Rabi oscillation and fractional population via the bound states in the continuum in a giant atom waveguide QED setup

Hongwei Yu; Jin Wang; Xiaojun Zhang; Zhihai Wang

REVIEW 4 major objections 5 minor 63 references

Rabi oscillation and fractional population via the bound states in the continuum in a giant atom waveguide QED setup

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read In a braided two-giant-atom setup coupled to a resonator waveguide, the number of bound states in the continuum dictates the dynamics: two BICs give persistent Rabi oscillations, one BIC gives fractional population decay.

desk verdict The BIC-count dichotomy is real and robust, but the time-local derivation is asserted, not derived, and the numerics lack details. read the letter →

arxiv 2411.14065 v1 pith:AGBYNYWO submitted 2024-11-21 quant-ph

Hongwei Yu , Xiaojun Zhang , Zhihai Wang , Jin Wang This is my paper · ORCID

classification quant-ph

keywords giantatomscoupledresonatorwaveguideboundstatesinthecontinuumRabioscillationsfractionalpopulationnon-Markoviandynamicsquantumelectrodynamicsopensystems

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that the fate of excitation in two 'giant' atoms — emitters each coupled to a resonator waveguide at two separated points, braided so their coupling regions overlap — is decided entirely by the number of bound states in the continuum (BICs) the joint system supports. When the configuration supports two BICs, the atomic excitation oscillates back and forth between the two atoms without decaying into the waveguide, with a period set by the energy splitting of the BICs. When only one BIC exists, the atoms decay only partially and converge to equal nonzero steady-state populations. The authors tie both behaviours to a single criterion, whether the imaginary parts of the eigenvalues of their reduced dynamical matrix vanish, and confirm it by watching where the photons go in the waveguide. If the claim holds, it overturns the default expectation that a reservoir always drives a quantum system to complete decay.

What carries the argument

The carrier of the argument is the reduced single-excitation dynamical equation $i\,d\vec{\alpha}(t)/dt = M(t)\vec{\alpha}(t)$, whose entries are memory integrals over Bessel functions: the diagonal terms $A_i(t)$ describe each atom's free oscillation plus the backaction of the waveguide, and the off-diagonal term $B(t)$ is the waveguide-mediated coupling between the atoms. The number of BICs is read off from the long-time imaginary parts of the eigenvalues $\lambda(t)$ of $M(t)$: an eigenvalue with vanishing imaginary part flags a channel that does not dissipate, hence one BIC. That eigenvalue criterion, adapted from the Markovian case, connects the transcendental eigenenergy equation of the full system to the reduced atomic dynamics, and it converts the geometric parameters — atom size $N = n_2 - n_1 = m_2 - m_1$ and relative distance $\Delta = m_1 - n_1$ — into a prediction about oscillation versus fractional decay.

What would settle it

Solve the exact integro-differential equations (B7)–(B8) directly, without the reduction to the time-local equation, at couplings $g/\xi \ge 0.3$; if the two-BIC case shows decaying oscillation amplitude or the one-BIC plateau drifts from $|\langle \psi(0)|E_{\mathrm{BIC}}\rangle\langle E_{\mathrm{BIC}}|\psi(0)\rangle|^2$, the BIC classification is an artifact of the weak-coupling reduction. A complementary experiment: in a superconducting coupled-resonator array with inter-site hopping $\xi/(2\pi) = 50$ MHz, prepare one pair of giant atoms in the $N=6$ braided geometry and one in the $N=8$, $\Delta=2$ geometry, and measure the long-time resonator populations; the prediction is persistent shuttling of the photon in the first case and a frozen two-site pattern in the second.

Watch

Extended reading notes

Core claim

A coupled resonator waveguide, despite hosting a continuous photonic band that normally acts as a dissipative reservoir, can harbour bound states inside that band — modes with real-space localization whose coupling to the emitters is cancelled by interference between the two contact points of each giant atom. The paper's central claim is that the number of such BICs fixes the reduced dynamics of the two braided atoms: with two BICs, an initial excitation of the first atom performs undamped Rabi oscillations between the atoms, and the waveguide photon periodically moves between the two waveguide regions the atoms touch; with one BIC, the excitation decays only partially, and both atoms settle at identical finite populations set by the projection of the initial state onto the BIC eigenstate. The same BIC count follows from two independent routes — the eigenenergy equation of the full atom–waveguide system and the long-time imaginary parts of the eigenvalues of the reduced $2\times 2$ dynamical matrix $M(t)$ — so the paper establishes a consistent map from the global spectrum to the open-system dynamics.

Load-bearing premise

The whole classification rests on the assumption that the simpler time-local equation the authors derive for the two atoms captures everything the exact memory-laden delay equations do, and the paper checks this agreement only at one weak-coupling value, $g = 0.1\xi$.

Editorial extensions

If this is right

Two BICs (for example atom size $N=6$ at any relative distance $\Delta$) turn the braided pair into a closed two-level system: the excitation oscillates indefinitely between the atoms with period $T = 2\pi/(E_1 - E_2)$ set by the BIC energies, and nothing leaks into the waveguide.
One BIC (for example $N=8$ with even $\Delta$) makes the atoms reach a shared fractional steady state: both atoms keep the same nonzero population $|\langle \psi(0)|E_{\mathrm{BIC}}\rangle\langle E_{\mathrm{BIC}}|\psi(0)\rangle|^2$ at infinite time, with the surviving photon frozen in a symmetric profile around the two atoms.
The environment's role is not fixed: the same waveguide that dissipates excitation when no BIC is present protects a decoherence-free subspace when BICs are present, so dissipation can be suppressed by choosing the atom–waveguide geometry.
The waveguide's photonic distribution tracks the atomic dynamics — oscillating between the two atom-covered regions in the two-BIC case and settling into the localized BIC pattern in the one-BIC case — giving an observable signature of the mechanism.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the same waveguide can be switched between full decay, fractional survival, and undamped oscillation by choosing atom size and relative distance, the braided geometry is a tunable resource: a testable extension is to encode one qubit in the two-BIC protected subspace of a superconducting circuit array and compare its coherence time with that of an unprotected configuration in the same devi
The eigenvalue criterion — vanishing imaginary part of a memory-matrix eigenvalue equals one BIC — looks like a special case of a more general counting rule for structured reservoirs; if so, the same argument should predict oscillation versus decay for three or more giant atoms, or for emitters in other band-gap environments such as photonic crystals.
Because the effective equations are checked numerically only at the weak coupling $g = 0.1\xi$, a natural next test is to solve the exact delay equations at stronger coupling (say $g/\xi \sim 0.5$) and see whether the Rabi period still tracks the BIC splitting and the fractional plateau still tracks the BIC projection of the initial state.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear [Colleague],

The punchline: the paper's central dichotomy is correct, and it is more robust than the derivation suggests. Two BICs give persistent Rabi oscillations; one BIC gives fractional population. I expected to find the TCL gap fatal, but on reading, the asymptotic behavior follows from exact BIC eigenstates, so the qualitative claim stands.

What's new: a concrete two-giant-atom braided setup in a CRW where the number of BICs—two vs one—changes the reduced dynamics. The paper shows via spectral analysis and real-space photonic distributions that the long-time Rabi oscillation is exactly oscillation between the two BIC components, and the single-BIC steady state is just the BIC projection. That's a clean result and a useful design rule. The derivations in the appendices follow standard methods, and the numerical check at g/ξ=0.1 matches the approximate equations.

The soft spots, in order:

1. The reduction from the exact convolution equations (B7)-(B8) to the time-local Eq. (15) is asserted, not shown. 'Weisskopf-Wigner beyond Markovian' is doing a lot of work. For the long-time behavior this doesn't matter, because the BIC components are exact. But the transient shape, the Rabi period, and the fractional values do depend on the approximation. At stronger coupling the transient could be wrong. The authors should either supply the TCL derivation or state that the asymptotic claims are exact and the approximation is only for the transient.

2. Sec. II.D extends Longhi's criterion to a time-dependent M(t) without proof. Instantaneous eigenvalues of a time-dependent generator don't generally control asymptotic decay. The agreement with the exact BIC count here is a consistency check, not a derivation. Should be flagged and proved or reframed.

3. Numerical details are missing: no chain length, no convergence data, no code/data. For a paper making quantitative predictions, that's a reproducibility gap. Minor, but easy to fix.

I don't think the paper overclaims. The phrase 'challenge the conventional notion' is a bit grand, but the underlying phenomenon is real. The citation pattern is fine; self-citations to [56,57] are relevant.

Who it's for: anyone in waveguide QED interested in BIC-protected dynamics or non-Markovian effects. It's a moderate step forward, not a revolution, but it deserves a serious referee.

My recommendation: send to peer review, conditional on the authors clarifying the approximation, proving or reframing the eigenvalue criterion, and providing numerical details. I'd accept it as a solid but incremental contribution.

Best.

Referee Report

4 major / 5 minor

Summary. The manuscript studies two giant atoms in a braided configuration coupled to a coupled-resonator waveguide, working in the single-excitation subspace. The authors identify bound states in the continuum (BICs) from the eigenenergy equation (13), and they derive, in Appendix B, integro-differential equations (B7)-(B8) for the atomic amplitudes. The main text then uses a time-local equation (15) for the two atomic amplitudes and connects the number of BICs to the eigenvalues of the time-dependent matrix M(t). The reported dynamical regimes are: two BICs give persistent Rabi oscillations between the two giant atoms with period fixed by the BIC energy splitting, and one BIC gives fractional stationary populations. The analytical predictions are compared with direct Schr\"odinger evolution at g/xi = 0.1, and the photonic distributions are analysed to support the association of the long-time state with the BIC.

Significance. If the central claim is correct, the paper provides a useful example in which a structured environment suppresses its own dissipative action through BICs, leading to protected Rabi oscillations or fractional population trapping. The work has clear strengths: the eigenenergy equation (13) is derived in detail, the exact memory equations (B7)-(B8) are obtained from the Schr\"odinger equation, and the approximate dynamics are checked against full numerical evolution at g/xi = 0.1, including real-space photonic distributions. However, the load-bearing step from the exact convolution equations to the time-local equation (15) is not shown, and the extension of a time-independent BIC-eigenvalue criterion to a time-dependent generator is asserted rather than proved. These gaps currently limit the claim to the weakly coupled, numerically tested regime.

major comments (4)

[Appendix B and Eq. (15)] The central dynamical equation is not derived. Equations (B7)-(B8) are exact integro-differential equations whose right-hand sides contain convolutions of alpha1(tau) and alpha2(tau) with Bessel-function kernels. The main text states that these reduce to the time-local equation (15) 'under the Weisskopf-Wigner approximation but beyond the Markovian approximation', but Appendix B ends at (B7)-(B8) without performing that reduction. Since the eigenvalues in Fig. 2 and the populations in Figs. 3-4 all rely on Eq. (15), the authors need to specify the reduction explicitly, for example as a second-order time-convolutionless approximation, and justify it with an error estimate or a consistency condition. The agreement with the full Schr\"odinger evolution at g/xi = 0.1 is encouraging, but it tests only one parameter point.
[Sec. II.D] The criterion of Ref. [41] applies to a time-independent generator M whose eigenvalues have non-positive imaginary parts. Here M(t) is explicitly time-dependent, and the text asserts without proof that the number of BICs still equals the number of zero eigenvalues of M(t). For a time-dependent generator, instantaneous eigenvalues do not in general determine the asymptotic decay or the existence of invariant subspaces of the propagator; additional conditions such as adiabaticity, a commuting-family structure, or an explicit solution of the time-ordered exponential are needed. Please provide such a justification, or verify directly from Eq. (15) that the long-time propagator has the claimed protected subspace in the one- and two-BIC cases.
[Secs. III-IV and parameter regime] All numerical checks are performed at g/xi = 0.1. The experimental parameters quoted in Sec. IV are xi/(2pi) = 50 MHz and g/(2pi) = 124.6 MHz from Refs. [58] and [60], which give g/xi approximately 2.5 if these numbers are combined; the validity of the uncontrolled reduction behind Eq. (15) in that regime is therefore not established. The authors should either test stronger couplings, for example g/xi = 0.5 and 1, and show that the Rabi-oscillation and fractional-population behavior persists, or explicitly restrict the conclusions to the weak-coupling regime.
[Eq. (23) and Sec. III.B] The fractional-population claim is anchored by the numerical equality |alpha1(infinity)|^2 = |alpha2(infinity)|^2 = |<psi(0)|E_BIC><E_BIC|psi(0)>|^2, which is stated without derivation or error estimate. This equality is a consistency check between the approximate dynamics and the eigenstate calculation, not a proof. Given that the central one-BIC/two-BIC dichotomy rests on this relation, the authors should provide a formal argument, such as a decomposition into bound and scattering components with a demonstration that the scattering part vanishes at long times, or should show convergence of the equality with increasing system size and evolution time.

minor comments (5)

[Title] The title contains a typo: 'bound st ates' should read 'bound states'.
[Figs. 3 and 4] The caption of Fig. 3 states that solid lines are analytical and dashed lines are numerical, whereas the text for Fig. 4 states the opposite convention; please make the convention consistent and correct both captions.
[Table I] For N1 = N2 = 6 and Delta = 2 or 4, Table I gives E1 = E2 = 0, so the two BICs are degenerate; the formula T = 2pi/(E1 - E2) used for the Rabi period in Sec. III.A does not apply to the degenerate case and this should be discussed.
[Fig. 2] The horizontal axis in Fig. 2 is evolution time but the units are not stated; please specify that time is in units of 1/xi and comment on whether t = 100/xi is sufficient for the eigenvalues to reach their asymptotic values.
[Appendix B, Eq. (B9)] The phrase 'the Weisskopf-Wigner approximation also allows us to derive the photonic dynamics' is misleading: Eqs. (B9)-(B11) follow exactly from the Schr\"odinger equation once the vacuum initial condition is imposed, with no approximation needed; please rephrase.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the BIC spectrum and the reduced dynamics are computed independently from the same Hamiltonian, and their agreement is a consistency check rather than an input.

full rationale

The paper's central dichotomy (two BICs lead to Rabi oscillations; one BIC leads to fractional population) is not obtained by fitting or by construct. The BIC energies and counts are computed from the stationary eigenvalue problem, Eq. (13), as summarized in Table I, while the time-dependent atomic dynamics are obtained from Eq. (15), whose memory kernels are derived separately from the same Hamiltonian in Appendix B. The long-time projection identity in Eq. (23) and the agreement with exact exp(-iHt) evolution at g/xi = 0.1 are posterior checks, not inputs. The self-citations [56,57] for the single-giant-atom BIC condition are not load-bearing, because the N = 4m + 2 decoupling condition is re-derived in Sec. II.B. I explicitly flag one non-circular support gap: Appendix B stops at the integro-differential equations (B7)-(B8), and the time-local reduction to Eq. (15) is asserted rather than derived; likewise, extending Longhi's eigenvalue criterion to the time-dependent M(t) in Sec. II.D is asserted without proof. These are approximation-validity and correctness concerns, not equivalence-by-construction, so they do not raise the circularity score.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper does not introduce new particles or forces. Its central claim rests on the standard single-excitation approximation, the infinite-chain idealization, an approximate time-convolutionless reduction, and a cited BIC-eigenvalue relation.

free parameters (3)

g/ξ = 0.1 (coupling-to-hopping ratio) = 0.1
Chosen by hand to illustrate the weak-coupling regime. The dynamics and the BIC energies depend on this ratio, but it is not fitted to any experimental data.
Atomic sizes N1=N2=6 and N1=N2=8 = 6 and 8
The two sizes are selected to realize the two-BIC and one-BIC regimes predicted by the single-atom BIC condition (N=4m+2 for N=6 and non-BIC for N=8). They are model parameters, not fitted.
Relative distance Δ = 3 (two-BIC case) and Δ = 2 (one-BIC case) = 3 and 2
The relative distance between the first coupling points of the two atoms determines whether the combined system supports two, one, or no BICs. These values are chosen to illustrate the two regimes.

assumptions (4)

domain assumption The system is restricted to the single-excitation subspace (|G⟩ and one excitation in atoms or waveguide).
The wavefunction ansatz (14) assumes at most one quantum of excitation. This is stated in Sec. II C and is standard for single-photon waveguide QED, but it excludes multi-photon or multi-excitation processes.
standard math The waveguide is infinite (N_c → ∞) and the Fourier transform and plane-wave form of the Hamiltonian are used.
This is a standard idealization for a translationally invariant coupled resonator waveguide, used throughout.
domain assumption The time-convolutionless (Weisskopf-Wigner) reduction from the exact integro-differential equations (B7)-(B8) to the closed equation (15) is valid for the parameters studied.
The paper asserts this approximation in Sec. II C without deriving it from the convolution equations; it is verified numerically for g/ξ=0.1 but not for the full parameter range.
domain assumption The number of BICs equals the number of zero imaginary eigenvalues of M(t) in the long-time limit (Ref. [41] for Markovian M, assumed to extend to time-dependent M).
This relation is taken from Ref. [41] and assumed to hold for the time-dependent matrix M(t) in Sec. II D; the paper checks it against the spectrum from Eq. (13) for the studied cases.

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Cite this review

Pith. "Pith review of Rabi oscillation and fractional population via the bound states in the continuum in a giant atom waveguide QED setup." pith.science (2026). https://pith.science/paper/AGBYNYWO

@misc{pith2026241114065,
  author       = {Pith},
  title        = {Pith review of: Rabi oscillation and fractional population via the bound states in the continuum in a giant atom waveguide QED setup},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AGBYNYWO}},
  note         = {Machine review of arXiv:2411.14065}
}

read the original abstract

We study the dynamics of two giant atoms interacting with a coupled resonator waveguide (CRW) beyond the Markovian approximation. The distinct atomic configurations determine the number of bound states in the continuum (BIC), leading to different dynamical behaviors. Our results show that when the system supports two BICs, Rabi oscillations dominate the dynamics, whereas fractional population dynamics emerge in the presence of a single BIC. The connection between these dynamics and the existence of BICs is further verified by analyzing the photonic distribution in the CRW during time evolution. These findings challenge the conventional notion that the environment always induces dissipation and decoherence. Instead, the bound states in the CRW-emitters coupled system can suppress complete dissipation of the emitters. This work offers an effective approach for controlling dissipative dynamics in open quantum systems.

Figures

Figures reproduced from arXiv: 2411.14065 by the authors.

**Figure 2.** FIG. 2. The imaginary parts of the eigenvalues of the matrix [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. (a) The population dynamics of the two giant atoms. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. (a) The population dynamics of the two giant atoms. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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Works this paper leans on

63 extracted references · 39 canonical work pages

[41]

Q. Qiu, Y. Wu, and X. L¨ u, Collective radiance of giant atoms in non-Markovian regime, Sci. China Phys. Mech. Astron. 66, 224212 (2023)

2023
[58]

L. Zhou, L. Yang, Y. Li, and C. Sun, Quantum routing of single photons with a cyclic three-level system, Phys. Rev. Lett. 111, 103604 (2013)

work page 2013
[60]

Zhang, C

X. Zhang, C. Liu, Z. Gong, and Z. Wang, Quantum in- terference and controllable magic cavity QED via a giant atom in a coupled resonator waveguide, Phys. Rev. A 108, 013704 (2023)

2023
[1]

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Optical atomic clocks, Rev. Mod. Phys. 87, 637 (2015)

2015
[2]

are summa- rized in Table I, while the corresponding eigenvalues λ(t) as functions of evolution time are illustrated in Fig. 2. For N1 = N2 = 6, as shown in Figs. 2(a) and (b), we observe that Im (λ1) = Im (λ2) ≈ 0, indicating that the system has two BICs, consistent with the ﬁrst two rows in Table I. This result suggests that when a single giant atom can...

work page
[3]

fractional population

(b) N1 = N2 = 6 , ∆ = 2. (c) N1 = N2 = 8 , ∆ = 3. (d) N1 = N2 = 8 , ∆ = 2. The parameters are set as Ω 1 = Ω 2 = ω c = 0, and g1 = g2 = 0. 1ξ. two braided giant atoms setup depends on their relative distance, as shown in the last two rows of Table I. In the setup with ∆ = 3, as depicted in Fig. 2(c), both Im (λ1) and Im (λ2) are negative, indicating the a...

work page
[4]

M. V. Gustafsson, T. Aref, A. F. Kockum, M. K. Ekstr¨ om, G. Johansson, and P. Delsing, Propagating phonons coupled to an artiﬁcial atom, Science 346, 207 (2014)

2014
[5]

C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Trapped-ion quantum computing: progress and challenges, Appl. Phys. Rev. 6, 021314 (2019)

work page 2019

Show all 63 references

[6]

Leibfried, R

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 (2003)

2003
[7]

Morgan, Surface Acoustic Wave Filters , 2nd ed

D. Morgan, Surface Acoustic Wave Filters , 2nd ed. (Aca- demic Press, 2007)

2007
[8]

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design de- rived from the Cooper pair box, Phys. Rev. A 76, 042319 (2007)

2007
[9]

Datta, Surface Acoustic Wave Devices (Prentice Hall, 1986)

S. Datta, Surface Acoustic Wave Devices (Prentice Hall, 1986)

1986
[10]

Andersson, B

G. Andersson, B. Suri, L. Guo, T. Aref, and P. Delsing, Non-exponential decay of a giant artiﬁcial atom, Nature Phys, 15, 1123 (2019)

2019
[11]

A. F. Kockum, G. Johansson, and F. Nori, Decoherence- free interaction between giant atoms in waveguide quan- tum electrodynamics, Phys. Rev. Lett. 120, 140404 (2018)

2018
[12]

Kannan, M

B. Kannan, M. J. Ruckriegel, D. L. Campbell, A. F. Kockum, J. Braum¨ uller, D. K. Kim, M. Kjaergaard, P. Krantz, A. Melville, B. M. Niedzielski, A. Veps¨ al¨ ainen, R. Winik, J. L. Yoder, F. Nori, T. P. Orlando, S. Gustavs- son, and W. D. Oliver, Waveguide quantum electrody- n...

2020
[13]

The results for the solutions of Eq

to determine the number and energy values of the BICs and connect them to the time-dependent eigen- valuesλ(t) of the matrix M . The results for the solutions of Eq. (
[14]

A. M. Vadiraj, A. Ask, T. G. McConkey, I. Nsanzineza, C. W. Sandbo Chang, A. F. Kockum, and C. M. Wilson, Engineering the level structure of a giant artiﬁcial atom in waveguide quantum electrodynamics, Phys. Rev. A 103, 023710 (2021)

2021
[15]

Z. Wang, Y. Wang, J. Yao, R. Shen, W. Wu, J. Qian, J. Li, S. Zhu, and J. You, Giant spin ensembles in waveguide magnonics, Nature Commun. 13, 7580 (2022)

2022
[16]

D. F. Walls and G. J. Milburn, Quantum Optics , 2nd ed. (Springer, 2008)

2008
[17]

A. F. Kockum, Quantum optics with giant atoms-the ﬁrst ﬁve years, International Symposium on Mathemat- ics, Quantum Theory, and Cryptography , edited by T. Takagi, M. Wakayama, K. Tanaka, N. Kunihiro, K. Ki- moto, and Y. Ikematsu (Springer Singapore, Singapore, 2021), p. 125

2021
[18]

Zhao and Z

W. Zhao and Z. Wang, Single-photon scattering and bound states in an atom-waveguide system with two or multiple coupling points, Phys. Rev. A 101, 053855 (2020)

2020
[19]

X. Gu, A. F. Kockum, A. Miranowicz, Y.-X. Liu, and F. Nori, Microwave photonics with superconducting quan- tum circuits, Phys. Rep. 718, 1 (2017)

2017
[20]

D. Roy, C. M. Wilson, and O. Firstenberg, Colloquium: strongly interacting photons in one-dimensional contin- uum, Rev. Mod. Phys. 89, 021001 (2017)

2017
[21]

R. H. Lehmberg, Radiation from an N-atom system. I. General formalism, Phys. Rev. A 2, 883 (1970)

1970
[22]

R. H. Lehmberg, Radiation from an N-atom system. II. Spontaneous emission from a pair of atoms, Phys. Rev. A 2, 889 (1970)

1970
[23]

Lalumi` ere, B

K. Lalumi` ere, B. C. Sanders, A. F. van Loo, A. Fedorov, A. Wallraﬀ, and A. Blais, Input-output theory for waveg- uide QED with an ensemble of inhomogeneous atoms, Phys. Rev. A 88, 043806 (2013)

2013
[24]

Zheng and H

H. Zheng and H. U. Baranger, Persistent quantum beats and long-distance entanglement from waveguide- mediated interactions, Phys. Rev. Lett. 110, 113601 (2013)

2013
[25]

Carollo, D

A. Carollo, D. Cilluﬀo, and F. Ciccarello, Mechanism of decoherence-free coupling between giant atoms, Phys. Rev. Res. 2, 043184 (2020)

2020
[26]

L. Guo, A. Grimsmo, A. F. Kockum, M. Pletyukhov, and G. Johansson, Giant acoustic atom: a single quantum system with a deterministic time delay, Phys. Rev. A 95, 053821 (2017)

2017
[27]

C. A. Gonz´ alez-Guti´ errez, J. Rom´ an-Roche, and D. Zueco, Distant emitters in ultrastrong waveguide QED: ground-state properties and non-Markovian dynamics, Phys. Rev. A 104, 053701 (2021)

2021
[28]

L. Guo, A. F. Kockum, F. Marquardt, and G. Johansson, Oscillating bound states for a giant atom, Phys. Rev. Res. 2, 043014 (2020)

2020
[29]

S. Guo, Y. Wang, T. Purdy, and J. Taylor, Beyond spon- taneous emission: Giant atom bounded in the continuum, Phys. Rev. A 102, 033706 (2020)

2020
[30]

X. Yin, W. Luo, and J. Liao, Non-Markovian disentan- glement dynamics in double-giant-atom waveguide-QED 10 systems, Phys. Rev. A 106, 063703 (2022)

2022
[31]

L. Du, Y. Zhang, and Y. Li, A giant atom with modu- lated transition frequency, Front. Phys. 18, 12301 (2023)

2023
[32]

S. L. Feng and W. Z. Jia, Manipulating single-photon transport in a waveguide-QED structure containing two giant atoms, Phys. Rev. A 104, 063712 (2021)

2021
[33]

Y. Chen, L. Du, L. Guo, Z. Wang, Y. Zhang, Y. Li, and J. Wu, Nonreciprocal and chiral single-photon scattering for giant atoms, Commun. Phys. 5, 215 (2022)

2022
[34]

Liu and A

Y. Liu and A. A. Houck, Quantum electrodynamics near a photonic bandgap, Nat. Phys. 13, 48 (2017)

2017
[35]

N. M. Sundaresan, R. Lundgren, G. Zhu, A. V. Gorshkov, and A. A. Houck, Interacting qubit-photon bound states with superconducting circuits, Phys. Rev. X 9, 011021 (2019)

2019
[36]

P. M. Harrington, M. Naghiloo, D. Tan, and K. W. Murch, Bath engineering of a ﬂuorescing artiﬁcial atom with a photonic crystal, Phys. Rev. A 99, 052126 (2019)

2019
[37]

F. H. Stillinger and D. R. Herrick, Bound states in the continuum, Phys. Rev. A 11, 446 (1975)

1975
[38]

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, Bound states in the continuum in photonics, Phys. Rev. Lett. 100, 183902 (2008)

2008
[39]

M. I. Molina, A. E. Miroshnichenko, and Y. S. Kivshar, Surface bound states in the continuum, Phys. Rev. Lett. 108, 070401 (2012)

2012
[40]

Calaj´ o, Y

G. Calaj´ o, Y. L. Fang, H. U. Baranger, and F. Ciccarello, Exciting a bound state in the continuum through multi- photon scattering plus delayed quantum feedback, Phys. Rev. Lett. 122, 073601 (2019)

2019
[42]

Z. Wang, Y. J. Ji, Yong Li, and D. L. Zhou, Dissipa- tion and decoherence induced by collective dephasing in a coupled-qubit system with a common bath, Phys. Rev. A 91, 013838 (2015)

2015
[43]

Shammah, S

N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, Open quantum systems with local and col- lective incoherent processes: Eﬃcient numerical simula- tions using permutational invariance, Phys. Rev. A 98, 063815 (2018)

2018
[44]

Longhi, Rabi oscillations of bound states in the con- tinuum, Opt

S. Longhi, Rabi oscillations of bound states in the con- tinuum, Opt. Lett. 46, 2091 (2021)

2021
[45]

K. H. Lim, W. -K. Mok, and L. -C. Kwek, Oscillating bound states in non-Markovian photonic lattices, Phys. Rev. A 107, 023716 (2023)

2023
[46]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljacic, Bound states in the continuum, Nat. Rev. Mater. 1, 16048 (2016)

2016
[47]

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y.-S. Kivshar, Fano resonances in photonics, Nature Photon. 11, 543 (2017)

2017
[48]

Koshelev, A

K. Koshelev, A. Bogdanov, and Y. Kivshar, Meta-optics and bound states in the continuum, Sci. Bull. 64, 836 (2019)

2019
[49]

Koshelev, G

K. Koshelev, G. Favraud, A. Bogdanov, Y. Kivshar, and A. Fratalocchi, Nonradiating photonics with resonant di- electric nanostructures, Nanophoton. 8, 725 (2019)

2019
[50]

Talukdar and D

J. Talukdar and D. Blume, Two emitters coupled to a bath with Kerr-like nonlinearity: Exponential decay, fractional populations, and Rabi oscillations, Phys. Rev. A 105, 063501 (2022)

2022
[51]

Yablonovitch, Inhibited spontaneous emission in solid- state physics and electronics, Phys

E. Yablonovitch, Inhibited spontaneous emission in solid- state physics and electronics, Phys. Rev. Lett. 58, 2059 (1987)

1987
[52]

John and J

S. John and J. Wang, Quantum electrodynamics near a photonic band gap: Photon bound states and dressed atoms, Phys. Rev. Lett. 64, 2418 (1990)

1990
[53]

Q. Tong, J. An, H. Luo, and C. H. Oh, Mechanism of entanglement preservation, Phys. Rev. A 81, 052330 (2010)

2010
[54]

H. Liu, J. An, C. Chen, Q. Tong, H. Luo, and C. H. Oh, Anomalous decoherence in a dissipative two-level system, Phys. Rev. A 87, 052139 (2013)

2013
[55]

Longhi, Optical bloch oscillations and zener tunnel- ing with nonclassical light, Phys

S. Longhi, Optical bloch oscillations and zener tunnel- ing with nonclassical light, Phys. Rev. Lett. 101, 193902 (2008)

2008
[56]

Longhi, Photonic simulation of giant atom decay, Opt

S. Longhi, Photonic simulation of giant atom decay, Opt. Lett. 45, 3017 (2020)

2020
[57]

L. Zhou, Z. Gong, Y. Liu, C. Sun, and F. Nori, Con- trollable scattering of a single photon inside a one- dimensional resonator waveguide, Phys. Rev. Lett. 101, 100501 (2008)

2008
[59]

H. Yu, Z. Wang, and J. Wu, Entanglement preparation and nonreciprocal excitation evolution in giant atoms by controllable dissipation and coupling, Phys. Rev. A 104, 013720 (2021)

2021
[61]

Roushan, C

P. Roushan, C. Neill, J. Tangpanitanon, V. M. Bastidas, A. Megrant, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, et al., Spectroscopic signatures of localiza - tion with interacting photons in superconducting qubits, Science 358, 1175 (2017)

2017
[62]

Zhang, E

X. Zhang, E. Kim, D. K. Mark, S. Chol, and O. Painter, A superconducting quantum simulator based on a photonic-bandgap metamaterial, Science 379, 278 (2023)

2023
[63]

E. Kim, X. Y. Zhang, V. S. Ferreira, J. Banker, J. K. Iverson, A. Sipahigil, M. Bello, A. Gonz´ alez-Tudela, M. Mirhosseini, and O. Painter, Quantum electrodynamics in a topological waveguide, Phys. Rev. X 11, 011015 (2021)

2021

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [41]

Q. Qiu, Y. Wu, and X. L¨ u, Collective radiance of giant atoms in non-Markovian regime, Sci. China Phys. Mech. Astron. 66, 224212 (2023)

2023

[2] [58]

L. Zhou, L. Yang, Y. Li, and C. Sun, Quantum routing of single photons with a cyclic three-level system, Phys. Rev. Lett. 111, 103604 (2013)

work page 2013

[3] [60]

Zhang, C

X. Zhang, C. Liu, Z. Gong, and Z. Wang, Quantum in- terference and controllable magic cavity QED via a giant atom in a coupled resonator waveguide, Phys. Rev. A 108, 013704 (2023)

2023

[4] [1]

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Optical atomic clocks, Rev. Mod. Phys. 87, 637 (2015)

2015

[5] [2]

are summa- rized in Table I, while the corresponding eigenvalues λ(t) as functions of evolution time are illustrated in Fig. 2. For N1 = N2 = 6, as shown in Figs. 2(a) and (b), we observe that Im (λ1) = Im (λ2) ≈ 0, indicating that the system has two BICs, consistent with the ﬁrst two rows in Table I. This result suggests that when a single giant atom can...

work page

[6] [3]

fractional population

(b) N1 = N2 = 6 , ∆ = 2. (c) N1 = N2 = 8 , ∆ = 3. (d) N1 = N2 = 8 , ∆ = 2. The parameters are set as Ω 1 = Ω 2 = ω c = 0, and g1 = g2 = 0. 1ξ. two braided giant atoms setup depends on their relative distance, as shown in the last two rows of Table I. In the setup with ∆ = 3, as depicted in Fig. 2(c), both Im (λ1) and Im (λ2) are negative, indicating the a...

work page

[7] [4]

M. V. Gustafsson, T. Aref, A. F. Kockum, M. K. Ekstr¨ om, G. Johansson, and P. Delsing, Propagating phonons coupled to an artiﬁcial atom, Science 346, 207 (2014)

2014

[8] [5]

C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Trapped-ion quantum computing: progress and challenges, Appl. Phys. Rev. 6, 021314 (2019)

work page 2019