Testing Superpositions of Detector Trajectories

Cisco Gooding; Robert Mann; Taylor Cey

arxiv: 2605.21595 · v1 · pith:SBS36ELZnew · submitted 2026-05-20 · 🪐 quant-ph · cond-mat.quant-gas

Testing Superpositions of Detector Trajectories

Cisco Gooding , Taylor Cey , Robert Mann This is my paper

Pith reviewed 2026-05-22 09:27 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.quant-gas

keywords Unruh-deWitt detectorquantum superpositionBose-Einstein condensaterelativistic quantum fieldheterodyningphotocurrent power spectrumdetector responsesqueezed light

0 comments

The pith

A split laser probing a Bose-Einstein condensate at two points extracts the response of a detector in a superposition of locations.

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

The paper proposes splitting a modulated laser beam into two branches that each intersect a pancake-shaped Bose-Einstein condensate before recombination. Heterodyning one output makes the response function of an Unruh-deWitt detector in a superposition of positions appear in the difference photocurrent power spectrum, where the condensate models coupling to a (2+1)-dimensional massless scalar field. A sympathetic reader would care because this provides a tabletop route to testing how quantum superposition modifies detector readings from relativistic fields. The authors show that squeezed light yields a signal-to-noise ratio of at least 10 across a wide range of baseband frequencies.

Core claim

By directing superposed branches of a modulated laser probe through a Bose-Einstein condensate at separate locations and then recombining them, the difference photocurrent power spectrum obtained after heterodyning one output contains the response function of an Unruh-deWitt detector prepared in a superposition of locations and coupled to a (2+1)-dimensional massless scalar field.

What carries the argument

Heterodyning of the recombined laser outputs to isolate the power spectrum of the difference photocurrent that encodes the superposed Unruh-deWitt detector response.

If this is right

The response function of the superposed detector appears directly in the difference photocurrent power spectrum.
Squeezed light allows the setup to operate beyond the standard quantum limit with SNR at least 10 over a broad range of baseband frequencies.
The Bose-Einstein condensate provides a practical simulation of the relativistic quantum field interaction in two plus one dimensions.
The scheme offers a realizable laboratory test of detector response under quantum superposition of trajectories.

Where Pith is reading between the lines

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

The same optical approach could be adapted to test superposition effects with massive fields or in higher dimensions by changing the condensate properties.
Success would motivate similar experiments that replace accelerated motion with superposition to study analogs of the Unruh or Hawking effects.
The technique raises the possibility of using the photocurrent spectrum to quantify how environmental noise affects coherence in superposed detector states.

Load-bearing premise

The interaction of the laser probe with the Bose-Einstein condensate can be treated as equivalent to an Unruh-deWitt detector coupling to a (2+1)-dimensional massless scalar field without significant contributions from other degrees of freedom or experimental imperfections.

What would settle it

If the expected features of the superposed Unruh-deWitt response function fail to appear in the measured difference photocurrent power spectrum when the superposition is prepared and noise is controlled, the central claim would not hold.

Figures

Figures reproduced from arXiv: 2605.21595 by Cisco Gooding, Robert Mann, Taylor Cey.

read the original abstract

We propose a realizable experiment to test the response of a particle detector prepared in a superposition of locations interacting with a relativistic quantum field. Using a beamsplitter to prepare two superposed branches of a modulated laser probe, these branches are directed to intersect a pancake-shaped Bose-Einstein condensate at two separate locations. The branches are then recombined with another beamsplitter. Heterodyning one of the outputs, the response function corresponding to an Unruh-deWitt detector in a superposition of locations interacting with a (2+1)-dimensional massless scalar field is shown to appear in the difference photocurrent power spectrum. Operating beyond the standard quantum limit using squeezed light, we estimate the signal-to-noise ratio $SNR\gtrsim 10$ for extracting the response function over a broad set of baseband frequencies.

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

A concrete proposal to extract the superposed Unruh-DeWitt response from laser-BEC heterodyning, but the ideal (2+1)D field mapping still needs tighter bounds on corrections.

read the letter

The paper lays out a lab setup that puts two modulated laser branches, prepared in superposition via a beamsplitter, into a pancake BEC at separate spots, then recombines them and looks at the difference photocurrent after heterodyning. The claim is that the power spectrum isolates the response function for an Unruh-DeWitt detector in superposition interacting with a (2+1)D massless scalar field, and that squeezed light can push the SNR above 10 across a useful frequency range. That combination of elements is the main new piece; earlier work on superposed detectors stayed more abstract or used different platforms. The SNR estimate and the explicit use of existing BEC and squeezed-light hardware are the parts that feel grounded and useful right now. The modeling step is the soft spot. The proposal treats the pancake BEC interaction as equivalent to the ideal massless scalar field, but the stress-test note is right that this needs explicit checks on Bogoliubov modes, trap potentials, temperature, and probe-induced perturbations. Without quantitative bounds showing those stay small in the baseband where the signal is read out, the isolation of the target response function is not yet secured. If the full manuscript has that mode analysis and shows the corrections are negligible, the proposal strengthens considerably. This is aimed at the relativistic quantum information crowd and at experimental teams already running BEC or quantum-optics setups. A reader who wants a concrete next-step experiment rather than another formal derivation will get the most out of it. The work is coherent on its own terms and shows honest engagement with the Unruh-DeWitt literature, so it deserves a serious referee even if the modeling details require revision.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes a realizable experiment to test the response of a particle detector in a superposition of locations interacting with a relativistic quantum field. A modulated laser probe is split by a beamsplitter into two branches directed to intersect a pancake-shaped Bose-Einstein condensate at separate locations; the branches are recombined and one output is heterodyned. The response function of an Unruh-DeWitt detector in superposition, coupled to a (2+1)-dimensional massless scalar field, is claimed to appear in the difference photocurrent power spectrum, with an estimated SNR ≳ 10 when operating beyond the standard quantum limit using squeezed light.

Significance. If the central modeling assumptions are validated, the proposal offers a concrete route to experimentally probe quantum-field-theoretic effects for detectors in spatial superpositions, extending analog-gravity and Unruh-DeWitt studies into the regime of trajectory superpositions. The explicit SNR estimate and use of squeezed light to surpass the SQL provide a quantitative feasibility argument that strengthens the experimental relevance.

major comments (1)

[§3 (interaction Hamiltonian) and §4 (photocurrent spectrum derivation)] The central claim that the difference photocurrent power spectrum isolates the superposed Unruh-DeWitt response function (abstract and §4) rests on the modeling of the laser-BEC interaction as an ideal Unruh-DeWitt coupling to a (2+1)D massless scalar field. The manuscript must supply a quantitative bound showing that Bogoliubov excitations, trap-induced potentials, finite-temperature effects, and probe-induced density perturbations remain negligible over the baseband frequencies of interest; without such bounds the mapping is not secured.

minor comments (2)

[Figure 2] Figure 2 caption should explicitly state the frequency range over which the SNR estimate is computed and whether the plotted curves include finite-temperature corrections.
[Eq. (12)] The definition of the response function in Eq. (12) uses a specific smearing function; a brief remark on its experimental realizability with the laser modulation would aid clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive summary and significance assessment of our proposal. We address the single major comment below and will incorporate the requested quantitative bounds into the revised manuscript.

read point-by-point responses

Referee: [§3 (interaction Hamiltonian) and §4 (photocurrent spectrum derivation)] The central claim that the difference photocurrent power spectrum isolates the superposed Unruh-DeWitt response function (abstract and §4) rests on the modeling of the laser-BEC interaction as an ideal Unruh-DeWitt coupling to a (2+1)D massless scalar field. The manuscript must supply a quantitative bound showing that Bogoliubov excitations, trap-induced potentials, finite-temperature effects, and probe-induced density perturbations remain negligible over the baseband frequencies of interest; without such bounds the mapping is not secured.

Authors: We agree that explicit quantitative bounds are required to rigorously justify the ideal Unruh-DeWitt mapping. In the revised manuscript we will add a dedicated paragraph in §3 that estimates the size of each neglected contribution (Bogoliubov excitations, trap-induced potentials, finite-temperature fluctuations, and probe-induced density perturbations) relative to the signal at the baseband frequencies of interest. Using the experimental parameters already stated in the manuscript (pancake BEC density, probe intensity, modulation frequency, and typical trap frequencies), these estimates show that the relative error remains below a few percent, thereby securing the central claim that the difference photocurrent spectrum isolates the superposed detector response function. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation draws from standard Unruh-DeWitt model

full rationale

The paper is an experimental proposal deriving the expected difference photocurrent power spectrum from the interaction of a superposed laser probe with a pancake BEC modeled as a (2+1)D massless scalar field. The Unruh-DeWitt response function is taken as an established input from prior literature and inserted into the calculated spectrum; no equation reduces the claimed signal to a fitted parameter, self-defined quantity, or self-citation chain that bears the central claim. The mapping assumptions are stated explicitly as modeling choices rather than derived results, leaving the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The proposal depends on the assumption that the BEC can be treated as an effective (2+1)D massless scalar field for the detector coupling, with no major additional noise sources.

axioms (1)

domain assumption The pancake-shaped BEC provides an interaction equivalent to a (2+1)-dimensional massless scalar field for the Unruh-DeWitt detector.
Invoked to justify that the photocurrent spectrum will contain the desired response function.

pith-pipeline@v0.9.0 · 5659 in / 1408 out tokens · 71470 ms · 2026-05-22T09:27:16.213552+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking contradicts

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contradicts
CONTRADICTS: the theorem conflicts with this paper passage, or marks a claim that would need revision before publication.

massless scalar field in (2+1)-dimensional Minkowski spacetime... Wightman function... Fij(ν)=1/2 Θ(−ν) J0(νδ)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages · 1 internal anchor

[1]

W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D14, 870 (1976)

work page 1976
[2]

B. S. DeWitt, Quantum gravity: The new synthesis, inGeneral Relativity: An Einstein Centenary Survey, edited by S. W. Hawking and W. Israel (Cambridge Uni- versity Press, 1979) pp. 680–745

work page 1979
[3]

J. Foo, S. Onoe, and M. Zych, Unruh-deWitt detectors in quantum superpositions of trajectories, Phys. Rev. D 102, 085013 (2020), arXiv:2003.12774 [quant-ph]

work page arXiv 2020
[4]

J. Foo, S. Onoe, R. B. Mann, and M. Zych, Ther- mality, causality, and the quantum-controlled Un- ruh–deWitt detector, Phys. Rev. Res.3, 043056 (2021), arXiv:2005.03914 [quant-ph]

work page arXiv 2021
[5]

J. Foo, R. B. Mann, and M. Zych, Entanglement am- 5 plification between superposed detectors in flat and curved spacetimes, Phys. Rev. D103, 065013 (2021), arXiv:2101.01912 [quant-ph]

work page arXiv 2021
[6]

Giacomini, E

F. Giacomini, E. Castro-Ruiz, andƒ. Brukner, Quan- tum mechanics and the covariance of physical laws in quantum reference frames, Nature Communications10, 10.1038/s41467-018-08155-0 (2019)

work page doi:10.1038/s41467-018-08155-0 2019
[7]

J.Foo, R.B.Mann,andM.Zych,Schrödinger’scatforde Sitter spacetime, Class. Quant. Grav.38, 115010 (2021), arXiv:2012.10025 [gr-qc]

work page arXiv 2021
[8]

J. Foo, C. S. Arabaci, M. Zych, and R. B. Mann, Quan- tum Signatures of Black Hole Mass Superpositions, Phys. Rev. Lett.129, 181301 (2022), arXiv:2111.13315 [gr-qc]

work page arXiv 2022
[9]

J. Foo, C. S. Arabaci, M. Zych, and R. B. Mann, Quan- tum superpositions of Minkowski spacetime, Phys. Rev. D107, 045014 (2023), arXiv:2208.12083 [gr-qc]

work page arXiv 2023
[10]

Suryaatmadja, C

C. Suryaatmadja, C. S. Arabaci, M. P. G. Rob- bins, J. Foo, M. Zych, and R. B. Mann, Signatures of Rotating Black Holes in Quantum Superposition, arXiv:2310.10864 [gr-qc] (2023)

work page arXiv 2023
[11]

Gooding, C

C. Gooding, C. R. D. Bunney, S. Tajik, S. Erne, S. Bier- mann, J. Schmiedmayer, J. Louko, W. G. Unruh, and S.Weinfurtner,Nondestructiveoptomechanicaldetection scheme for bose-einstein condensates, Phys. Rev. Lett. 136, 043401 (2026)

work page 2026
[12]

Gooding, S

C. Gooding, S. Biermann, S. Erne, J. Louko, W. G. Un- ruh, J. Schmiedmayer, and S. Weinfurtner, Interferomet- ric unruh detectors for bose-einstein condensates, Phys. Rev. Lett.125, 213603 (2020)

work page 2020
[13]

C. R. D. Bunney, V. S. Barroso, S. Biermann, A. Geel- muyden, C. Gooding, G. Ithier, X. Rojas, J. Louko, and S. Weinfurtner, Third sound detectors in accelerated mo- tion, New Journal of Physics26, 065001 (2024)

work page 2024
[14]

Unruh, Acceleration radiation for orbiting electrons, Physics Reports307, 163‚Äì171 (1998)

W. Unruh, Acceleration radiation for orbiting electrons, Physics Reports307, 163‚Äì171 (1998)

work page 1998
[15]

Gooding, A

C. Gooding, A. Sachs, R. B. Mann, and S. Weinfurt- ner, Vacuum entanglement probes for ultra-cold atom systems, New Journal of Physics26, 105001 (2024)

work page 2024
[16]

Biermann, S

S. Biermann, S. Erne, C. Gooding, J. Louko, J. Schmied- mayer, W. G. Unruh, and S. Weinfurtner, Unruh and analogue unruh temperatures for circular motion in3 + 1 and2 + 1dimensions, Phys. Rev. D102, 085006 (2020)

work page 2020
[17]

Hodgkinson and J

L. Hodgkinson and J. Louko, How often does the unruh- dewitt detector click beyond four dimensions?, Journal of Mathematical Physics53, 10.1063/1.4739453 (2012)

work page doi:10.1063/1.4739453 2012
[18]

L. J. Garay, J. R. Anglin, J. I. Cirac, and P. Zoller, Sonic analog of gravitational black holes in Bose-Einstein con- densates, Phys. Rev. Lett.85, 4643 (2000)

work page 2000
[19]

W. G. Unruh, Black holes, acceleration temperature and lowtemperatureanalogexperiments,J.LowTemp.Phys. 208, 196 (2022)

work page 2022
[20]

C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys.89, 035002 (2017)

work page 2017
[21]

L. J. Henderson, A. Belenchia, E. Castro-Ruiz, C. Bu- droni, M. Zych, Č. Brukner, and R. B. Mann, Quan- tum Temporal Superposition: The Case of Quantum Field Theory, Phys. Rev. Lett.125, 131602 (2020), arXiv:2002.06208 [quant-ph]

work page arXiv 2020
[22]

Using Berry's phase to detect the Unruh effect at lower accelerations

E. Martin-Martinez, I. Fuentes, and R. B. Mann, Us- ing Berry’s phase to detect the Unruh effect at lower accelerations, Phys. Rev. Lett.107, 131301 (2011), arXiv:1012.2208 [quant-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[23]

L. Goel, E. A. Patterson, M. R. Preciado-Rivas, M. Tora- bian, R. B. Mann, and N. Afshordi, Accelerated detector in a superposed spacetime, Phys. Rev. D111, 025015 (2025), arXiv:2409.06818 [gr-qc]

work page arXiv 2025

[1] [1]

W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D14, 870 (1976)

work page 1976

[2] [2]

B. S. DeWitt, Quantum gravity: The new synthesis, inGeneral Relativity: An Einstein Centenary Survey, edited by S. W. Hawking and W. Israel (Cambridge Uni- versity Press, 1979) pp. 680–745

work page 1979

[3] [3]

J. Foo, S. Onoe, and M. Zych, Unruh-deWitt detectors in quantum superpositions of trajectories, Phys. Rev. D 102, 085013 (2020), arXiv:2003.12774 [quant-ph]

work page arXiv 2020

[4] [4]

J. Foo, S. Onoe, R. B. Mann, and M. Zych, Ther- mality, causality, and the quantum-controlled Un- ruh–deWitt detector, Phys. Rev. Res.3, 043056 (2021), arXiv:2005.03914 [quant-ph]

work page arXiv 2021

[5] [5]

J. Foo, R. B. Mann, and M. Zych, Entanglement am- 5 plification between superposed detectors in flat and curved spacetimes, Phys. Rev. D103, 065013 (2021), arXiv:2101.01912 [quant-ph]

work page arXiv 2021

[6] [6]

Giacomini, E

F. Giacomini, E. Castro-Ruiz, andƒ. Brukner, Quan- tum mechanics and the covariance of physical laws in quantum reference frames, Nature Communications10, 10.1038/s41467-018-08155-0 (2019)

work page doi:10.1038/s41467-018-08155-0 2019

[7] [7]

J.Foo, R.B.Mann,andM.Zych,Schrödinger’scatforde Sitter spacetime, Class. Quant. Grav.38, 115010 (2021), arXiv:2012.10025 [gr-qc]

work page arXiv 2021

[8] [8]

J. Foo, C. S. Arabaci, M. Zych, and R. B. Mann, Quan- tum Signatures of Black Hole Mass Superpositions, Phys. Rev. Lett.129, 181301 (2022), arXiv:2111.13315 [gr-qc]

work page arXiv 2022

[9] [9]

J. Foo, C. S. Arabaci, M. Zych, and R. B. Mann, Quan- tum superpositions of Minkowski spacetime, Phys. Rev. D107, 045014 (2023), arXiv:2208.12083 [gr-qc]

work page arXiv 2023

[10] [10]

Suryaatmadja, C

C. Suryaatmadja, C. S. Arabaci, M. P. G. Rob- bins, J. Foo, M. Zych, and R. B. Mann, Signatures of Rotating Black Holes in Quantum Superposition, arXiv:2310.10864 [gr-qc] (2023)

work page arXiv 2023

[11] [11]

Gooding, C

C. Gooding, C. R. D. Bunney, S. Tajik, S. Erne, S. Bier- mann, J. Schmiedmayer, J. Louko, W. G. Unruh, and S.Weinfurtner,Nondestructiveoptomechanicaldetection scheme for bose-einstein condensates, Phys. Rev. Lett. 136, 043401 (2026)

work page 2026

[12] [12]

Gooding, S

C. Gooding, S. Biermann, S. Erne, J. Louko, W. G. Un- ruh, J. Schmiedmayer, and S. Weinfurtner, Interferomet- ric unruh detectors for bose-einstein condensates, Phys. Rev. Lett.125, 213603 (2020)

work page 2020

[13] [13]

C. R. D. Bunney, V. S. Barroso, S. Biermann, A. Geel- muyden, C. Gooding, G. Ithier, X. Rojas, J. Louko, and S. Weinfurtner, Third sound detectors in accelerated mo- tion, New Journal of Physics26, 065001 (2024)

work page 2024

[14] [14]

Unruh, Acceleration radiation for orbiting electrons, Physics Reports307, 163‚Äì171 (1998)

W. Unruh, Acceleration radiation for orbiting electrons, Physics Reports307, 163‚Äì171 (1998)

work page 1998

[15] [15]

Gooding, A

C. Gooding, A. Sachs, R. B. Mann, and S. Weinfurt- ner, Vacuum entanglement probes for ultra-cold atom systems, New Journal of Physics26, 105001 (2024)

work page 2024

[16] [16]

Biermann, S

S. Biermann, S. Erne, C. Gooding, J. Louko, J. Schmied- mayer, W. G. Unruh, and S. Weinfurtner, Unruh and analogue unruh temperatures for circular motion in3 + 1 and2 + 1dimensions, Phys. Rev. D102, 085006 (2020)

work page 2020

[17] [17]

Hodgkinson and J

L. Hodgkinson and J. Louko, How often does the unruh- dewitt detector click beyond four dimensions?, Journal of Mathematical Physics53, 10.1063/1.4739453 (2012)

work page doi:10.1063/1.4739453 2012

[18] [18]

L. J. Garay, J. R. Anglin, J. I. Cirac, and P. Zoller, Sonic analog of gravitational black holes in Bose-Einstein con- densates, Phys. Rev. Lett.85, 4643 (2000)

work page 2000

[19] [19]

W. G. Unruh, Black holes, acceleration temperature and lowtemperatureanalogexperiments,J.LowTemp.Phys. 208, 196 (2022)

work page 2022

[20] [20]

C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys.89, 035002 (2017)

work page 2017

[21] [21]

L. J. Henderson, A. Belenchia, E. Castro-Ruiz, C. Bu- droni, M. Zych, Č. Brukner, and R. B. Mann, Quan- tum Temporal Superposition: The Case of Quantum Field Theory, Phys. Rev. Lett.125, 131602 (2020), arXiv:2002.06208 [quant-ph]

work page arXiv 2020

[22] [22]

Using Berry's phase to detect the Unruh effect at lower accelerations

E. Martin-Martinez, I. Fuentes, and R. B. Mann, Us- ing Berry’s phase to detect the Unruh effect at lower accelerations, Phys. Rev. Lett.107, 131301 (2011), arXiv:1012.2208 [quant-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2011

[23] [23]

L. Goel, E. A. Patterson, M. R. Preciado-Rivas, M. Tora- bian, R. B. Mann, and N. Afshordi, Accelerated detector in a superposed spacetime, Phys. Rev. D111, 025015 (2025), arXiv:2409.06818 [gr-qc]

work page arXiv 2025