arxiv: 2604.26947 · v1 · submitted 2026-04-29 · ❄️ cond-mat.mes-hall · quant-ph

Large quantum dot energy level shifts in anomalous photon-assisted tunneling

Jared Benson , C. E. Sturner , A. R. Huffman , Sanghyeok Park , Valentin John , Brighton X. Coe , Tyler J. Kovach , Stefan D. Oosterhout

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Lucas E. A. Stehouwer Francesco Borsoi Giordano Scappucci Menno Veldhorst Benjamin D. Woods Mark Friesen M. A. Eriksson

This is my paper

Pith reviewed 2026-05-07 10:19 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph

keywords germanium quantum dotssinglet-triplet splittingphoton-assisted tunnelinggate voltage dependencehole spin qubitsdouble quantum dotorbital energy levels

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The pith

Singlet-triplet splittings in germanium double quantum dots shift linearly with top gate voltage

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines orbital energy splittings in a Ge/SiGe double quantum dot, parameters important for hole spin qubit operation. Standard views hold that these splittings change negligibly when adjusting top plunger gates, yet photon-assisted tunneling measurements display large anomalous shifts. Data from both photon-assisted tunneling and pulsed-gate spectroscopy are combined into a model that accounts for the observed linear gate-voltage dependence of the splittings. The same linear trend appears for both dots after retuning changes their splitting ratio. A reader would care because this dependence directly affects how gate voltages are used to control qubits.

Core claim

In a Ge/SiGe heterostructure double quantum dot, the singlet-triplet splittings display a strong linear dependence on top gate voltages, which produces anomalous photon-assisted tunneling signals. A phenomenological model fitted to combined photon-assisted tunneling and pulsed-gate spectroscopy data describes this linear dependence, and the two dots exhibit similar linear dependences even when their splitting ratio is significantly altered by retuning.

What carries the argument

The phenomenological model combining photon-assisted tunneling and pulsed-gate spectroscopy data to capture the linear gate-voltage dependence of singlet-triplet splittings.

If this is right

Qubit control sequences that change plunger gates must compensate for the varying singlet-triplet splittings to prevent errors.
Theoretical models of quantum dot potentials must treat lateral confinement as strongly voltage-dependent rather than fixed.
Retuning the device to alter the ratio of the two dots' splittings preserves the linear dependence in each dot.
Anomalous photon-assisted tunneling can be used to map and correct for gate-induced orbital shifts during operation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Qubit calibration routines may require real-time adjustment of gate pulses to track the shifting energy levels.
Arrays of coupled dots could face added complexity in maintaining uniform control if each dot shows its own voltage-dependent shifts.
The effect might be tested by comparing devices with different heterostructure designs to see whether the linear slope is tied to germanium-specific confinement.

Load-bearing premise

The linear dependence arises purely from changes in lateral confinement, and the phenomenological model includes all dominant effects without missing higher-order terms or device artifacts.

What would settle it

An independent calculation of the confinement potential or a measurement in a retuned device showing that the observed slope of singlet-triplet splitting versus gate voltage cannot be produced by lateral confinement changes alone.

Figures

Figures reproduced from arXiv: 2604.26947 by A. R. Huffman, Benjamin D. Woods, Brighton X. Coe, C. E. Sturner, Francesco Borsoi, Giordano Scappucci, Jared Benson, Lucas E. A. Stehouwer, M. A. Eriksson, Mark Friesen, Menno Veldhorst, Sanghyeok Park, Stefan D. Oosterhout, Tyler J. Kovach, Valentin John.

**Figure 1.** Figure 1: Device layout and anomalous photon-assisted tunneling view at source ↗

**Figure 2.** Figure 2: Measuring the dependence of ST splittings on gate voltages with pulsed-gate spectroscopy. (a) A charge stability diagram with view at source ↗

**Figure 3.** Figure 3: Modeling the energy dispersion using PAT and pulsed-gate spectroscopy data. (a) A charge stability diagram with insets showing view at source ↗

**Figure 4.** Figure 4: Energy dispersion modeling under different device tun view at source ↗

read the original abstract

Orbital energy splittings are important quantum dot parameters for the operation of hole spin qubits. They are known to depend on the lateral confinement of the quantum dots. However, when changing top, plunger gate voltages, which are the typical control parameter for qubit applications, such energy splitting changes are typically negligible, both as measured in experiment and as assumed in effective theories. Here, we study the singlet-triplet (ST) splittings, which depend on the orbital splittings, of a double quantum dot (DQD) in a Ge/SiGe heterostructure using photon-assisted tunneling (PAT) and pulsed-gate spectroscopy. We find that the ST splittings have a surprising, strong dependence on the top gate voltages, leading to anomalous PAT measurements. We combine data from both measurements in a model that well describes the linear gate-voltage dependence of the ST splittings. Finally, we show that the ST splittings of the two dots exhibit similar linear gate-voltage dependences when the device is retuned such that their ratio is significantly different.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper finds a strong linear top-gate dependence of singlet-triplet splittings in Ge/SiGe dots that produces anomalous PAT, with consistent data from two techniques, but the model is purely phenomenological and does not rule out strain or vertical-field contributions.

read the letter

The key point is that these Ge/SiGe double dots show a much stronger dependence of singlet-triplet splittings on top-gate voltage than the literature usually assumes, and this dependence makes the photon-assisted tunneling look anomalous. The authors map the effect with both PAT and pulsed-gate spectroscopy, combine the datasets into a single linear fit, and then show that both dots follow similar linear trends even after retuning changes their splitting ratio. That consistency across methods and device configurations is the clearest new result here. It directly challenges the common assumption that plunger-gate tuning leaves orbital splittings essentially fixed. For people running hole qubits in germanium, this is practical information because orbital energies set the scale for several control and coherence issues. The measurements appear careful enough to be worth reporting. The main limitation is that the linear model is fitted to the data rather than derived or simulated from first principles. The paper attributes the slope to changes in lateral confinement, but top-gate voltage in a Ge/SiGe heterostructure also moves the vertical electric field, alters hole penetration into the barrier, and can modulate local strain. Any of those could produce a comparable shift in effective orbital spacing. Without an electrostatic or strain calculation that matches the measured coefficient, the attribution stays plausible but not unique. The abstract states that the model describes the data well, yet the details of error bars, exclusion of other contributions, and fit quality are not visible in the summary. This work is aimed at experimental groups building or characterizing hole spin qubits in planar germanium. A reader who tunes similar devices would want to check whether their own dots show the same gate dependence. It is solid enough to deserve peer review; the dual-technique data adds weight even if the modeling section would benefit from more discussion of alternative mechanisms.

Referee Report

2 major / 2 minor

Summary. The manuscript reports the observation of a strong, linear dependence of singlet-triplet (ST) splittings on top-gate voltage in a Ge/SiGe double quantum dot, measured via photon-assisted tunneling (PAT) and pulsed-gate spectroscopy. The authors combine the two datasets into a single phenomenological linear model that accounts for the observed gate-voltage dependence and demonstrate that the two dots exhibit similar linear trends when the device is retuned to a different inter-dot ratio.

Significance. If the central observation holds, the result is moderately significant for hole-spin qubit research: it shows that orbital splittings can exhibit large, gate-tunable shifts under typical plunger-gate operation, contrary to the usual assumption of negligible dependence. The use of two independent spectroscopic techniques provides useful cross-checks. However, the purely phenomenological character of the model and the absence of supporting electrostatic or strain calculations limit the depth of the physical insight and the generality of the conclusions.

major comments (2)

[Model and Discussion] The attribution of the observed linear ST-splitting shift exclusively to changes in lateral confinement is not supported by any independent electrostatic modeling or strain calculation. In a Ge/SiGe heterostructure, top-gate voltage can also modulate the vertical electric field, hole wave-function penetration into the barrier, or local strain; none of these alternative channels are quantified or ruled out, so the interpretation that the slope arises purely from orbital-level spacing changes remains unverified.
[Results] The linear model is constructed by fitting the combined PAT and pulsed-gate data; the manuscript does not report the explicit functional form, the weighting between the two datasets, the extracted slope with uncertainty, or any goodness-of-fit metric. Without these details it is impossible to assess whether the model is over-constrained or whether the linearity is robust against reasonable variations in analysis choices.

minor comments (2)

Figure captions and axis labels should explicitly state the gate-voltage ranges and the extracted ST-splitting values with error bars so that the linear trend can be visually assessed without reference to the main text.
A brief statement of the device geometry (dot size, barrier heights, heterostructure layer thicknesses) would help readers judge whether the reported slope is consistent with expected confinement changes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major comment below and have revised the manuscript to improve clarity and completeness where appropriate.

read point-by-point responses

Referee: [Model and Discussion] The attribution of the observed linear ST-splitting shift exclusively to changes in lateral confinement is not supported by any independent electrostatic modeling or strain calculation. In a Ge/SiGe heterostructure, top-gate voltage can also modulate the vertical electric field, hole wave-function penetration into the barrier, or local strain; none of these alternative channels are quantified or ruled out, so the interpretation that the slope arises purely from orbital-level spacing changes remains unverified.

Authors: We agree that the manuscript presents a phenomenological description and does not include independent electrostatic modeling or strain calculations. Our attribution to lateral confinement follows from the conventional expectation for plunger-gate effects on orbital splittings together with the observed linearity and reproducibility across device retunings. We acknowledge that contributions from vertical electric field, wave-function penetration, or local strain cannot be quantitatively excluded on the basis of the present data alone. In the revised manuscript we have added an explicit paragraph in the discussion section stating these limitations and noting that a full microscopic model would be required to separate the mechanisms. revision: partial
Referee: [Results] The linear model is constructed by fitting the combined PAT and pulsed-gate data; the manuscript does not report the explicit functional form, the weighting between the two datasets, the extracted slope with uncertainty, or any goodness-of-fit metric. Without these details it is impossible to assess whether the model is over-constrained or whether the linearity is robust against reasonable variations in analysis choices.

Authors: We thank the referee for noting this omission. The revised manuscript now states the explicit linear functional form used to combine the two datasets, describes the weighting procedure applied during the joint fit, reports the extracted slope together with its uncertainty, and includes the relevant goodness-of-fit metrics. These additions are placed in the main text and allow readers to evaluate the robustness of the linear dependence. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental measurements and phenomenological fit to observed linear dependence

full rationale

The paper reports direct experimental observations of singlet-triplet splittings via photon-assisted tunneling and pulsed-gate spectroscopy, noting an unexpected linear dependence on top-gate voltage. It then combines the two datasets into a model that describes this observed linear dependence. This is a data-driven phenomenological description rather than a first-principles derivation or prediction that reduces to its own inputs by construction. No self-citations, uniqueness theorems, or ansatzes are invoked to force the result; the central claims rest on the measurements themselves and remain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The claim rests on experimental spectroscopy data interpreted through a linear phenomenological model; standard domain assumptions about quantum dot confinement are invoked but no new entities are introduced.

free parameters (1)

linear coefficient of ST splitting versus top gate voltage
The model is stated to describe the linear dependence, implying slopes fitted to the combined PAT and spectroscopy data.

axioms (2)

domain assumption Orbital energy splittings depend on the lateral confinement of the quantum dots
Explicitly stated as known in the abstract.
domain assumption Changes in ST splittings with top or plunger gate voltages are typically negligible
Described as the usual assumption in effective theories and prior experiments.

pith-pipeline@v0.9.0 · 5550 in / 1404 out tokens · 73987 ms · 2026-05-07T10:19:18.863830+00:00 · methodology

discussion (0)

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