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Physical Review A

Experimental retrodiction of trajectories of single photons in double interferometers

Yuan Yuan, Zhibo Hou, Kang‐Da Wu, Guo‐Yong Xiang, Chuan‐Feng Li, Guang‐Can Guo

Published Jun 15, 2018• 3 citations
Publisher

Abstract

When a photon passes through an interferometer, quantum mechanics does not provide a clear answer as to its past. Quantum retrodiction is a quantitative theory, which endeavors to make statements about the past of a system based on present knowledge. Quantum retrodiction may be used to analyze the past of a photon, that is, its trajectory. Here we experimentally retrodict the trajectories of single photons in double interferometers by measuring the final state of the photon. A sequence of measurements is made on a photon to determine which path the photon followed, so a series of retrodiction of measurement results can be regarded as a photon trajectory. We obtain information about the partial trajectory and the entire trajectory of the photon. Furthermore, we also observe the effect of different measurements in the extraction of trajectory information. Our experiment highlights the application of retrodiction theory to the study of the photon's past, and provides potential application in quantum communications.

DOI
10.1103/physreva.97.062115

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When a photon passes through an interferometer, quantum mechanics does not provide a clear answer as to its past. Quantum retrodiction is a quantitative theory, which endeavors to make statements about the past of a system based on present knowledge. Quantum retrodiction may be used to analyze the past of a photon, that is, its trajectory. Here we experimentally retrodict the trajectories of single photons in double interferometers by measuring the final state of the photon. A sequence of measurements is made on a photon to determine which path the photon followed, so a series of retrodiction of measurement results can be regarded as a photon trajectory. We obtain information about the partial trajectory and the entire trajectory of the photon. Furthermore, we also observe the effect of different measurements in the extraction of trajectory information. Our experiment highlights the application of retrodiction theory to the study of the photon's past, and provides potential application in quantum communications.
We present surprising experimental evidence regarding the past of photons passing through an interferometer. The information about the positions through which the photons pass in the interferometer is retrieved from modulations of the detected signal at the vibration frequencies of mirrors the photons bounce off. From the analysis we conclude that the past of the photons is not represented by continuous trajectories, although a "common sense" analysis adopted in various welcher weg measurements, delayed-choice which-path experiments, and counterfactual communication demonstrations yields a single trajectory. The experimental results have a simple explanation in the framework of the two-state vector formalism of quantum theory.
We study how well we can retrodict results of measurements made on a quantum system if we can make measurements on its final state. We know what measurements were made, but not their results. An initial examination shows that we can gain anywhere from no information to perfect information about the results of previous measurements, depending on the measurements and the initial state of the system. The case of two two-outcome measurements, the second of which is a projective measurement, is examined in some detail. We then look at a model of a qubit interferometer in which measurements are made in order to determine the path the qubit followed. The measurement made on the final state of the qubit depends on the information about previous measurement results that we are trying to determine. One can attempt to find the result of just one of the measurements or all of them or to find a measurement sequence that was not realized. We study all three possibilities.
Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a "common sense" approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.
Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a ``common sense'' approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.
Prediction, of course, is the making of statements about the likelihood of future events. retrodiction (or postdiction) is the making of statement about past events. In these lectures we shall study the rules governing retrodictive probabilities both in the quantum and classical domains. In doing so we develop a powerful tool with which to interpret physical phenomena and both analyse and interpret experiments. We use retrodictive methods to analyze a number of phenomena in quantum optics including the familiar photon antibunching, entanglement and ghost imaging and the perhaps less familiar ideas of quantum scissors, quantum computation in the past a single-particle analysis of two-particle interference. Quantum retrodiction is a quantitative theory and the familiar techniques for evolving quantum states and modelling open systems are applicable to retrodictive problems, but only with the introduction of some novel features. We conclude with a few remarks on more philosophical issues related to the arrow of time and wavefunction "collapse" in the measurement process. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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.