Pith. sign in

REVIEW 3 major objections 5 minor 42 references

Anomalous dependence of sensitivity on observation time caused by memory retention in the time crystal

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that in a ring-coupled atom-cavity system, time-crystal memory turns linear observation-time sensitivity into quadratic scaling.

desk verdict Legitimate new T^2 scaling result for an atom-cavity-ring time crystal, but the practical claim needs a quantified loss budget before it generalizes beyond the lossless model. read the letter →

arxiv 2411.13313 v2 pith:2EZO537G submitted 2024-11-20 quant-ph physics.optics

T. T. Sergeev , A. A. Zyablovsky , E. S. Andrianov This is my paper · ORCID
classification quant-phphysics.optics
keywords discretetimecrystalringresonatorsensitivityscalingmemoryretentionquantumsensingopticalgyroscopetranslationsymmetrybreakingatom-cavitysystem
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

This paper argues that a discrete time crystal can serve as a resource for sensing: in a composite atom-cavity system coupled to a ring resonator, sensitivity to perturbations grows as the square of observation time, $S \sim T^2$, instead of the usual linear $S \sim T$. The origin is memory retention: in the time-crystal regime the atom's probability amplitude does not fully decay, so the phase perturbation accumulated on each round trip of the ring adds coherently. Outside the time-crystal regime the atom resets within one round trip and only the last pass contributes, giving linear scaling. The quadratic regime also includes the transition area to the normal state, where memory is partially retained. If correct, this provides a concrete route to rotation sensors and gyroscopes whose resolution improves quadratically with integration time.

What carries the argument

The mechanism is memory of the initial atomic state, carried by the single-excitation probability amplitudes $C_{\sigma}$, $C_a$, $C_j^+$, $C_j^-$ that obey the coupled Schr\"odinger equations (3)-(6). Each ring round trip of duration $T_R$ returns pulses to the atom with a phase difference $\Delta\phi \sim \Omega_{\mathrm{rot}} T_R$; if the atom survives many round trips, successive perturbation contributions sum and $S(T) \sim T^2$, while if the atom decays within $T_R$, only the last pulse acts and $S(T) \sim T$. The paper quantifies memory through $p(t)=|\langle\Psi(0)|\Psi(t)\rangle|^2$ and its time average $M$, which decreases monotonically with coupling strength and tracks the extracted exponent $\alpha$. The critical coupling $\Omega_{\mathrm{TC}}=g$ separates the time-crystal order (oscillation period $2T_R$, nonzero averaged phase difference over one bypass) from the normal state.

What would settle it

Add a loss rate $\kappa$ to the atomic amplitude equation, $dC_{\sigma}/dt = -i\omega_0 C_{\sigma} - i\Omega C_a - \kappa C_{\sigma}$, and compute $S(T)$ for $\kappa T_R \sim 1$: the numerically extracted exponent should fall from $\sim 2$ to $\sim 1$ as $\kappa T_R$ increases. Equivalently, in a ring-resonator experiment with tunable round-trip loss, measure $S$ at $T = 20 T_R$ for fixed perturbation $\varepsilon$; if $S/T^2$ does not decrease as loss increases, memory retention is not the cause of the quadratic scaling.

Watch

Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that the sensitivity $S$, defined as the relative change in the time-averaged atomic excitation probability under a perturbation of the ring-mode frequencies, obeys $S \sim T^{\alpha}$ with $\alpha \approx 2$ in the time-crystal regime ($\Omega < 4\Omega_{\mathrm{TC}}$) and in the transition region, and $\alpha \approx 1$ in the normal regime ($\Omega > 6\Omega_{\mathrm{TC}}$). The perturbation is rotation, which shifts the clockwise and counterclockwise ring modes by opposite amounts $\varepsilon$. The quadratic law follows because the atom's state persists over many round trips, so the phase difference accumulated between counter-propagating pulses on each pass feeds back into the atom's state; the memory measure $M$, the time-averaged overlap $|\langle\Psi(0)|\Psi(t)\rangle|^2$, stays large exactly where the exponent is two. The authors note that the quadratic scaling saturates at long times because the atomic probability is bounded, with the saturation time set by the perturbation-induced oscillation period $\sim \varepsilon^{-1}$.

Load-bearing premise

The quadratic sensitivity law assumes the atom's excitation survives many ring round trips without decay or dephasing; if any realistic loss resets the atom within one round trip, the coherent sum becomes a finite geometric series and the quadratic law drops to linear or saturating behavior.

Editorial extensions

If this is right

  • In the time-crystal regime, doubling the observation time quadruples sensitivity, so rotation sensors built on this system gain a factor of $T$ in resolution compared with normal-state operation.
  • The transition region between time crystal and normal state also gives quadratic scaling, so the effect does not require sitting exactly at the critical point.
  • Because the single-atom equations coincide with those of a macroscopic ensemble of $N$ atoms (with coupling $\Omega = \sqrt{N}\Omega_0$), the quadratic sensitivity law carries over to many-atom devices.
  • The quadratic growth is bounded: sensitivity saturates when the atomic probability reaches its limit or after times $\sim \varepsilon^{-1}$, so the advantage appears for observation times between a few $T_R$ and the perturbation-dependent saturation time.
  • Measuring the exponent $\alpha$ at a given coupling strength provides a practical diagnostic of whether the system retains memory of its initial state.

Reading between the lines

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

  • An implicit design rule follows: the optimal operating point is not the critical coupling but roughly $\Omega \sim 2\Omega_{\mathrm{TC}}$, where sensitivity at fixed $T$ is maximal because stronger coupling increases the perturbation influence while enough memory is preserved.
  • Adding realistic loss or dephasing to the atomic amplitude should interpolate the exponent $\alpha$ from 2 to 1; since the model equations contain no loss terms, the predicted quadratic law is an upper envelope for ideal cavities.
  • The memory metric $M$ could serve as a universal figure of merit for time-crystal sensors in other platforms: any system with a large time-averaged overlap with its initial state should show superlinear sensitivity, and the predicted $M$-versus-$\alpha$ mapping is testable.
  • The mechanism could be probed directly by injecting a weak probe pulse at a controlled delay: if memory persists, the perturbation response should depend on the full history of round trips, not only the most recent one.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper considers a composite system of a two-level atom in a single-mode cavity coupled to a ring resonator, with counter-propagating modes whose frequencies are shifted by rotation (a small perturbation ε). Using the single-excitation Schrödinger equations (3)-(6), the authors numerically compute a sensitivity S(T,ε,Ω), defined as the relative change in the time-averaged atomic excitation probability due to the perturbation. They find that S grows as T^α with α≈2 for coupling strengths Ω below about 4Ω_TC (the time-crystal regime and its transition area), and α≈1 for Ω above about 6Ω_TC (the normal regime). They attribute the quadratic growth to the system's ability to retain memory of the atom's initial state, quantified by M = ∫|⟨Ψ(0)|Ψ(t)⟩|^2 dt. The paper also states that the quadratic scaling saturates at long times because the atomic probability is bounded, and Appendix B gives a rough estimate of experimental parameters.

Significance. If the reported T^2 scaling is robust, the result is of interest for quantum metrology and time-crystal-based sensing, as it identifies a concrete mechanism by which a time-crystal system can show an enhanced sensitivity that grows quadratically with observation time. The model is simple, the equations are explicitly given, and the numerical demonstration is transparent and potentially reproducible from the text. The memory-retention metric M is a useful diagnostic, and the authors honestly acknowledge the saturation of the effect. However, the practical relevance is conditional on two issues that are not yet resolved: the reliability of the power-law exponent extraction, and the absence of any dissipation or decoherence in the model used for the simulations. The paper is clearly written, but these gaps prevent a full endorsement of the central claim.

major comments (3)
  1. [§III, Figure 3] The central quantitative claim that S ~ T^α with α≈2 in the time-crystal regime and α≈1 outside is based on fitting log S versus log T over a short time window (T/TR between about 5 and 20, i.e., only four or five data points in Figure 2b), yet no error bars, fit residuals, or confidence intervals are reported. The text does not state the fitting procedure or the number of points used. Because the entire message rests on the distinction between α=2 and α=1, the authors must provide the fitting details, the goodness of fit, and uncertainty estimates (e.g., bootstrap or covariance) so that the reader can judge whether the power-law is an adequate description and whether the difference is statistically significant.
  2. [§IV and Appendix B] Equations (3)-(6) are a closed unitary system with no loss or decoherence terms, yet the interpretation in Section IV explicitly states that the quadratic dependence requires that the atom's state "does not have time to decay during the observation time," while decay within one bypass gives S(T) ~ T. The decay rate γ' = Ω²/γ is mentioned only as a heuristic to locate the time-crystal boundary and is never introduced into the numerical simulations of Figures 1-5. Consequently, the T^2 scaling is demonstrated only for an ideal lossless resonator. The claim in Appendix B that the effect "can be observed in real systems" is therefore not supported by any quantitative estimate of ring loss, cavity loss, or atomic spontaneous emission. The authors should either add dissipative terms and show that the T^2 scaling survives for realistic parameters, or provide an explicit quantitative condition (e.g., loss rates much smaller than 1/T_R) under which the ideal model is a legitimate approximation.
  3. [§IV, Eq. (8)] The claim that the quadratic sensitivity dependence is caused by memory retention is asserted rather than demonstrated. The pulse-accumulation picture in Section IV is heuristic, and the memory metric M is only shown to correlate with the exponent α; no derivation from equations (3)-(6) connects M to the power-law exponent. As written, the causal statement "This effect is due to ability of the system to retain the memory" is an interpretation, not a result. The authors should provide a more direct analytical or semi-analytical argument (e.g., a stroboscopic map or an effective two-level description) showing how the survival of the atomic amplitude over many round trips leads to S(T) ~ T^2.
minor comments (5)
  1. [Appendix A] The sentence "after substituting the wave function (2) into the Schrödinger equation with Hamiltonian (1)" should refer to Eqs. (10) and (9), respectively, since the multi-atom wave function and Hamiltonian are introduced in Appendix A.
  2. [§IV] The displayed formula for S(T) is garbled: "S (T ) = A TR 0 ΩrotTRdTR ∼ T 2" does not parse. Presumably it should read S(T) = A ∫₀^T Ω_rot t dt ~ T^2; please correct the typesetting.
  3. [Appendix B] The phrase "the period, T, limited the area of the quadratic scaling" should read "limits the area."
  4. [Figure 3] The two quantities plotted (α and ⟨Δφ⟩/π) share the figure with different vertical scales, but the axis labels are not explicitly separated; consider using two panels or a clearer legend.
  5. [§III] The phrase "the sensitivity S increases in the power law S ∼ T α" should be "in a power law" or "as a power law."

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the S~T^2 scaling is a direct numerical result from the Schrödinger equations, not a fit or a renamed input.

full rationale

The central claim is a numerical result: the sensitivity S(T, ε, Ω) defined by Eq. (7) is computed directly from the probability amplitudes obtained by integrating Eqs. (3)-(6), and the exponent α is extracted from the S versus T data in Figure 3. The memory measure M of Eq. (8) is used only as a correlative diagnostic ('This result is consistent with the sensitivity behavior'), not as a fitted parameter that sets α. The critical coupling Ω_TC = g is derived in Section III from the condition γ'T_R ~ 1 with γ' = Ω^2/γ, so it is not imported as an unexplained fit. The self-citation [35] is used to identify the time-crystal regime, but the paper independently reproduces the regime boundary through the phase-difference calculation shown in Figure 3, and the quadratic-scaling result is computed from the model rather than assumed from the citation. The lossless, unitary character of Eqs. (3)-(6) is a physical assumption about idealized dynamics, not a circular step: the paper's own Section IV explicitly states the decay case would give S~T, and the absence of Lindblad terms is a limitation of scope, not a tautology. No load-bearing step reduces by construction to its own input.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The model has no constants fitted to independent data; all parameters are chosen for the simulation. The load-bearing assumptions are the single-excitation manifold, uniform ring-mode coupling, the resonance condition, and the absence of dissipation. No new particles, forces, or conserved quantities are introduced.

free parameters (5)
  • Ring-mode coupling g = 6 x 10^-3 omega_0
    Chosen for all simulations; sets Omega_TC = g and the cavity-ring feedback rate.
  • Mode spacing delta-omega = 4 x 10^-3 omega_0
    Chosen for all simulations; sets the round-trip time TR = 2 pi / delta-omega and maps rotation rate to epsilon = Omega_rot / delta-omega.
  • Number of ring modes N = 50
    Chosen for all simulations; defines the finite reservoir of modes around omega_0.
  • Perturbation amplitude epsilon = 10^-5 (10^-4 in Fig. 1)
    Chosen; authors state the quadratic scaling holds for epsilon < 10^-3, but no systematic scan is shown.
  • Observation times = m TR, m = 5, 10, 15, 20
    Chosen for the exponent fit in Figure 3; no error bars or fit diagnostics are provided.
assumptions (5)
  • domain assumption Only one excitation quantum exists in the atom-cavity-ring system at all times.
    Wave function (2) truncates to the single-excitation sector; Appendix A argues equivalence to a many-atom system with one excitation rather than to a general many-excitation state.
  • domain assumption All ring modes couple to the cavity with identical strength g_j = g.
    Stated after Eq. (1); required for the mode structure and the round-trip feedback picture in Section IV.
  • domain assumption The atom and cavity frequencies satisfy the resonance condition omega_0 / delta-omega = j0 with integer j0.
    Section II; makes the atom resonant with a ring mode and defines the perturbation epsilon as a frequency shift of clockwise and counterclockwise modes.
  • domain assumption The evolution is unitary: no cavity, ring, or atomic losses or dephasing are included.
    Equations (3)-(6) contain no damping terms; the memory retention and the summing of perturbation contributions over many round trips in Section IV depend on this.
  • domain assumption The Born-Markov approximation is valid for estimating the atom's dissipation rate gamma used to define Omega_TC.
    Section III; this estimate only identifies the regime boundary, while the sensitivity is computed from the full Schrodinger dynamics.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Anomalous dependence of sensitivity on observation time caused by memory retention in the time crystal." pith.science (2026). https://pith.science/paper/2EZO537G

@misc{pith2026241113313,
  author       = {Pith},
  title        = {Pith review of: Anomalous dependence of sensitivity on observation time caused by memory retention in the time crystal},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2EZO537G}},
  note         = {Machine review of arXiv:2411.13313}
}
read the original abstract

In this work, we consider a composite atom-cavity system interacting with a ring resonator. In such a structure, time crystal regime can be observed. We show that a quadratic observation time dependence of the system's sensitivity to perturbations takes place in the time crystal regime and also in the transition area to the normal state. This dependence is due to ability of the system to retain the memory of the atom's initial state. Outside these areas, the system is not able to retain the memory of the atom's initial state and the sensitivity scales linearly on the observation time. Our results open up a new way for implementation of discrete time crystals in sensing and metrology.

Figures

Figures reproduced from arXiv: 2411.13313 by the authors.

Figure 1
Figure 1. FIG. 1. Dependence of the atom’s probability density [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) The dependence of the sensitivity [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The dependence of the observation time exponent [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) The dependence of [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Dependence of the atom’s probability density [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 19 canonical work pages

  1. [35]

    T. T. Sergeev, A. A. Zyablovsky, E. S. Andrianov, and Y. E. Lozovik, Spontaneous breaking of time translation symmetry in a system without periodic external driving, 8 Opt. Lett. 49, 4783 (2024)

    work page 2024

  2. [1]

    Wilczek, Quantum time crystals, Phys

    F. Wilczek, Quantum time crystals, Phys. Rev. Lett. 109, 160401 (2012)

    2012

  3. [2]

    Bruno, Impossibility of spontaneously rotating time crystals: a no-go theorem, Phys

    P. Bruno, Impossibility of spontaneously rotating time crystals: a no-go theorem, Phys. Rev. Lett. 111, 070402 (2013)

    work page 2013

  4. [3]

    Nozi` eres, Time crystals: Can diamagnetic currents drive a charge density wave into rotation?, Europhys

    P. Nozi` eres, Time crystals: Can diamagnetic currents drive a charge density wave into rotation?, Europhys. Lett. 103, 57008 (2013)

    work page 2013

  5. [4]

    Watanabe and M

    H. Watanabe and M. Oshikawa, Absence of quantum time crystals, Phys. Rev. Lett. 114, 251603 (2015)

    2015

  6. [5]

    N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vish- wanath, Discrete time crystals: Rigidity, criticality, and realizations, Phys. Rev. Lett. 118, 030401 (2017)

    2017

  7. [6]

    Z. Gong, R. Hamazaki, and M. Ueda, Discrete time- crystalline order in cavity and circuit qed systems, Phys. Rev. Lett. 120, 040404 (2018)

    2018

  8. [7]

    D. V. Else, C. Monroe, C. Nayak, and N. Y. Yao, Discrete time crystals, Annu. Rev. Condens. Matter Phys.11, 467 (2020)

    2020

Show all 42 references
  1. [8]

    M. P. Zaletel, M. Lukin, C. Monroe, C. Nayak, F. Wilczek, and N. Y. Yao, Colloquium: Quantum and classical discrete time crystals, Rev. Mod. Phys. 95, 031001 (2023)

    2023

  2. [9]

    Keßler, P

    H. Keßler, P. Kongkhambut, C. Georges, L. Mathey, J. G. Cosme, and A. Hemmerich, Observation of a dissi- pative time crystal, Phys. Rev. Lett. 127, 043602 (2021)

    2021

  3. [10]

    Zhang, P

    J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I.-D. Potirniche, A. C. Potter, A. Vishwanath, et al., Observation of a discrete time crys- tal, Nature 543, 217 (2017)

    2017

  4. [11]

    S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V. Khemani, et al., Ob- servation of discrete time-crystalline order in a disordered dipolar many-body system, Nature 543, 221 (2017)

    2017

  5. [12]

    Rovny, R

    J. Rovny, R. L. Blum, and S. E. Barrett, Observation of discrete-time-crystal signatures in an ordered dipolar many-body system, Phys. Rev. Lett. 120, 180603 (2018)

    2018

  6. [13]

    S. Pal, N. Nishad, T. Mahesh, and G. Sreejith, Temporal order in periodically driven spins in star-shaped clusters, Phys. Rev. Lett. 120, 180602 (2018)

    2018

  7. [14]

    Barnes, J

    E. Barnes, J. M. Nichol, and S. E. Economou, Stabiliza- tion and manipulation of multispin states in quantum-dot time crystals with heisenberg interactions, Phys. Rev. B 99, 035311 (2019)

    2019

  8. [15]

    Greilich, N

    A. Greilich, N. Kopteva, A. Kamenskii, P. Sokolov, V. Korenev, and M. Bayer, Robust continuous time crys- tal in an electron–nuclear spin system, Nat. Phys. 20, 631 (2024)

    2024

  9. [16]

    Sarkar and Y

    S. Sarkar and Y. Dubi, Time crystals from single- molecule magnet arrays, ACS Nano 18, 27988 (2024)

    2024

  10. [17]

    H. P. Ojeda Collado, G. Usaj, C. A. Balseiro, D. H. Zanette, and J. Lorenzana, Emergent parametric reso- nances and time-crystal phases in driven bardeen-cooper- schrieffer systems, Phys. Rev. Res. 3, L042023 (2021)

    2021

  11. [18]

    H. O. Collado, G. Usaj, C. A. Balseiro, D. H. Zanette, and J. Lorenzana, Dynamical phase transitions in peri- odically driven bardeen-cooper-schrieffer systems, Phys. Rev. Res. 5, 023014 (2023)

    2023

  12. [19]

    Nalitov, H

    A. Nalitov, H. Sigurdsson, S. Morina, Y. Krivosenko, I. Iorsh, Y. Rubo, A. Kavokin, and I. Shelykh, Optically trapped polariton condensates as semiclassical time crys- tals, Phys. Rev. A 99, 033830 (2019)

    2019

  13. [20]

    Carraro-Haddad, D

    I. Carraro-Haddad, D. Chafatinos, A. Kuznetsov, I. Papuccio-Fern´ andez, A. Reynoso, A. Bruchhausen, K. Biermann, P. Santos, G. Usaj, and A. Fainstein, Solid- state continuous time crystal in a polariton condensate with a built-in mechanical clock, Science384, 995 (2024)

    2024

  14. [21]

    D. Chen, Z. Peng, J. Li, S. Chesi, and Y. Wang, Discrete time crystal in an open optomechanical system, Phys. Rev. Res. 6, 013130 (2024)

    2024

  15. [22]

    Preskill, Quantum computing in the nisq era and be- yond, Quantum 2, 79 (2018)

    J. Preskill, Quantum computing in the nisq era and be- yond, Quantum 2, 79 (2018)

    2018

  16. [23]

    Ippoliti, K

    M. Ippoliti, K. Kechedzhi, R. Moessner, S. Sondhi, and V. Khemani, Many-body physics in the nisq era: Quan- tum programming a discrete time crystal, PRX Quantum 2, 030346 (2021)

    2021

  17. [24]

    Fr´ erot and T

    I. Fr´ erot and T. Roscilde, Quantum critical metrology, Phys. Rev. Lett. 121, 020402 (2018)

    2018

  18. [25]

    Bennett, D

    R. Bennett, D. Steinbrecht, Y. Gorbachev, and S. Y. Buhmann, Symmetry breaking in a condensate of light and its use as a quantum sensor, Phys. Rev. Appl. 13, 044031 (2020)

    2020

  19. [26]

    S. Choi, N. Y. Yao, and M. D. Lukin, Quantum metrol- ogy based on strongly correlated matter, arXiv preprint arXiv:1801.00042 (2017)

    2017 arXiv

  20. [27]

    H. Zhou, J. Choi, S. Choi, R. Landig, A. M. Douglas, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, P. Cappellaro, et al., Quantum metrology with strongly interacting spin systems, Phys. Rev. X 10, 031003 (2020)

    2020

  21. [28]

    L. J. I. Moon, P. M. Schindler, R. J. Smith, E. Druga, Z.- R. Zhang, M. Bukov, and A. Ajoy, Discrete time crystal sensing, arXiv preprint arXiv:2410.05625 (2024)

    2024 arXiv

  22. [29]

    C. Lyu, S. Choudhury, C. Lv, Y. Yan, and Q. Zhou, Eternal discrete time crystal beating the heisenberg limit, Phys. Rev. Res. 2, 033070 (2020)

    2020

  23. [30]

    Montenegro, M

    V. Montenegro, M. G. Genoni, A. Bayat, and M. G. Paris, Quantum metrology with boundary time crystals, Commun. Phys. 6, 304 (2023)

    2023

  24. [31]

    Cabot, F

    A. Cabot, F. Carollo, and I. Lesanovsky, Continuous sensing and parameter estimation with the boundary time crystal, Phys. Rev. Lett. 132, 050801 (2024)

    2024

  25. [32]

    Iemini, R

    F. Iemini, R. Fazio, and A. Sanpera, Floquet time crys- tals as quantum sensors of ac fields, Phys. Rev. A 109, L050203 (2024)

    2024

  26. [33]

    Gribben, A

    D. Gribben, A. Sanpera, R. Fazio, J. Marino, and F. Iem- ini, Boundary time crystals as ac sensors: enhancements and constraints, arXiv preprint arXiv:2406.06273 (2024)

    2024 arXiv

  27. [34]

    R. K. Shukla, L. Chotorlishvili, S. K. Mishra, and F. Iem- ini, Prethermal floquet time crystals in chiral multiferroic chains and applications as quantum sensors of ac fields, arXiv preprint arXiv:2410.17530 (2024)

    2024 arXiv

  28. [36]

    M. ´A. Guill´ en-Torres, E. Cretu, N. A. Jaeger, and L. Chrostowski, Ring resonator optical gyro- scopes—parameter optimization and robustness analysis, J. Light. Technol. 30, 1802 (2012)

    2012

  29. [37]

    L. Feng, J. Wang, Y. Zhi, Y. Tang, Q. Wang, H. Li, and W. Wang, Transmissive resonator optic gyro based on silica waveguide ring resonator, Opt. Express 22, 27565 (2014)

    2014

  30. [38]

    V. S. Ferreira, J. Banker, A. Sipahigil, M. H. Matheny, A. J. Keller, E. Kim, M. Mirhosseini, and O. Painter, Collapse and revival of an artificial atom coupled to a structured photonic reservoir, Phys. Rev. X 11, 041043 (2021)

    2021

  31. [39]

    M. O. Scully and M. S. Zubairy, Quantum optics (Cam- bridge University Press, 1999)

    1999

  32. [40]

    Carmichael, An open systems approach to quantum op- tics, Vol

    H. Carmichael, An open systems approach to quantum op- tics, Vol. 18 (Springer Science & Business Media, 2009)

    2009

  33. [41]

    Gardiner and P

    C. Gardiner and P. Zoeller, Quantum noise (Springer- verlag, Berlin, 1991)

    1991

  34. [42]

    T. T. Sergeev, I. V. Vovcenko, A. A. Zyablovsky, and E. S. Andrianov, Environment-assisted strong coupling regime, Quantum 6, 684 (2022)

    2022

Pith tools

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