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Physical Review Research

Aharonov-Bohm effect in the time domain

Sara Meir, Yuval Tamir, Hamootal Duadi, Eliahu Cohen, Moti Fridman

Published Jun 5, 2025• 11 citations
Publisher

Abstract

In the Aharonov-Bohm effect, charged particles accumulate a phase as they travel in space, encircling a source of magnetic flux. We develop a temporal analog of the Aharonov-Bohm effect, where the photons' path is in the time-domain instead of the spatial domain, and moreover demonstrate it experimentally with entangled photon pairs rather than single, uncorrelated quanta. Relying on the temporal SU(1,1) interferometer, the constructed interferometric scheme excels in its temporal resolution and sensitivity. This system can be applied for quantum-enhanced measurements, metrology at GHz frequencies, advanced sensing of dispersion properties, and high-precision temporal measurements.

DOI
10.1103/3phs-9rmc

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In the Aharonov-Bohm effect, charged particles accumulate a phase as they travel in space, encircling a source of magnetic flux. We develop a temporal analog of the Aharonov-Bohm effect, where the photons' path is in the time-domain instead of the spatial domain, and moreover demonstrate it experimentally with entangled photon pairs rather than single, uncorrelated quanta. Relying on the temporal SU(1,1) interferometer, the constructed interferometric scheme excels in its temporal resolution and sensitivity. This system can be applied for quantum-enhanced measurements, metrology at GHz frequencies, advanced sensing of dispersion properties, and high-precision temporal measurements.
Temporal optics revolutionize the field of ultrafast detection with time-lens and time-stretch schemes. We developed a temporal interferometer that enables us to measure ultrafast phase shifts. With this interferometer, we measured phase shifts of correlated beams traveling in different temporal trajectories. This allows us to demonstrate the Aharonov-Bohm effect in the time domain. We developed the theoretical basis of this temporal Aharonov-Bohm effect and showed it in experimental measurements. In the talk, we will explain this effect, describe the experimental setup, and show the results.
In this proceeding, we expand upon our recent work on the temporal Aharonov-Bohm (AB) effect, focusing on the joint temporal function (JSF) analysis to enhance the sensitivity and understanding of the system’s performance. Our original paper demonstrated the existence of a temporal analog of the Aharonov-Bohm effect using entangled photons and a temporal SU(1,1) interferometer. Here, we provide a more detailed exploration of the JSF, highlighting its role in improving signal-to-noise ratios (SNR) and its impact on measuring fast phase changes with enhanced temporal resolution. By leveraging the quantum properties of the system and utilizing the JSF between the signal and idler beams, we show that this approach allows for unprecedented sensitivity in detecting temporal phase shifts. This proceeding will also discuss how the JSF contributes to the interferometer’s ability to resolve femto-second dynamics and its potential applications for simulating space-time phenomena, including rotating black holes and gravitational frame dragging. Our analysis offers deeper insights into the interplay between the quantum characteristics of the system and its utility for high-precision measurements in spatio-temporal dynamics.
Recent works showed that the Aharonov-Bohm (AB) phase difference for a quantum charged particle can be written in terms of electric and magnetic fluxes in a space-time surface whose boundaries are the possible particle worldlines in the interferometer, relative to the possible paths. After presenting this result in a more detailed way, reinforcing its topological nature, we study the magnetic and electric versions of the AB effect in different inertial reference frames. We find a particular reference frame for a magnetic AB effect where the magnetic flux has a null contribution for the AB phase difference, which is entirely due to an electric flux. Also, we find a particular reference frame for an electric AB effect where the electric flux has a null contribution for the AB phase difference, which is entirely due to a magnetic flux. In this sense, the nomenclatures magnetic AB effect and electric AB effect lose their meaning. We have electromagnetic AB effects.
We discuss the consequences of the Aharonov-Bohm (AB) effect in setups involving several charged particles, wherein none of the charged particles encloses a closed loop around the magnetic flux. We show that in such setups, the AB phase is encoded either in the relative phase of a bipartite or multipartite entangled photons states, or alternatively, gives rise to an overall AB phase that can be measured relative to another reference system. These setups involve processes of annihilation or creation of electron-hole pairs. We discuss the relevance of such effects in ``vacuum birefringence" in QED, and comment on their connection to other known effects.
We propose an electrodynamic Aharonov-Bohm (AB) scheme where a nonzero AB phase difference appears even if the interferometer paths do not enclose a magnetic flux and are subjected to negligible scalar potential differences during the propagation of the quantum charged particle. In the proposal, the current in a solenoid outside the interferometer varies in time while the quantum particle is in a superposition state inside two Faraday cages, such that it is always subjected to negligible electromagnetic fields. At first glance, this result could challenge the topological nature of the AB effect. However, by considering the topology of the electromagnetic field configuration and the possible particle trajectories in spacetime, we demonstrate the topological nature of this situation.
The Aharonov-Bohm effect is a physical phenomenon in which the quantum state of a charged particle acquires a phase shift that is directly proportional to the magnetic flux, ΦΦΦ, due to a (classical) magnetic field, B{\mathbf B}B, which is confined in a spatial region from which the magnetic field cannot escape. Even though the charged particle is not allowed to interact with the magnetic field, it accumulates a phase shift that affects the interference pattern produced. Not surprisingly, this apparent nonlocality is puzzling and counter intuitive. In this work, we provide an explanation that explains the physics underlying this apparent nonlocality. We find that the role of the confined magnetic field is to impart a puncture in the configuration space, R2\mathbb{R}^2R2, of the charge. Therefore, the quantum state corresponding to the charged quantum particle acquires the phase shift due to its response to the modified topology of the configuration space, R2−{0}\mathbb{R}^2-\{0\}R2−{0}, corresponding to the charge.