Testing Electromagnetic Memory via Acceleration-Induced Phase Imprints in Superconductors

This paper proposes a tabletop experimental protocol using gravitational acceleration-induced electric fields in normal conductors to imprint a detectable gauge-invariant phase on superconducting coherent states, offering a potential route to verify the long-elusive phenomenon of electromagnetic memory.

The Gist

The Big Idea: The Universe's "Ghost" Memory

Imagine you shout a loud noise in a canyon. The sound waves travel out, hit the walls, and eventually fade away until it's silent again. However, the canyon itself has "remembered" that shout. If you were to measure the air pressure perfectly, you might find a tiny, permanent shift caused by that noise, even though the sound is gone.

In physics, this is called Electromagnetic Memory. It's a theory suggesting that when electromagnetic forces (like light or radio waves) pass through space, they leave a permanent "scar" or record on the universe, even after the forces themselves have vanished.

The problem? This effect is incredibly tiny. It's like trying to hear a whisper in a hurricane. Scientists have predicted it for decades, but no one has ever been able to catch it in a lab.

The New Proposal: Using Gravity as a Switch

This paper proposes a clever, tabletop experiment to catch this "ghost memory" using three main ingredients: Superconductors (magic wires with zero resistance), Normal Metal (regular wire), and Gravity.

Here is the step-by-step story of their idea:

1. The "Heavy" and the "Light" (Creating the Field)

Imagine a metal rod standing upright on Earth. Gravity pulls everything down.

• The heavy atoms in the metal (the nuclei) feel the pull strongly and want to sink.
• The light electrons (the "gas" of electricity) also feel gravity, but they are also pushed up by a "crowd pressure" (Fermi pressure) because they don't like being squished together.

Because the heavy atoms and the light electrons react differently to gravity, they get slightly out of sync. The heavy atoms sink a tiny bit more than the electrons. This separation creates a tiny, invisible electric field inside the metal, just because it's sitting in gravity.

2. The "Elevator" Trick (Turning the Field On and Off)

The scientists propose putting this metal rod inside an elevator.

• Phase 1 (The Reset): The elevator is in free fall (like a skydiver before the parachute opens). In free fall, you feel weightless. The gravity-induced electric field disappears because everything is falling together. The scientists use this moment to "reset" their memory, making sure the two ends of the metal rod have the exact same electrical "phase" (like syncing two clocks).
• Phase 2 (The Imprint): The elevator stops falling and sits still on the ground. Suddenly, gravity kicks in. The heavy atoms sink, the electrons lag, and that tiny electric field appears inside the rod. It stays there for a short time (say, 1 millisecond).
• Phase 3 (The Vanish): The elevator goes into free fall again. The electric field vanishes instantly.

3. The "Superconducting" Memory Bank

The rod is connected to two superconductors (special wires that can carry electricity forever without losing energy).

• While the electric field was "on" (during Phase 2), it left a permanent mark on the quantum "phase" of the electrons in the superconductors. Think of this like a dancer who was spun around; even after the music stops, the dancer keeps a slight spin in their body.
• When the field turns off (Phase 3), the "spin" (the phase difference) remains stored in the superconductors. This is the Electromagnetic Memory.

4. Reading the Result

Finally, the scientists reconnect the two superconductors to form a loop. Because one side was "spun" by the gravity-field and the other wasn't, they don't match up perfectly. This mismatch forces a tiny electric current to flow, which creates a measurable magnetic signal.

Why This is Special

Usually, to create an electric field, you need a battery or a power plug. But power plugs are messy; they create noise and interference that would hide the tiny memory signal.

This paper suggests using gravity as the switch. It's a "clean" switch because gravity is always there, and you can turn the effect on and off just by dropping the elevator and catching it. It avoids the messy noise of traditional electronics.

The Bottom Line

The authors calculate that with current technology (using sensitive magnetic detectors called SQUIDs), this experiment is actually possible. If they see the predicted magnetic signal, it would be the first time humans have directly observed this "memory" of electromagnetic fields, proving that the universe keeps a record of forces long after they are gone.

In short: They want to use a falling elevator to turn gravity into a switch, imprint a tiny "memory" onto a superconductor, and then read that memory to prove a fundamental law of physics.

Technical Summary

Technical Summary: Testing Electromagnetic Memory via Acceleration-Induced Phase Imprints in Superconductors

Problem Statement
Electromagnetic (EM) memory is a fundamental prediction of gauge theory, positing that an electromagnetic process leaves a persistent, gauge-invariant record after the radiative field has passed. While the classical manifestation involves a permanent momentum kick to charged particles, the quantum aspect suggests that transient EM configurations can imprint a persistent phase difference on charged coherent states. Despite its theoretical importance regarding soft photons and large $U(1)$ gauge transformations, EM memory remains experimentally unverified. Previous proposals utilizing superconductors to detect this phase have faced significant challenges: generating the required transient electric fields without introducing background potentials or switching disturbances that are indistinguishable from the memory signal itself.

Methodology
The authors propose a tabletop experimental protocol that utilizes gravitational acceleration to generate a "clean" transient electric field, thereby imprinting a quantum memory phase onto superconducting states. The core mechanism relies on the following physical principles and experimental design:

1. Gravity-Induced Electric Field: Inside a normal conductor, gravitational acceleration ($g$) causes a differential compression between the ionic lattice and the electron gas. Because the lattice (mass $M$) and electrons (mass $m_e$) respond differently to gravity and Fermi pressure, a stable internal electric field $E$ is induced. This field is given by $E \approx \frac{g}{e}(\gamma M - m_e)$, where $\gamma$ is a material-dependent parameter. Crucially, this field arises from intrinsic atomic polarization rather than external voltage pulses.
2. Superconducting Protocol: The experimental setup consists of two superconducting nodes (SC-1 and SC-2) separated by a normal conductor (NC) of length $\delta$, with thin insulating barriers to prevent unintended Josephson coupling (forming an S-I-N-I-S structure).
   • Initialization: The nodes are connected via a superconducting loop to align their phases ($\Delta \phi = 0$) while the apparatus is in free fall ($a_{eff} = 0$), ensuring no acceleration-induced field exists.
   • Imprinting: The circuit is disconnected, and the apparatus is brought to rest ($a_{eff} \approx g$). The induced electric field persists for a duration $\tau$, distorting the vector potential $A$. The gauge-invariant phase difference accumulates as $\Delta \phi_{sig} = e^* \int A \cdot dl \approx 2e |E| \delta \tau$.
   • Readout: The apparatus is returned to free fall, switching off the electric field. The phase difference remains "stored" as an EM memory. The nodes are then reconnected, inducing a supercurrent and a measurable magnetic flux $\Delta \Phi$ in the loop to satisfy flux quantization, which compensates for the stored phase.

Key Contributions

• Clean Source Generation: The paper identifies gravitational acceleration as a unique mechanism to switch a transient electric field on and off without external voltage pulses. This avoids the background noise and switching transients that have plagued previous attempts to isolate the EM memory effect.
• Quantum Phase Observable: The authors formalize the detection of EM memory not as a momentum kick, but as a gauge-invariant phase difference between superconducting condensates, leveraging the Aharonov-Bohm effect.
• Feasibility Analysis: The study provides a detailed sensitivity analysis, demonstrating that for representative parameters (e.g., $\delta \sim 100$ nm, $\tau \sim 1$ ms), the predicted phase shift is $\Delta \phi_{sig} \sim 0.1$. This signal is estimated to be distinguishable from quantum number-phase uncertainty limits ($\Delta \phi \sim 10^{-3}$) and thermal Johnson-Nyquist noise at cryogenic temperatures ($T \sim 1$ mK).

Results and Predictions
The theoretical calculations predict a measurable phase shift of approximately $0.3 \times (\tau/1\text{ ms}) (\delta/100\text{ nm}) (|E|/10^{-6}\text{ V/m})$.

• Signal Characteristics: The proposed signal is expected to scale linearly with the holding time $\tau$ and the length of the normal conductor $\delta$. It should reverse sign if the device orientation relative to gravity is inverted and vanish entirely if the apparatus remains in free fall.
• Noise Suppression: The authors argue that by using the free-fall/elevator protocol, the system avoids the "switching disturbances" inherent in voltage-based methods. The signal is predicted to exceed the sensitivity of state-of-the-art SQUID magnetometers (noise $< 1 \mu\Phi_0/\sqrt{\text{Hz}}$) in the kHz frequency range.

Significance
The paper claims that this proposal offers a viable "tabletop route" to experimentally verify electromagnetic memory as an infrared observable of QED. By converting a tiny, transient electromagnetic effect into a cumulative, measurable phase difference, the protocol addresses the historical difficulty of distinguishing memory effects from background perturbations. Furthermore, the work highlights a novel intersection between classical gravity (inducing electric fields in conductors) and quantum mechanics (superconducting phase coherence), potentially providing a new framework to test the compatibility of gravity with quantum fermion statistics in a regime that has not yet been directly verified. The authors emphasize that while the existence of the memory phase relies on the persistence of coherence, the proposed millisecond timescale is well within the range of verified coherence for fluxonium qubits and Josephson oscillations.