent are the momentum kicks. It has been shown earlier that for perfect which-way detection, the quanton receives a momentum kick fifty percent of the time. Here it is shown that for imperfect which-way detection, the quanton receives momentum kicks of the same magnitude, but less often. A precise relation between the frequency of kicks and the visibility of interference is found here.