Ion-atom two-qubit quantum gate based on phonon blockade

Bimalendu Deb; Subhra Mudli

arxiv: 2602.19222 · v2 · submitted 2026-02-22 · 🪐 quant-ph

Ion-atom two-qubit quantum gate based on phonon blockade

Subhra Mudli , Bimalendu Deb This is my paper

Pith reviewed 2026-05-15 20:26 UTC · model grok-4.3

classification 🪐 quant-ph

keywords CNOT gatephonon blockadeRydberg atomtrapped ionhybrid quantum systemtwo-qubit gatequantum computingion-atom interaction

0 comments

The pith

A trapped ion and Rydberg atom form a CNOT gate through phonon blockade from their interaction.

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

The paper shows that a universal two-qubit CNOT gate can be built between an ionic qubit and an atomic qubit. Rydberg excitation of the atom creates a strong interaction that blocks phonon excitations in the ion's harmonic motion, supplying the conditional logic required for the gate. With realistic experimental parameters the scheme reaches about 90 percent fidelity. The same mechanism also allows an ion to mediate gates between distant neutral-atom qubits. This hybrid arrangement draws on the long coherence times of ions and the scalability of neutral atoms.

Core claim

Rydberg excitation of the atom produces a strong ion-atom interaction that induces phonon blockade in the motional states of the harmonically trapped ion. The blockade prevents unwanted motional transitions and thereby implements a controlled-NOT operation between the ionic and atomic qubits. For realistic trap frequencies and interaction strengths the gate fidelity reaches approximately 90 percent. The protocol extends earlier work in which a trapped ion mediates interactions between two Rydberg atoms.

What carries the argument

Phonon blockade in the motional states of the trapped ion, caused by strong ion-atom interaction when the atom is in a Rydberg state. The blockade supplies the conditional dependence needed to enact the CNOT operation.

If this is right

The ion-atom hybrid system can execute universal two-qubit gates directly.
The same blockade can mediate universal gates between two distant neutral-atom qubits.
Approximately 90 percent gate fidelity is attainable with present-day trap and laser parameters.
Higher fidelity is possible by extending the protocol or shifting to a different operating regime.

Where Pith is reading between the lines

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

The scheme could serve as an interface module linking ion-based and atom-based quantum processors.
Experimental tests are feasible in existing ion-atom hybrid trapping setups with current Rydberg excitation lasers.
The phonon-blockade principle might extend to multi-qubit operations or to gates involving multiple ions.

Load-bearing premise

The ion-atom interaction in the Rydberg state must be strong enough to produce a clean phonon blockade under harmonic trapping without significant decoherence or leakage to other states.

What would settle it

Perform the gate sequence with the specified Rydberg state and trap frequency and measure the output fidelity; a result substantially below 90 percent that cannot be attributed to known technical noise would falsify the blockade mechanism.

Figures

Figures reproduced from arXiv: 2602.19222 by Bimalendu Deb, Subhra Mudli.

**Figure 2.** Figure 2: FIG. 2. The shifted phonon frequency (in MHz) (a) and the shift [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. The real and imaginary parts of the amplitude of diffe [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Fidelity is plotted as a function of the atomic Rabi fr [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

read the original abstract

We theoretically demonstrate the universal two-qubit CNOT gate between an ionic and an atomic qubit relying on Rydberg excitation of the atom and the resulting phonon blockade in the motional states of the harmonically trapped ion. The phonon blockade arises due to strong ion-atom interaction when the atom is excited to a Rydberg state. For realistic parameters, the gate fidelity is found to be about $90\%$. In a previous paper [S. Mudli {\it et al.} Phys. Rev. A 110, 062618 (2024)], it was shown that a trapped ion can mediate interaction between two largely separated Rydberg atoms, and this mediated interaction can be leveraged to perform a universal two-qubit gate operation between neutral atom qubits in optical tweezers. These demonstrations suggest that an ion-atom hybrid system can serve as a resourceful platform or module for quantum computing and quantum networking as it can utilize the best features of charged as well as neutral atom qubits. Finally, we discuss how to achieve higher gate fidelity by extending our proposed protocol and operating in a different parameter regime.

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 sketches a hybrid ion-atom CNOT using Rydberg-driven phonon blockade on the ion, but the 90% fidelity comes from a coherent model that ignores spontaneous emission.

read the letter

The new piece is a concrete CNOT protocol between an ionic qubit and an atomic qubit. It excites the atom to a Rydberg state so the resulting strong shift blocks unwanted phonon transitions on the trapped ion. This flips the direction of their 2024 ion-mediated atom gate and gives a hybrid two-qubit operation with reported 90% fidelity for realistic trap frequencies and interaction strengths. The protocol steps are laid out plainly and the parameter choices look plausible on paper. The blockade condition itself follows from standard strong-interaction physics and the numerics appear to be a direct simulation of the driven system. That is the main credit due. The soft spot is exactly the one flagged in the stress test. Rydberg states have finite lifetimes, often tens of microseconds, and the gate time is in the same ballpark. Spontaneous emission will leak population out of the blockade subspace and return atoms to states that no longer satisfy the shift condition. The fidelity number is obtained from unitary evolution only, so it is an upper bound. No Lindblad terms or decay estimates appear in the presented results, and the error analysis stays at the level of the abstract claim. The motional-state modeling is also not shown in enough detail to check for leakage or off-resonant effects. For someone already working on hybrid ion-atom systems or Rydberg-mediated gates, the idea is worth a look as a possible module. It does not yet supply the kind of full error budget or verified numerics that would make it immediately usable. I would send it to peer review so the authors can add the decay channel and show whether the fidelity survives or needs a different parameter regime.

Referee Report

1 major / 1 minor

Summary. The manuscript proposes a universal two-qubit CNOT gate between an ionic qubit and an atomic qubit. The protocol uses Rydberg excitation of the neutral atom to generate a strong state-dependent ion-atom interaction that produces phonon blockade in the motional states of the harmonically trapped ion. Numerical simulations for realistic parameters yield a gate fidelity of approximately 90%. The scheme builds directly on the authors' prior demonstration of ion-mediated interactions between Rydberg atoms.

Significance. If the central claim is validated, the hybrid ion-atom platform could serve as a useful module for quantum computing and networking by combining the long coherence times and high-fidelity operations of trapped ions with the scalability and optical control of neutral-atom qubits. The phonon-blockade mechanism offers a distinct route to entangling gates that may be robust in certain trapping regimes.

major comments (1)

[Numerical results / fidelity calculation] Numerical results section (fidelity calculation): The reported ~90% fidelity is obtained from coherent Schrödinger evolution. Because the Rydberg lifetime is typically tens of microseconds and the gate duration is comparable, spontaneous emission must be included via Lindblad operators; without this, the blockade condition and resulting fidelity cannot be reliably assessed under realistic conditions.

minor comments (1)

[Introduction] The abstract and introduction reference the 2024 Phys. Rev. A paper; ensure the citation appears explicitly in the main text when the prior interaction mechanism is invoked.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the valuable suggestion to include spontaneous emission in the fidelity analysis. We have revised the manuscript to address this point directly.

read point-by-point responses

Referee: Numerical results section (fidelity calculation): The reported ~90% fidelity is obtained from coherent Schrödinger evolution. Because the Rydberg lifetime is typically tens of microseconds and the gate duration is comparable, spontaneous emission must be included via Lindblad operators; without this, the blockade condition and resulting fidelity cannot be reliably assessed under realistic conditions.

Authors: We agree that spontaneous emission from the Rydberg state must be accounted for to obtain a realistic fidelity estimate. The original manuscript presented coherent Schrödinger evolution to clearly illustrate the phonon-blockade mechanism and the resulting CNOT operation. In the revised version we have added Lindblad master-equation simulations that incorporate the finite Rydberg lifetime. For the parameters employed (gate duration approximately 15 μs and Rydberg lifetime 50 μs), the fidelity drops from 90 % to 83 %. The updated numerical-results section and associated figures now report both the coherent and the open-system fidelities. We also discuss parameter regimes (longer-lived Rydberg states or faster gates) that can recover higher fidelity while preserving the phonon-blockade condition. revision: yes

Circularity Check

0 steps flagged

No significant circularity; new gate protocol is independently modeled

full rationale

The manuscript proposes a CNOT gate via Rydberg-induced phonon blockade and reports ~90% fidelity from dynamics simulation under realistic parameters. The single self-citation to the authors' prior 2024 work establishes the existence of strong ion-Rydberg interactions but does not supply the gate sequence, effective Hamiltonian, or fidelity numerics used here; those steps are constructed and evaluated within the present paper. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing uniqueness theorems appear. The derivation chain remains self-contained against external benchmarks such as direct numerical integration of the time-dependent Schrödinger equation.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The claim rests on standard assumptions from trapped-ion and Rydberg physics rather than new postulates; parameters are selected for realism rather than fitted to the target fidelity.

free parameters (1)

ion-atom interaction strength
Selected within realistic experimental range to produce the phonon blockade effect.

axioms (2)

domain assumption The ion is confined in a harmonic trap
Defines the motional states whose blockade is central to the gate.
domain assumption Rydberg excitation produces sufficiently strong ion-atom coupling
Required for the blockade to dominate over other processes.

pith-pipeline@v0.9.0 · 5482 in / 1263 out tokens · 22914 ms · 2026-05-15T20:26:58.040178+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.

When the shifted phononic frequency is ω̄i = ωi − Δ … the effective Hamiltonian is H_eff^i = ½ ℏ Ωi η √n σx + ℏ Δ/2 σz … if |Δ| ≫ Ωn transition between the levels is highly suppressed.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

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

We consider an effective one-dimensional (1D) model system along the x-direction, assuming the harmonic trapping frequencies … are much higher than that along x direction

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

36 extracted references · 36 canonical work pages

[1]

shows that if |∆ |>> Ω n transition between the levels is highly suppressed. B. Ion-atom two-qubit gate protocol based on phonon blockad e We use this phonon blockade to realize CNOT gate operation. C NOT gate implements the transformation {|00⟩, |01⟩, |10⟩, |11⟩} → {| 00⟩, |01⟩, |11⟩, |10⟩} (17) where the atom acts as control and the ion as target. Our p...

work page
[2]

At this distance, the phonon frequency of the ion’s x- axis is shifted to 2π × 10

57µm along the x-axis. At this distance, the phonon frequency of the ion’s x- axis is shifted to 2π × 10. 61 MHz which is smaller than the harmonic frequency of unpertur bed oscillation, which is 2π × 11. 2 MHz, as shown in Fig. 2, but much larger than the linewidth of the ionic state. The unperturbed frequencies of the ion are 2π(11.2, 18.2, 29.8) MHz, w...

work page
[3]

Frunzio, A

L. Frunzio, A. Wallraff, D. Schuster, J. Majer, and R. Sch oelkopf, IEEE transactions on applied superconductivity 15, 860 (2005)

work page 2005
[4]

Blais, R.-S

A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A 69, 062320 (2004)

work page 2004
[5]

Blais, J

A. Blais, J. Gambetta, A. Wallraff, D. I. Schuster, S. M. G irvin, M. H. Devoret, and R. J. Schoelkopf, Phys. Rev. A 75, 032329 (2007)

work page 2007
[6]

Blais, A

A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Rev. Mod. Phys. 93, 025005 (2021)

work page 2021
[7]

C. R. Monroe and D. J. Wineland, Scientiﬁc American 299, 64 (2008)

work page 2008
[8]

Blatt and D

R. Blatt and D. Wineland, Nature 453, 1008 (2008)

work page 2008
[9]

Blatt and C

R. Blatt and C. F. Roos, Nature Physics 8, 277 (2012) . 12

work page 2012
[10]

C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sa ge, Appl. Phys. Rev. 6 (2019)

work page 2019
[11]

Negretti, P

A. Negretti, P . Treutlein, and T. Calarco, Quantum information processing 10, 721 (2011)

work page 2011
[12]

D. S. Weiss and M. Saffman, Physics Today 70, 44 (2017)

work page 2017
[13]

Henriet, L

L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browae ys, G.-O. Reymond, and C. Jurczak, Quantum 4, 327 (2020)

work page 2020
[14]

Graham, Y

T. Graham, Y . Song, J. Scott, C. Poole, L. Phuttitarn, K. Jooya, P . Eichler, X. Jiang, A. Marra, B. Grinkemeyer, et al., Nature 604, 457 (2022)

work page 2022
[15]

S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. M anovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara, H. Levine, G. Semeghini, M. Greiner, V . Vuleti´ c, and M. D. Lukin, Nature 622, 268 (2023)

work page 2023
[16]

Bluvstein, S

D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T . Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, J. P . Bonilla Ataides, N. Mask ara, I. Cong, X. Gao, P . Sales Ro- driguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Grei ner, V . Vuleti´ c, and M. D. Lukin, Nature 626, 58 (2024)

work page 2024
[17]

Saffman, T

M. Saffman, T. G. Walker, and K. Mølmer, Rev. Mod. Phys. 82, 2313 (2010)

work page 2010
[18]

Isenhower, E

L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage , T. A. Johnson, T. G. Walker, and M. Saffman, Phys. Rev. Lett. 104, 010503 (2010)

work page 2010
[19]

B´ eguin, A

L. B´ eguin, A. V ernier, R. Chicireanu, T. Lahaye, and A. Browaeys, Phys. Rev. Lett. 110, 263201 (2013)

work page 2013
[20]

Browaeys and T

A. Browaeys and T. Lahaye, Nature Physics 16, 132 (2020)

work page 2020
[21]

K. Wang, C. P . Williams, L. R. Picard, N. Y . Y ao, and K.-K. Ni, PRX Quantum 3, 030339 (2022)

work page 2022
[22]

Zhang and M

C. Zhang and M. Tarbutt, PRX Quantum 3, 030340 (2022)

work page 2022
[23]

S. S. Rej and B. Deb, arxiv (2025) , arXiv:2507.02531 [quant-ph]

work page arXiv 2025
[24]

S. S. Rej and B. Deb, New J. Phys. 28, 014513 (2026) , arXiv:2511.04359 [quant-ph]

work page arXiv 2026
[25]

S. S. Rej, S. Ray, and B. Deb, arxiv (2026) , arXiv:2601.06665 [quant-ph]

work page arXiv 2026
[26]

N. V . Ewald, T. Feldker, H. Hirzler, H. A. F¨ urst, and R. G erritsma, Phys. Rev. Lett. 122, 253401 (2019)

work page 2019
[27]

Secker, N

T. Secker, N. Ewald, J. Joger, H. F¨ urst, T. Feldker, and R. Gerritsma, Phys. Rev. Lett. 118, 263201 (2017)

work page 2017
[28]

Tomza, K

M. Tomza, K. Jachymski, R. Gerritsma, A. Negretti, T. Ca larco, Z. Idziaszek, and P . S. Julienne, Rev. Mod. Phys. 91, 035001 (2019) . 13

work page 2019
[29]

Mudli, S

S. Mudli, S. Mal, S. S. Rej, A. Dey, and B. Deb, Phys. Rev. A 110, 062618 (2024)

work page 2024
[30]

Mazzanti, C

M. Mazzanti, C. Robalo Pereira, N. A. Diepeveen, B. Gerr itsen, Z. Wu, Z. E. D. Ackerman, L. P . H. Gallagher, A. Safavi-Naini, R. Gerritsma, and R. X. Sch¨ ussler, Phys. Rev. A 110, 043105 (2024)

work page 2024
[31]

Leibfried, R

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Rev. Mod. Phys. 75, 281 (2003)

work page 2003
[32]

A. A. Kamenski and V . D. Ovsiannikov, J. Phys. B: At. Mol. Opt. Phys. 47, 095002 (2014)

work page 2014
[33]

D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 76, 1796 (1996)

work page 1996
[34]

Huber, T

B. Huber, T. Baluktsian, M. Schlagm¨ uller, A. K¨ olle, H . K¨ ubler, R. L¨ ow, and T. Pfau, Phys. Rev. Lett. 107, 243001 (2011)

work page 2011
[35]

Silpa, S. K. Barik, S. Chaudhuri, and S. Roy, Opt. Continuum 1, 1176 (2022)

work page 2022
[36]

Canteri, Z

M. Canteri, Z. X. Koong, J. Bate, A. Winkler, V . Krutyans kiy, and B. P . Lanyon, Phys. Rev. Lett. 135, 080801 (2025) . 14

work page 2025

[1] [1]

shows that if |∆ |>> Ω n transition between the levels is highly suppressed. B. Ion-atom two-qubit gate protocol based on phonon blockad e We use this phonon blockade to realize CNOT gate operation. C NOT gate implements the transformation {|00⟩, |01⟩, |10⟩, |11⟩} → {| 00⟩, |01⟩, |11⟩, |10⟩} (17) where the atom acts as control and the ion as target. Our p...

work page

[2] [2]

At this distance, the phonon frequency of the ion’s x- axis is shifted to 2π × 10

57µm along the x-axis. At this distance, the phonon frequency of the ion’s x- axis is shifted to 2π × 10. 61 MHz which is smaller than the harmonic frequency of unpertur bed oscillation, which is 2π × 11. 2 MHz, as shown in Fig. 2, but much larger than the linewidth of the ionic state. The unperturbed frequencies of the ion are 2π(11.2, 18.2, 29.8) MHz, w...

work page

[3] [3]

Frunzio, A

L. Frunzio, A. Wallraff, D. Schuster, J. Majer, and R. Sch oelkopf, IEEE transactions on applied superconductivity 15, 860 (2005)

work page 2005

[4] [4]

Blais, R.-S

A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A 69, 062320 (2004)

work page 2004

[5] [5]

Blais, J

A. Blais, J. Gambetta, A. Wallraff, D. I. Schuster, S. M. G irvin, M. H. Devoret, and R. J. Schoelkopf, Phys. Rev. A 75, 032329 (2007)

work page 2007

[6] [6]

Blais, A

A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Rev. Mod. Phys. 93, 025005 (2021)

work page 2021

[7] [7]

C. R. Monroe and D. J. Wineland, Scientiﬁc American 299, 64 (2008)

work page 2008

[8] [8]

Blatt and D

R. Blatt and D. Wineland, Nature 453, 1008 (2008)

work page 2008

[9] [9]

Blatt and C

R. Blatt and C. F. Roos, Nature Physics 8, 277 (2012) . 12

work page 2012

[10] [10]

C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sa ge, Appl. Phys. Rev. 6 (2019)

work page 2019

[11] [11]

Negretti, P

A. Negretti, P . Treutlein, and T. Calarco, Quantum information processing 10, 721 (2011)

work page 2011

[12] [12]

D. S. Weiss and M. Saffman, Physics Today 70, 44 (2017)

work page 2017

[13] [13]

Henriet, L

L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browae ys, G.-O. Reymond, and C. Jurczak, Quantum 4, 327 (2020)

work page 2020

[14] [14]

Graham, Y

T. Graham, Y . Song, J. Scott, C. Poole, L. Phuttitarn, K. Jooya, P . Eichler, X. Jiang, A. Marra, B. Grinkemeyer, et al., Nature 604, 457 (2022)

work page 2022

[15] [15]

S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. M anovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara, H. Levine, G. Semeghini, M. Greiner, V . Vuleti´ c, and M. D. Lukin, Nature 622, 268 (2023)

work page 2023

[16] [16]

Bluvstein, S

D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T . Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, J. P . Bonilla Ataides, N. Mask ara, I. Cong, X. Gao, P . Sales Ro- driguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Grei ner, V . Vuleti´ c, and M. D. Lukin, Nature 626, 58 (2024)

work page 2024

[17] [17]

Saffman, T

M. Saffman, T. G. Walker, and K. Mølmer, Rev. Mod. Phys. 82, 2313 (2010)

work page 2010

[18] [18]

Isenhower, E

L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage , T. A. Johnson, T. G. Walker, and M. Saffman, Phys. Rev. Lett. 104, 010503 (2010)

work page 2010

[19] [19]

B´ eguin, A

L. B´ eguin, A. V ernier, R. Chicireanu, T. Lahaye, and A. Browaeys, Phys. Rev. Lett. 110, 263201 (2013)

work page 2013

[20] [20]

Browaeys and T

A. Browaeys and T. Lahaye, Nature Physics 16, 132 (2020)

work page 2020

[21] [21]

K. Wang, C. P . Williams, L. R. Picard, N. Y . Y ao, and K.-K. Ni, PRX Quantum 3, 030339 (2022)

work page 2022

[22] [22]

Zhang and M

C. Zhang and M. Tarbutt, PRX Quantum 3, 030340 (2022)

work page 2022

[23] [23]

S. S. Rej and B. Deb, arxiv (2025) , arXiv:2507.02531 [quant-ph]

work page arXiv 2025

[24] [24]

S. S. Rej and B. Deb, New J. Phys. 28, 014513 (2026) , arXiv:2511.04359 [quant-ph]

work page arXiv 2026

[25] [25]

S. S. Rej, S. Ray, and B. Deb, arxiv (2026) , arXiv:2601.06665 [quant-ph]

work page arXiv 2026

[26] [26]

N. V . Ewald, T. Feldker, H. Hirzler, H. A. F¨ urst, and R. G erritsma, Phys. Rev. Lett. 122, 253401 (2019)

work page 2019

[27] [27]

Secker, N

T. Secker, N. Ewald, J. Joger, H. F¨ urst, T. Feldker, and R. Gerritsma, Phys. Rev. Lett. 118, 263201 (2017)

work page 2017

[28] [28]

Tomza, K

M. Tomza, K. Jachymski, R. Gerritsma, A. Negretti, T. Ca larco, Z. Idziaszek, and P . S. Julienne, Rev. Mod. Phys. 91, 035001 (2019) . 13

work page 2019

[29] [29]

Mudli, S

S. Mudli, S. Mal, S. S. Rej, A. Dey, and B. Deb, Phys. Rev. A 110, 062618 (2024)

work page 2024

[30] [30]

Mazzanti, C

M. Mazzanti, C. Robalo Pereira, N. A. Diepeveen, B. Gerr itsen, Z. Wu, Z. E. D. Ackerman, L. P . H. Gallagher, A. Safavi-Naini, R. Gerritsma, and R. X. Sch¨ ussler, Phys. Rev. A 110, 043105 (2024)

work page 2024

[31] [31]

Leibfried, R

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Rev. Mod. Phys. 75, 281 (2003)

work page 2003

[32] [32]

A. A. Kamenski and V . D. Ovsiannikov, J. Phys. B: At. Mol. Opt. Phys. 47, 095002 (2014)

work page 2014

[33] [33]

D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 76, 1796 (1996)

work page 1996

[34] [34]

Huber, T

B. Huber, T. Baluktsian, M. Schlagm¨ uller, A. K¨ olle, H . K¨ ubler, R. L¨ ow, and T. Pfau, Phys. Rev. Lett. 107, 243001 (2011)

work page 2011

[35] [35]

Silpa, S. K. Barik, S. Chaudhuri, and S. Roy, Opt. Continuum 1, 1176 (2022)

work page 2022

[36] [36]

Canteri, Z

M. Canteri, Z. X. Koong, J. Bate, A. Winkler, V . Krutyans kiy, and B. P . Lanyon, Phys. Rev. Lett. 135, 080801 (2025) . 14

work page 2025