Weak Measurement of Polarization by a Slit

James M. Knight, Lev Vaidman A

L. P. Withers, Frank A. Narducci

The recent single-photon double-slit experiment of Steinberg et al., based on a weak measurement method proposed by Wiseman, showed that, by encoding the photon’s transverse momentum behind the slits into its polarization state, the momentum profile can subsequently be measured on average, from a difference of the separated fringe intensities for the two circular polarization components. They then integrated the measured average velocity field, to obtain the average trajectories of the photons enroute to the detector array. In this paper, we propose a modification of their experiment, to demonstrate that the average particle velocities and trajectories change when the mode of detection changes. The proposed experiment replaces a single detector by a pair of detectors with a given spacing between them. The pair of detectors is configured so that it is impossible to distinguish which detector received the particle. The pair of detectors is then analogous to the simple pair of slits, in that it is impossible to distinguish which slit the particle passed through. To establish the paradoxical outcome of the modified experiment, the theory and explicit three-dimensional formulas are developed for the bilocal probability and current densities, and for the average velocity field and trajectories as the particle wavefunction propagates in the volume of space behind the Gaussian slits. Examples of these predicted results are plotted. Implementation details of the proposed experiment are discussed.

WJ Mullin

A weak measurement does not completely collapse the wave function into one of the components of a superposition. A subsequent projective measurement on the weakly measured wave function can result in an amplification of the result for the original weak measurement. This chapter illustrates the procedure by a measurement of the average trajectories taken by particles in the two-slit experiment, in which the local momentum of a photon is encoded into its polarization, by means of a birefringent calcite crystal. The particle trajectories show the interference pattern. A second experimental example finds the real part and the imaginary part of a particle’s complex wave function. The amplitude and phase of the wave function are expressed in terms of its real and imaginary parts.

M. Iinuma

Tom Rivlin

The quantum eraser variant of the double-slit experiment, and its 'delayed choice' sub-variant, are considered from the perspective of weak value and weak measurement theory (which is briefly reintroduced here). The interference fringes that appear when measuring certain spin states, which can then be 'erased' when measuring other spin states, are shown to be anomalous weak values that depend on particular post-selection choices. By framing the choice of spin measurement as a weak value of a certain weak measurement, it is then made clear what physical claims can and cannot be made about what occurs in the quantum eraser experiment. Specifically, claims about the choice of spin-state `retrocausally' influencing the choice of slit(s) for the particles to travel through are discredited, and a simple framework is presented for understanding how the fringes arise and why they can be 'erased'.

D. Clarke, J. F. Grainger