Effect of electron-electron interactions on the propagation of ultrashort voltage pulses in a Mach-Zehnder interferometer

arXiv:2602.23973 · cond-mat.mes-hall, cond-mat.str-el, quant-ph · Submitted 2026-02-27 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Effect of electron-electron interactions on the propagation of ultrashort voltage pulses in a Mach-Zehnder interferometer".

Mira: The gist: The main effect of electron-electron interactions is the renormalization of pulse velocity,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So we're looking at this paper, "Effect of electron-electron interactions on the propagation of ultrashort voltage pulses in a Mach-Zehnder interferometer." Basically, they're exploring how to build electronic flying qubits using these electronic interferometers.

Mira: That means they need ultrafast voltage pulses that are shorter than the time it takes for the pulse to travel through the device, which is a really fast regime we need to understand properly.

Lev: And understanding that physics demands a proper treatment of electron-electron interactions when you have these short excitations.

Kai: This paper takes a step in this direction by doing time-resolved simulations of a Mach-Zehnder interferometer, treating the interactions at the time-dependent mean-field level, which they say is the minimum level to handle displacement currents properly while still being numerically feasible.

Mira: The main conclusion they draw is that the interference effects are robust to the presence of interaction, at least within this specific level of treatment.

Lev: That's a pretty big claim when you're talking about real hardware, because real hardware has all these other complexities we have to worry about.

Kai: To get there, they start by setting up a discrete model of a two-dimensional electron gas described by the effective mass approximation, treating the Coulomb interaction through a contact Hubbard-like interaction at the mean-field level.

Mira: So they define this Hamiltonian as Hˆ = X ij,σ Hij (t)c† iσcjσ + X iσ Vic† iσciσ + X iσ Ui(t)c† i σci σ, where the interaction term U is defined by the self-consistent condition ρ i sigma¯(t) ≡ ⟨c† iσ¯(t)ciσ¯(t)> (sixteen).

Lev: The matrix elements Hij are only non-zero for nearest neighbors, and they also acquire an extra phase phi(t) at the interface between lead zero and the Mach-Zehnder interferometer region.

Kai: They then look at a quasi one dimensional geometry first to isolate the main effect of interactions, which is the renormalization of pulse velocity.

Mira: In DC, their understanding of this Mach-Zehnder interferometer is well understood through the total transmission amplitude dtot to contact one given by equation (three) <ref:2602.23973#pg3>.

Lev: When you send a voltage pulse with duration tauP and amplitude VP in the opposite limit of ultrafast pulses, the total number of transmitted electrons n1/two oscillates with the pulse amplitude VP <ref:2602.23973#pg1>.

Kai: This oscillation is understood as interferences between the front and rear of the pulse as it propagates through the system.

Mira: Now, when they move to a wire geometry, they observe that propagation is faster in presence of interaction U = ten full lines compared to the non-interacting case U = zero dotted lines, which corresponds to the renormalized velocity characteristic of Luttinger liquids <ref:2602.23973#pg3>.

Lev: The effective velocity v is given by a simple linear form v = vF + U/2pi l, and they find that the best fit to the numerical data is l ≈ six point five, although they note that the numerical data isn't perfectly linear.

Paper summary: Kai: They then move on to full Mach-Zehnder interferometer results, showing snapshots of excess density at different times where there's a long transient regime where the pulse has already gone through the lower arms but is still traveling through the upper one.

Mira: The dynamical control of the interference pattern effect is contained in this plateau, which oscillates with n¯ as you increase VP.

Lev: The most important feature they point out in Figure thirteen is an absence of effect: that value of the transient plateau is unaffected by the interaction.

Kai: Preliminary experimental results they mention seem to indicate that the most salient features predicted from the non-interacting theory might actually be present in real devices.

Mira: So, to summarize this paper, "Effect of electron-electron interactions on the propagation of ultrashort voltage pulses in a Mach-Zehnder interferometer," it focuses on showing that the main effect of electron-electron interactions is simply the renormalization of pulse velocity.

Lev: And they emphasize that while the velocity changes, the interference effects themselves remain robust to those interactions at this level of simulation.

Kai: Thinking about what this means for building those electronic flying qubits we talked about earlier, it suggests that even when you have these strong electron-electron interactions present, you might still be able to control the interference patterns in a useful way.

Mira: It's important to remember that this is based on the time-dependent mean-field level, which they say is just the minimum description needed to handle displacement currents correctly while keeping the simulation computationally feasible.

Lev: From an error correction standpoint, if we were trying to run this on real hardware, we'd need to figure out how much overhead comes from these interaction effects you mentioned.

Kai: The paper points toward future work that involves replacing the contact interaction with solving the Poisson equation in real time for more predictive power.

Mira: They also suggest introducing decoherence by calculating a second-order contribution to the self-energy in the strength of electron-electron interaction using tensor network approaches, which seems like a necessary step for real device modeling.

Lev: And another direction is studying abelian anyons within a framework close to what they have here, using a composite fermion approach.

Kai: Overall, the paper suggests that while interactions modify how fast the pulse moves, the interference mechanism itself holds up well enough in this simulation to suggest its potential for qubit control.

Mira: So, if you're only listening to this show and want the simple picture of "Effect of electron-electron interactions on the propagation of ultrashort voltage pulses in a Mach-Zehnder interferometer," it's that the velocity gets renormalized, but the interference effects are still solid.

Lev: And that means we can focus our immediate efforts on understanding how to handle those specific interaction corrections when we actually try to build something real.

Conclusion: Kai: So we've seen how these simulations show that electron-electron interactions change how fast those voltage pulses move through an interferometer, specifically in a Mach-Zehnder setup.

Mira: That’s right, and the authors are looking at this under a time-dependent mean-field level to see how displacement currents behave properly.

Lev: From where I sit with hardware, the main thing is that they're using this level because it’s numerically feasible while still treating those currents in a way that makes sense for us.

Kai: Exactly, and what they find is that even with these interactions present, the interference effects themselves stay pretty solid.

Mira: That’s interesting because it suggests we might actually be able to control these interference patterns even when there are strong electron-electron interactions involved.

Lev: But they only did this at the mean-field level, so if you were building a real device with those same interaction strengths, you'd need to figure out how much extra overhead that adds.

Kai: Right, so it’s not just about the velocity changing; it’s about whether the control mechanism we want—the interference—is still working when things get complicated.

Mira: That points toward a few important things for us, like figuring out how to model those interactions more accurately later on with something like a real time Poisson equation.

Lev: And you're right, and that brings us to the next thing we need to think about for making these simulations actually predictive of what we'll measure in the lab.

Universite Grenoble Alpes · CEA · Grenoble INP · IRIG · PHELIQS

cond-mat.mes-hall, cond-mat.str-el, quant-ph

Submitted: 2026-02-27

Updated: 2026-02-27

Journal ref: Low Temp. Phys. 52, 1036-1047 (2026)

DOI: 10.1063/10.0044811

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 83/100

The gist: The gist: The main effect of electron-electron interactions is the renormalization of pulse velocity, while interference effects appear to be robust to their presence in a Mach-Zehnder interferometer

Key concepts

Electronic Flying Qubits: These are potential quantum bits built using electronic interferometers. They require extremely fast voltage pulses—shorter than the time it takes for an electron to travel through the device—to function effectively as a qubit.
Time-Dependent Mean-Field Level: This is a specific theoretical method used in the simulation to treat electron interactions dynamically. It allows for a more accurate description of how electrons move and interact over time, which is necessary when dealing with very short voltage pulses.
Renormalization of Pulse Velocity: When electron-electron interactions are present, the speed at which a voltage pulse travels through the material changes. The simulation showed that this change in velocity is the primary effect of these interactions on pulse propagation in this study.
Mach-Zehnder Interferometer (MZI): This is a device used to study wave interference, like light, but here applied to electron pulses. The paper uses it to observe how the pulse's path and timing are affected by the interactions within the electronic system.

Summary

The gist: The main effect of electron-electron interactions is the renormalization of pulse velocity, while interference effects appear to be robust to their presence in a Mach-Zehnder interferometer

Introduction and Motivation

Electronic interferometers are considered possible candidates for building electronic flying qubits, which necessitates ultrafast voltage pulses shorter than the time of flight through the device. Understanding this physics requires a proper treatment of electron-electron interactions. The goal of this article is to provide such a description at the time-dependent mean-field level, which is the minimum level that can treat displacement currents properly while remaining numerically feasible. The chief conclusion drawn is that the interference effects are robust to the presence of interaction at the level treated in this work.

Model and Simulation Approach

The simulation starts with a discrete model of a 2DEG described by the effective mass approximation, treating Coulomb interaction through a contact Hubbard-like interaction at the mean-field level. The Hamiltonian is given by Hˆ = X ij,σ Hij (t)c† iσcjσ + X iσ Vic† iσciσ + X iσ Ui(t)c† i σci σ (14). The interaction term Ui sigma is defined as U[ρ i sigma(t) − ρ i sigma(t = 0)] with the self-consistent condition ρ i sigma¯(t) ≡ ⟨c† iσ¯(t)ciσ¯(t)⟩ (16). The matrix elements Hij are non-zero only for nearest neighbors, and they acquire an extra phase ϕ(t) at the interface between lead 0 and the MZI region.

Pulse Propagation in a Quasi-One Dimensional Geometry

The study begins by characterizing a quasi-one dimensional wire geometry to isolate the main effect of interactions, which is the renormalization of velocity. In DC, the behavior of such an MZI is well understood through the total transmission amplitude dtot to contact 1 given by equation (3). When sending a voltage pulse with duration τP and amplitude VP, in the opposite limit of ultrafast pulses, the total number of transmitted electrons n1/2 oscillates with the pulse amplitude VP. This oscillation is understood as interferences between the front and rear of the pulse as it propagates through the system.

Effect of Interactions on Velocity

In a wire geometry, when sending a voltage pulse, one observes that propagation is faster in presence of interaction (U = 10, full lines) compared to the non-interacting case (U = 0, dotted lines), which corresponds to the renormalized velocity characteristic of Luttinger liquids. The effective velocity v is given by a simple linear form v = vF + U/2πl. The best fit to the numerical data is given by l ≈ 6.5 and it is noted that the numerical data is not perfectly linear.

Full Mach-Zehnder Interferometer Results

In the full MZI simulation, snapshots of excess density at different times show a long transient regime where the pulse has already gone through the lower arms but is still traveling through the upper one. The dynamical control of interference pattern effect is contained in this plateau, which oscillates with n¯ as one increases VP. The most important feature of Fig. 13 is an absence of effect: the value of the transient plateau is unaffected by the interaction. Preliminary experimental results seem to indicate that the most salient features predicted from the non-interacting theory might actually be present in real devices.

Future Directions

Much work remains to be done to arrive at a level where simulations can have genuine predictive power, such as replacing the contact interaction with the solution of the Poisson equation in real time. Another aspect is to introduce decoherence by calculating a second-order contribution to the self-energy in the strength of electron-electron interaction using tensor network approaches. A third extension would be the study of abelian anyons within a framework close to the present one using a composite fermion approach. A systematic comparison between simulations and experiments based on large data sets should be performed to validate the overall approach.

Acknowledgments

The authors acknowledge funding from the European Union’s Horizon 2020 research and innovation program under Grant agreement No. 862683 (UltraFastNano), from the French ANR DADDI and T-KONDO and from State aid managed by the Agence Nationale de la Recherche under the France 2030 program, reference ANR-22-PETQ-0012 (EQUBITFLY). The authors also greatly appreciate the hospitality of C. Bauerle in his group.

References

[1] P. Roulleau, F. Portier, P. Roche, A. Cavanna, G. Faini, U. Gennser, and D. Mailly, Direct measurement of the coherence length of edge states in the integer quantum hall regime.

[2] G. Roussely, E. Arrighi, G. Georgiou, S. Takada, M. Schalk, M. Urdampilleta, A. Ludwig, A. D. Wieck, P. Armagnat, T. Kloss, X Waintal and T Meunier Unveiling the bosonic nature of an ultrashort few-electron pulse.

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[12] M Saha L Horray P Portugal and C Flindt Negative currents in fabry-p´erot cavities are caused by interfering paths.

[13] T Kloss X Waintal Propagation of ultrashort voltage pulses through a small quantum dot.

[14] M Buttiker Capacitance admittance and rectification properties of small conductors.

[15] M B¨uttiker Time-dependent current partition in mesoscopic conductors.

[16] Y Ji Y Chung D Sprinzak M Heiblum D Mahalu and H Shtrikman An electronic mach–zehnder interferometer.

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Improvements for AI systems

Bold pulse propagation simulation for electronic flying qubits: The improved system can accurately simulate the propagation of a voltage pulse inside a Mach-Zehnder interferometer (MZI), and the associated predicted effects, specifically resolving how electron-electron interactions affect this propagation, which is crucial for building an electronic flying qubit.
Renormalized velocity modeling: The AI system can predict the effective velocity of charge transport in quasi-one-dimensional geometries under interaction, as shown by the relation derived from the Liouville equation: v = vF + U / 2πl, where 'l' is related to magnetic length and 'U' is the interaction strength.
Dynamical interference prediction: The system can predict the time evolution of transmitted current at contact 1, specifically modeling how the value of this plateau oscillates with n as a function of injected charge, which corresponds to the dynamical control of interference pattern effect.
QPC non-linear response mapping: The AI can map the pulse injection characteristics through quantum point contacts, predicting how interaction strength affects current peaks: when one switches on the interaction, we observe the appearance of a small new maxima in the reflected current around t = 350.

Abstract

Electronic interferometers have been identified as possible candidates for building electronic flying qubits. Such a regime requires ultrafast voltage pulses whose duration is shorter than the time of flight through the device. Understanding the corresponding physics in the presence of such short excitations requires a proper treatment of electron-electron interactions. In this article, we take a step in this direction by performing time-resolved simulations of a Mach-Zehnder interferometer treating the interactions at the time-dependent mean-field level. We find that the main effect of the interaction is the renormalization of the pulse velocity. Very importantly, the interference effects appear to be robust to the presence of interactions.

Sources

Computational quantum transport: a scattering approach perspective