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Science

Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer

Sacha Kocsis, Boris Braverman, Sylvain Ravets, Martin J. Stevens, Richard P. Mirin, Lynden K. Shalm, Aephraim M. Steinberg

Published Jun 3, 2011• 649 citations
Publisher

Abstract

A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or "trajectory" that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.

DOI
10.1126/science.1202218

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A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or "trajectory" that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.
The interference pattern produced by a quantum particle in Young's double-slit setup is attributed to the particle's wave function having gone through both slits. In the path integral formulation, this interference involves a superposition of paths, going through either slit, linking the source to the detection point. We show how these paths superpositions can in principle be observed by implementing a series of minimally perturbing weak measurements between the slits and the detection plane. We further propose a simplified protocol in order to observe these ``weak trajectories'' with single photons.
The notion of the trajectory of an individual particle is strictly inhibited in quantum mechanics because of the uncertainty principle. Nonetheless, the weak value, which has been proposed as a novel and measurable quantity definable to any quantum observable, can offer a possible description of trajectory on account of its statistical nature. In this paper, we explore the physical significance provided by this “weak trajectory” by considering various situations where interference takes place simultaneously with the observation of particles, that is, in prototypical quantum situations for which no classical treatment is available. These include the double slit experiment and Lloyd's mirror, where in the former case it is argued that the real part of the weak trajectory describes an average over the possible classical trajectories involved in the process, and that the imaginary part is related to the variation of interference. It is shown that this average interpretation of the weak trajectory holds universally under the complex probability defined from the given transition process. These features remain essentially unaltered in the case of Lloyd's mirror where interference occurs with a single slit.
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.