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arXiv:2211.05813

Decoherence of a 2-Path System by Infrared Photons

Colby DeLisle, Philip C. E. Stamp

Published Nov 10, 2022• 0 citations
arXivHTMLPDF

Abstract

We calculate the decoherence caused by photon emission for a charged particle travelling through an interferometer; the decoherence rate gives a quantitative measure of how much "which-path" quantum information is gained by the electromagnetic field. We isolate the quantum information content of both leading and sub-leading soft photons, and show that it can be extracted entirely from information about the endpoints of the particle's paths. When infrared dressing is used to cure the infrared divergences in the theory, the leading order soft photons then give no contribution to decoherence, and carry no quantum information. The sub-leading soft photons in contrast may carry finite which-path information, and the sub-leading contribution to decoherence takes an extremely simple, time-independent form depending only on the size of the interferometer. An interesting open question is whether or not dressing should also be applied at sub-leading order; we discuss the possibility of answering this question experimentally.

DOI
10.48550/arxiv.2211.05813

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We calculate the decoherence caused by photon emission for a charged particle travelling through an interferometer; the decoherence rate gives a quantitative measure of how much "which-path" quantum information is gained by the electromagnetic field. We isolate the quantum information content of both leading and sub-leading soft photons, and show that it can be extracted entirely from information about the endpoints of the particle's paths. When infrared dressing is used to cure the infrared divergences in the theory, the leading order soft photons then give no contribution to decoherence, and carry no quantum information. The sub-leading soft photons in contrast may carry finite which-path information, and the sub-leading contribution to decoherence takes an extremely simple, time-independent form depending only on the size of the interferometer. An interesting open question is whether or not dressing should also be applied at sub-leading order; we discuss the possibility of answering this question experimentally.
We calculate the decoherence caused by photon emission for a charged particle traveling through an interferometer; the decoherence rate gives a quantitative measure of how much ``which-path'' quantum information is gained by the electromagnetic field. We isolate the quantum information content of both leading and subleading soft photons, and show that it can be extracted entirely from information about the end points of the particle's paths. When infrared dressing is used to cure the infrared divergences in the theory, the leading-order soft photons then give no contribution to decoherence, and carry no quantum information. The subleading soft photons in contrast may carry finite which-path information, and the subleading contribution to decoherence takes an extremely simple, time-independent form depending only on the size of the interferometer. An interesting open question is whether or not dressing should also be applied at subleading order; we discuss the possibility of answering this question experimentally.
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.
Which-path information of a quantum particle in interferometers is the key to infer the past of the quantum particle. It has led to many extensive discussions, including discussions of quantum complementarity and the path-visibility relation. The basics of these discussions are the description, detection, and control of which-path information. In this paper, we focus on the investigation of multidimensional which-path information in a nested Mach-Zehnder interferometer. A general expression of which-path information is given and can be partially extracted by different detection methods. Further analysis shows that the which-path information can be controlled by the phase differences and beam-splitting ratios between the arms of the nested Mach-Zehnder interferometer. Moreover, an alternative which-path information elimination phenomenon has been predicted and demonstrated experimentally. Our work can help us to understand the physics of quantum particles, with potential applications for quantum information processing and quantum metrology.
Abstract Observable scattering processes entail emission-absorption of soft photons. As these degrees of freedom go undetected, some information is lost. Whether some of this information can be recovered in the observation of the hard particles, depends of the actual pattern of the scrambling of information. We compute the information scrambling of electron and soft photon scattering by the tripartite mutual information in terms of the 2-Renyi entropy, and find a finite amount of scrambling is present. We show that scrambling is a byproduct of decoherence achieved by the scattering system in its interaction with the environment, due to the emission-absorption of soft photons in fully unitary processes.
We have scattered photons from an interfering path of a multiple beam Ramsey interference experiment realized with a cesium atomic beam. It is demonstrated that in multiple beam interference the decoherence from photon scattering cannot only lead to a decrease but, under certain conditions, also to an increase of the Michelson fringe contrast. In all cases, the atomic quantum state loses information with photon scattering, as "which-path" information is carried away by the photon field. We outline an approach to quantify this which-path information from observed fringe signals, which allows for an appropriate measure of decoherence in multiple path interference.