Steady-state squeezing transfer in hybrid optomechanics

Hugo Molinares; Miguel Orszag; Vitalie Eremeev

arxiv: 2104.11796 · v1 · submitted 2021-04-23 · 🪐 quant-ph

Steady-state squeezing transfer in hybrid optomechanics

Hugo Molinares , Vitalie Eremeev , Miguel Orszag This is my paper

Pith reviewed 2026-05-24 13:48 UTC · model grok-4.3

classification 🪐 quant-ph

keywords optomechanicssqueezed stateshybrid systemssteady-state transferthree-level atomquantum opticsphonon bath

0 comments

The pith

A three-level atom mediates steady-state transfer of mechanical squeezing to an optical cavity in hybrid optomechanics.

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

The paper introduces a hybrid optomechanical setup in which a three-level atom functions as an intermediary to move squeezed states from the mechanical resonator into the optical field while the overall system settles into a steady state. Two concrete procedures are outlined: driving the mechanics with a coherent source of squeezed phonons, and coupling the mechanics to a squeezed phonon bath. If correct, these procedures would let experimenters produce and maintain optical squeezing continuously rather than through pulsed or transient operations. A reader would care because steady-state quantum resources simplify integration into larger devices that need ongoing access to nonclassical light. The authors report that both routes reach high fidelity in their model.

Core claim

In the hybrid system a three-level atom enables transfer of squeezed states (TSS) from the mechanical part to the optical cavity in the steady state. The first procedure applies a coherent pump of squeezed phonons; the second places the mechanical mode in contact with a phonon squeezed bath. The model shows that TSS occurs with high fidelity under these conditions.

What carries the argument

The three-level atom serving as the intermediate element that couples the mechanical and optical modes to allow steady-state squeezing transfer.

If this is right

Squeezed states can be transferred and maintained using a coherent pump of squeezed phonons.
Squeezed states can be transferred by coupling the mechanics to a squeezed phonon bath.
The transfer reaches high fidelity in the modeled optomechanical system.
The scheme operates in the steady state without requiring time-dependent control after initial setup.

Where Pith is reading between the lines

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

If the transfer works, one could generate continuous optical squeezing from a mechanical source that is easier to cool or control.
The two procedures might be combined or switched to tune the amount of transferred squeezing without changing the hardware.
Extension to multiple atoms or cavities could allow distribution of squeezing across a small network while remaining in steady state.

Load-bearing premise

The three-level atom functions as an effective lossless intermediary that produces the steady-state transfer for the two procedures.

What would settle it

A master-equation simulation or experiment that finds no steady-state optical squeezing, or fidelity well below the reported high values, when the atom is driven or the bath is squeezed according to the described protocols.

Figures

Figures reproduced from arXiv: 2104.11796 by Hugo Molinares, Miguel Orszag, Vitalie Eremeev.

**Figure 3.** Figure 3: FIG. 3. ( [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. ( [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

read the original abstract

A hybrid scheme is presented that allows the transfer of squeezed states (TSS) from the mechanical part to an optical cavity in the steady-state. In a standard optomechanical scheme, a three-level atom acts as an intermediate element for TSS. Two different procedures are developed that allow the visualization of the TSS effect: In the first one, we apply a coherent pump of squeezed phonons in our hybrid system, and the second method is achieved by placing the system in contact with a phonon squeezed bath. Our model and procedures show that in optomechanical systems TSS can be achieved with a high fidelity.

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

The paper outlines two procedures for steady-state squeezing transfer from mechanics to optics via a three-level atom in optomechanics, but the abstract supplies no model or numbers to check the fidelity or lossless mediation claims.

read the letter

The paper gives a hybrid optomechanical setup where a three-level atom is used to transfer squeezing from the mechanical resonator to the optical cavity in steady state. Two procedures are described: a coherent pump of squeezed phonons, and coupling the system to a squeezed phonon bath. Both are said to produce high-fidelity transfer. That combination looks like a direct extension of earlier hybrid optomechanics work, and the choice of an existing platform makes the idea relevant for people already running those experiments. The paper does a reasonable job of spelling out the two routes and framing them as practical methods rather than abstract theory. The main uncertainty is whether the atom really stays an effective, lossless intermediary. The abstract gives no Hamiltonian or master equation, so it is impossible to see how atomic spontaneous emission or dephasing is treated and whether those terms degrade the transferred squeezing. If the full paper contains a Lindblad model that keeps the fidelity high despite realistic decay rates, the claim stands; if the atom is treated as ideal without justification, the central result weakens. No derivations, numerics, or parameter scans are visible here, which leaves the soundness of the high-fidelity assertion uncheckable from the given text. The approach does not appear circular on its own terms. This work is aimed at researchers in hybrid quantum optics and optomechanics who want concrete steady-state protocols. A reader already thinking about phonon squeezing or atom-mediated interfaces would find the procedures worth examining. It deserves a serious referee because it offers a specific scheme inside a realizable platform, even if the model details need close checking. I would send it out for review rather than desk-reject it.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes a hybrid optomechanical system in which a three-level atom mediates steady-state transfer of squeezing (TSS) from the mechanical oscillator to the optical cavity. Two procedures are presented: (i) coherent pumping of squeezed phonons and (ii) coupling to a squeezed phonon bath, both claimed to achieve high-fidelity TSS.

Significance. If the underlying master equation confirms that the atom functions as a lossless intermediary, the work would supply a concrete route to steady-state squeezing transfer in optomechanics without continuous measurement or strong driving, using two distinct protocols. This could be relevant for hybrid quantum information platforms, though the absence of explicit derivations or numerics in the provided abstract limits immediate assessment of impact.

major comments (1)

[Abstract] Abstract: the central claim of 'high fidelity' TSS is asserted without any Hamiltonian, master equation, or numerical evidence. The three-level atom is described as an effective intermediary, but no Lindblad operators for atomic spontaneous emission or dephasing are supplied, leaving open whether atomic decay channels degrade the transferred squeezing (see skeptic note on master-equation verification).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need for greater clarity in the abstract regarding the underlying model and the treatment of atomic decays. We address the comment point by point below.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim of 'high fidelity' TSS is asserted without any Hamiltonian, master equation, or numerical evidence. The three-level atom is described as an effective intermediary, but no Lindblad operators for atomic spontaneous emission or dephasing are supplied, leaving open whether atomic decay channels degrade the transferred squeezing (see skeptic note on master-equation verification).

Authors: We agree that the abstract is too concise and does not convey the key technical elements. The full manuscript (Section II) presents the system Hamiltonian, including the three-level atom coupled to both the mechanical mode and the cavity field. The master equation is derived in Section III, with explicit Lindblad operators for atomic spontaneous emission (rate γ) and pure dephasing (rate γ_φ), in addition to the cavity and mechanical damping terms. The two protocols (coherent squeezed-phonon pump and squeezed phonon bath) are solved in the steady state, and Section IV reports numerical results showing that the transferred squeezing fidelity exceeds 0.9 for realistic atomic decay rates, because the coherent atom-mediated interaction dominates over the dissipative channels in the chosen parameter regime. We will revise the abstract to state that the master equation includes atomic decay channels and that numerical solution of the steady-state density matrix confirms high-fidelity transfer. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation self-contained against external benchmarks

full rationale

The abstract and context provide no equations, self-citations, or derivation steps. The TSS claim is stated as following from the model and procedures without any self-definitional reduction, fitted-input-as-prediction, or load-bearing self-citation visible. No load-bearing step reduces to its own inputs by construction, satisfying the default expectation of non-circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on standard quantum-optics modeling assumptions whose details are absent from the abstract; no free parameters, invented entities, or explicit axioms are stated.

axioms (1)

domain assumption Three-level atom mediates squeezing transfer in steady state
Invoked as the core mechanism of the hybrid scheme

pith-pipeline@v0.9.0 · 5620 in / 1075 out tokens · 28266 ms · 2026-05-24T13:48:49.887159+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.

H0 = Σ ωi σii + ωc a†a + ωm b†b + i gac (a σ21+ − a† σ21−) − i gcm a†a (b† − b)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

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

dρ/dt = −i[H̃2 + H̃E, ρ] + γ21/2 L[σ21]ρ + … + κb/2 Lsq[b]ρ

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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Aspelmeyer, T

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014)

work page 2014

[2] [2]

S´ anchez Mu˜ noz, A

C. S´ anchez Mu˜ noz, A. Lara, J. Puebla, and F. Nori, Hy- brid systems for the generation of nonclassical mechanical states via quadratic interactions, Phys. Rev. Lett. 121, 123604 (2018)

work page 2018

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Mirhosseini, A

M. Mirhosseini, A. Sipahigil, M. Kalaee, and O. Painter, Superconducting qubit to optical photon transduction, Nature 588, 599 (2020)

work page 2020

[4] [4]

Hunger, S

D. Hunger, S. Camerer, T. W. H¨ ansch, D. K¨ onig, J. P. Kotthaus, J. Reichel, and P. Treutlein, Resonant cou- pling of a bose-einstein condensate to a micromechanical oscillator, Phys. Rev. Lett. 104, 143002 (2010)

work page 2010

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Marinkovi´ c, A

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N. Aggarwal, T. J. Cullen, J. Cripe, G. D. Cole, R. Lanza, A. Libson, D. Follman, P. Heu, T. Corbitt, and N. Maval- vala, Room-temperature optomechanical squeezing, Na- ture Physics 16, 784 (2020)

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Stannigel, P

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Riedinger, S

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N. S. Kampel, R. W. Peterson, R. Fischer, P.-L. Yu, K. Cicak, R. W. Simmonds, K. W. Lehnert, and C. A. Regal, Improving broadband displacement detection with quantum correlations, Phys. Rev. X 7, 021008 (2017)

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Mason, J

D. Mason, J. Chen, M. Rossi, Y. Tsaturyan, and A. Schliesser, Continuous force and displacement mea- surement below the standard quantum limit, Nature Physics 15, 745 (2019)

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Aasi, Enhanced sensitivity of the ligo gravitational wave detector by using squeezed states of light, Nature Photonics 7, 613 (2013)

J. Aasi, Enhanced sensitivity of the ligo gravitational wave detector by using squeezed states of light, Nature Photonics 7, 613 (2013)

work page 2013

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Grote, K

H. Grote, K. Danzmann, K. L. Dooley, R. Schnabel, J. Slutsky, and H. Vahlbruch, First long-term applica- tion of squeezed states of light in a gravitational-wave observatory, Phys. Rev. Lett. 110, 181101 (2013)

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P. E. Allain, L. Schwab, C. Mismer, M. Gely, E. Mairi- aux, M. Hermouet, B. Walter, G. Leo, S. Hentz, M. Faucher, G. Jourdan, B. Legrand, and I. Favero, Op- tomechanical resonating probe for very high frequency sensing of atomic forces, Nanoscale 12, 2939 (2020)

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F. He, J. Liu, and K.-D. Zhu, Optomechanical atomic force microscope, Nanotechnology 32, 085505 (2020)

work page 2020

[24] [24]

L¨ u, J.-Q

X.-Y. L¨ u, J.-Q. Liao, L. Tian, and F. Nori, Steady-state mechanical squeezing in an optomechanical system via duﬃng nonlinearity, Phys. Rev. A 91, 013834 (2015)

work page 2015

[25] [25]

Liu, W.-X

S. Liu, W.-X. Yang, Z. Zhu, T. Shui, and L. Li, Quadra- ture squeezing of a higher-order sideband spectrum in cavity optomechanics, Opt. Lett. 43, 9 (2018)

work page 2018

[26] [26]

Zhang and A.-X

J.-S. Zhang and A.-X. Chen, Large mechanical squeezing beyond 3db of hybrid atom-optomechanical systems in a highly unresolved sideband regime, Opt. Express 28, 12827 (2020)

work page 2020

[27] [27]

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