Quantum Response of a Harmonically Trapped Detector to Classical and Non-classical Gravitational Fields

Anom Trenggana; Freddy P. Zen; Seramika Ariwahjoedi

arxiv: 2504.19971 · v2 · pith:KJ446L3Dnew · submitted 2025-04-28 · 🌀 gr-qc · hep-th

Quantum Response of a Harmonically Trapped Detector to Classical and Non-classical Gravitational Fields

Anom Trenggana , Freddy P. Zen , Seramika Ariwahjoedi This is my paper

Pith reviewed 2026-05-22 17:41 UTC · model grok-4.3

classification 🌀 gr-qc hep-th

keywords gravitational fieldsdetector responsesqueezed statescoherent statesharmonic oscillatortwo-time correlation functiontransition probabilitiesquantum gravity

0 comments

The pith

A harmonically trapped detector shows non-linear time dependence in transition probabilities for squeezed gravitational states that no stationary classical field can match.

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

This paper examines the response of a detector confined in a harmonic oscillator potential to classical and quantum gravitational fields, with the response measured by transition probabilities between energy levels. The probabilities are determined by the two-time correlation function of the gravitational field. Coherent states of the field yield correlation functions that match those of suitably chosen stationary classical fields. Squeezed states produce extra contributions to the correlation function that stationary classical fields cannot replicate, resulting in non-linear time dependence for the transition probabilities.

Core claim

The influence of the gravitational field on the detector transition probabilities is encoded in the two-time correlation function of the field. For coherent states, the structure of this two-time correlation function can be reproduced by an appropriately modeled classical gravitational field, particularly when the classical field is stationary. In contrast, for squeezed states, the two-time correlation function contains additional contributions that cannot be replicated within a classical description when the classical field is stationary, leading to a non-linear time dependence of the detector transition probabilities.

What carries the argument

The two-time correlation function of the gravitational field, which encodes the detector response and distinguishes quantum squeezed states from stationary classical models.

Load-bearing premise

The detector response is fully determined by the two-time correlation function of the gravitational field without significant back-reaction or higher-order curvature effects.

What would settle it

Calculate or measure the transition probabilities for a squeezed gravitational state and verify whether their time dependence deviates from all possible stationary classical field predictions.

read the original abstract

In this work, we study the response of a detector confined in a harmonic oscillator potential when interacting with classical and quantum gravitational fields. The detector response is characterized through transition probabilities between its energy levels, with the aim of investigating how non-classical properties of the gravitational field affect the detector dynamics. The quantum states of the gravitational field considered include coherent states and squeezed states. Our results show that the influence of the gravitational field on the detector transition probabilities is encoded in the two-time correlation function of the field. For coherent states, the structure of this two-time correlation function can be reproduced by an appropriately modeled classical gravitational field, particularly when the classical field is stationary. In contrast, for squeezed states, the two-time correlation function contains additional contributions that cannot be replicated within a classical description when the classical field is stationary, leading to a non-linear time dependence of the detector transition probabilities.

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

Squeezed gravitational states produce non-linear time dependence in trapped-detector transition probabilities that stationary classical fields cannot match, but the result sits on first-order linear response whose validity for large squeezing is not checked.

read the letter

The main thing to know is that this paper calculates transition probabilities for a harmonically trapped detector coupled to gravitational fields and finds that squeezed states introduce extra correlation terms that yield non-linear time dependence, unlike anything a stationary classical field can produce. Coherent states, by contrast, can be reproduced classically under the same conditions. The distinction follows directly from applying standard two-time correlation functions to the different field states. This is a concrete, incremental extension of Unruh-DeWitt-style detector models into the gravitational setting with squeezing. The logic chain from field state to correlation function to detector probability is laid out plainly and stays internally consistent. The calculation gives a clear diagnostic that could be checked in principle against future quantum-gravity-inspired experiments. The soft spot is the unexamined assumption that the detector response is fully captured by the two-point function in first-order perturbation theory. Squeezed states carry parametrically large fluctuations, so for squeezing parameters of order one or larger the energy uncertainty could make back-reaction or second-order processes comparable to the leading term. The abstract gives no explicit interaction Hamiltonian, no error estimates, and no discussion of the weak-coupling regime, leaving open whether the reported non-linearity survives outside a narrow parameter window. This is a paper for readers already working on detector-based probes of quantum gravity or quantum-optics analogues in curved spacetime. Someone building similar models would get value from the explicit mapping and the comparison between coherent and squeezed cases. It is narrow in scope but the execution is honest and grounded in standard methods. I would send it to peer review; the central claim is falsifiable in its stated regime and the work is coherent enough to benefit from referee scrutiny on the validity range.

Referee Report

1 major / 1 minor

Summary. The manuscript studies the response of a harmonically trapped detector interacting with classical and quantum gravitational fields, using transition probabilities between detector energy levels. It argues that these probabilities are fully determined by the two-time correlation function of the gravitational field. Coherent states of the field produce correlation functions that can be reproduced by a suitably chosen stationary classical gravitational field, whereas squeezed states generate additional contributions that cannot be matched by any stationary classical field, resulting in a non-linear time dependence in the detector transition probabilities.

Significance. If the central mapping from field states to detector response via the two-time correlation function holds under the stated approximations, the work supplies a concrete, falsifiable signature that distinguishes non-classical gravitational states from classical ones. This could inform proposals for quantum-enhanced gravitational sensors or tests of quantum gravity effects in the weak-field regime. The explicit contrast between coherent and squeezed states, together with the stationarity condition on the classical side, is a clear strength.

major comments (1)

The central claim that squeezed-state correlation functions produce non-linear time dependence in the transition probabilities rests on the assumption that the detector response is exactly given by the first-order perturbative expression involving only the two-time field correlator (see abstract and the modeling choice described in the reader's weakest_assumption). For squeezing parameter r of order 1 or larger, the parametrically enhanced variance raises the possibility that second-order processes or back-reaction become comparable to the leading term, potentially invalidating the linear-response premise. The manuscript should either derive an explicit bound on r (or on the coupling strength) under which the reported non-linearity survives, or demonstrate that the non-linear time dependence persists beyond the strict weak-coupling regime.

minor comments (1)

The abstract states that the influence is 'encoded in the two-time correlation function' but does not specify the precise form of the interaction Hamiltonian or the detector's internal degrees of freedom beyond the harmonic potential; adding a brief equation or reference to the standard Unruh-DeWitt-type coupling would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and for the constructive comment on the range of validity of our perturbative treatment. We address the concern below and will incorporate the requested clarification in the revised version.

read point-by-point responses

Referee: The central claim that squeezed-state correlation functions produce non-linear time dependence in the transition probabilities rests on the assumption that the detector response is exactly given by the first-order perturbative expression involving only the two-time field correlator (see abstract and the modeling choice described in the reader's weakest_assumption). For squeezing parameter r of order 1 or larger, the parametrically enhanced variance raises the possibility that second-order processes or back-reaction become comparable to the leading term, potentially invalidating the linear-response premise. The manuscript should either derive an explicit bound on r (or on the coupling strength) under which the reported non-linearity survives, or demonstrate that the non-linear time dependence persists beyond the strict weak-coupling regime.

Authors: We agree that the validity of the first-order perturbative result must be carefully delimited when the gravitational field is squeezed. In the present work the detector-field interaction is treated to linear order in the coupling, so that the transition probability is proportional to the two-time correlation function of the metric perturbation. For a squeezed state with parameter r the relevant variance grows as sinh(2r), which can make higher-order contributions non-negligible unless the dimensionless coupling g is correspondingly reduced. We will add a new subsection that derives an explicit upper bound on r (or equivalently a lower bound on the required weakness of g) by comparing the magnitude of the second-order correction to the leading term. The bound will be expressed in terms of the detector frequency, the squeezing parameter, and the characteristic amplitude of the gravitational field, thereby ensuring that the reported non-linear time dependence remains the dominant signature within the stated regime of the calculation. revision: yes

Circularity Check

0 steps flagged

Standard perturbative mapping from field correlators to detector response shows no circularity

full rationale

The paper derives detector transition probabilities from first-order time-dependent perturbation theory applied to the interaction Hamiltonian between the harmonically trapped detector and the metric perturbation. This yields the standard result that probabilities are determined by the field's two-time correlation function, a general QFT relation independent of the specific states considered. Coherent-state correlators match those of a stationary classical field by direct computation of the expectation value, while squeezed-state correlators introduce extra terms from the squeezing operator that produce non-linear time dependence; neither step reduces to a fitted parameter, self-definition, or self-citation chain. The modeling assumptions (weak coupling, negligible back-reaction) are stated explicitly as inputs rather than derived outputs. The central distinction therefore follows from the algebraic properties of the chosen field states and does not collapse to the paper's own premises by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum mechanics for the harmonic-oscillator detector and the assumption that gravitational fields can be prepared in coherent or squeezed states whose two-time correlations fully determine the detector response.

axioms (2)

domain assumption The detector is a quantum harmonic oscillator whose energy levels are unaffected by the gravitational field except through the linear interaction term.
Invoked when transition probabilities are computed from the interaction with the field correlation function.
domain assumption Gravitational field operators admit coherent and squeezed states whose correlation functions can be calculated independently of the detector.
Required to contrast classical versus non-classical contributions in the abstract.

pith-pipeline@v0.9.0 · 5689 in / 1562 out tokens · 39349 ms · 2026-05-22T17:41:53.779622+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/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The influence of the gravitational field on the detector transition probabilities is encoded in the two-time correlation function of the field.
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

For squeezed states, the two-time correlation function contains additional contributions that cannot be replicated within a classical description

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

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